feat: bump to Lean v4.28.0-rc1#36

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Vtec234 merged 1 commit into from
Jul 10, 2026
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feat: bump to Lean v4.28.0-rc1 #36

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4 changes: 0 additions & 4 deletions Poly/ForMathlib/CategoryTheory/Comma/Over/Basic.lean
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Expand Up@@ -35,10 +35,6 @@ lemma homMk_comp'_assoc {X Y Z W : T} (f : X ⟶ Y) (g : Y ⟶ Z) (h : Z ⟶ W)
lemma homMk_id {X B : T} (f : X ⟶ B) (h : 𝟙 X ≫ f = f) : homMk (𝟙 X) h = 𝟙 (mk f) :=
rfl

@[simp]
theorem mkIdTerminal_from_left {B : T} (U : Over B) : (mkIdTerminal.from U).left = U.hom := by
simp [mkIdTerminal, CostructuredArrow.mkIdTerminal, Limits.IsTerminal.from, Functor.preimage]

/-- `Over.Sigma Y U` is a shorthand for `(Over.map Y.hom).obj U`.
This is a category-theoretic analogue of `Sigma` for types. -/
abbrev Sigma {X : T} (Y : Over X) (U : Over (Y.left)) : Over X :=
Expand Down
12 changes: 3 additions & 9 deletions Poly/ForMathlib/CategoryTheory/Comma/Over/Pullback.lean
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Expand Up@@ -9,7 +9,7 @@ import Mathlib.CategoryTheory.Limits.Constructions.Over.Basic
import Mathlib.CategoryTheory.Monad.Products
import Poly.ForMathlib.CategoryTheory.Comma.Over.Basic
import Poly.ForMathlib.CategoryTheory.NatTrans
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

noncomputable section

Expand All@@ -19,7 +19,7 @@ namespace CategoryTheory

open Category Limits Comonad MonoidalCategory CartesianMonoidalCategory

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

variable {C : Type u₁} [Category.{v₁} C]

Expand DownExpand Up@@ -211,7 +211,7 @@ lemma star_map [HasBinaryProducts C] {X : C} {Y Z : C} (f : Y ⟶ Z) :
instance [HasBinaryProducts C] (X : C) : (forget X).IsLeftAdjoint :=
⟨_, ⟨forgetAdjStar X⟩⟩

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

lemma whiskerLeftProdMapId [HasFiniteLimits C] {X : C} {A A' : C} {g : A ⟶ A'} :
X ◁ g = prod.map (𝟙 X) g := by
Expand DownExpand Up@@ -298,12 +298,6 @@ def starIsoToOverTerminal [HasTerminal C] [HasBinaryProducts C] :

variable {C}

/-- A natural isomorphism between the functors `star X` and `star Y ⋙ pullback f`
for any morphism `f : X ⟶ Y`. -/
def starPullbackIsoStar [HasBinaryProducts C] [HasPullbacks C] {X Y : C} (f : X ⟶ Y) :
star Y ⋙ pullback f ≅ star X :=
conjugateIsoEquiv ((mapPullbackAdj f).comp (forgetAdjStar Y)) (forgetAdjStar X) (mapForget f)

/-- The functor `Over.pullback f : Over Y ⥤ Over X` is naturally isomorphic to
`Over.star : Over Y ⥤ Over (Over.mk f)` post-composed with the
iterated slice equivlanece `Over (Over.mk f) ⥤ Over X`. -/
Expand Down
33 changes: 17 additions & 16 deletions Poly/ForMathlib/CategoryTheory/Comma/Over/Sections.lean
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Expand Up@@ -28,7 +28,7 @@ variable {C : Type u₁} [Category.{v₁} C]

attribute [local instance] hasBinaryProducts_of_hasTerminal_and_pullbacks
attribute [local instance] hasFiniteProducts_of_has_binary_and_terminal
attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

section

Expand DownExpand Up@@ -69,11 +69,11 @@ end

variable [HasTerminal C] [HasPullbacks C]

variable (I : C) [Exponentiable I]
variable (I : C) [Closed I]

/-- The first leg of a cospan constructing a pullback diagram in `C` used to define `sections` . -/
def curryId : ⊤_ C ⟶ (I ⟹ I) :=
CartesianClosed.curry (fst I (⊤_ C))
MonoidalClosed.curry (fst I (⊤_ C))

variable {I}

Expand All@@ -90,14 +90,14 @@ pullback diagram:
⊤_ C ----> I ⟹ I
```-/
abbrev sectionsObj (X : Over I) : C :=
Limits.pullback (curryId I) ((exp I).map X.hom)
Limits.pullback (curryId I) ((ihom I).map X.hom)

/-- The functoriality of `sectionsObj`. -/
def sectionsMap {X X' : Over I} (u : X ⟶ X') :
sectionsObj X ⟶ sectionsObj X' := by
fapply pullback.map
· exact 𝟙 _
· exact (exp I).map u.left
· exact (ihom I).map u.left
· exact 𝟙 _
· simp only [comp_id, id_comp]
· simp only [comp_id, ← Functor.map_comp, w]
Expand DownExpand Up@@ -130,29 +130,30 @@ variable {I}
in `C`. See `sectionsCurry`. -/
def sectionsCurryAux {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
A ⟶ (I ⟹ X.left) :=
CartesianClosed.curry (u.left)
MonoidalClosed.curry (u.left)

/-- The currying operation `Hom ((star I).obj A) X → Hom A (I ⟹ X.left)`. -/
def sectionsCurry {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
A ⟶ (sections I).obj X := by
apply pullback.lift (terminal.from A)
(CartesianClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left)) (uncurry_injective _)
rw [uncurry_natural_left]
simp [curryId, uncurry_natural_right, uncurry_curry]
(MonoidalClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left))
(MonoidalClosed.uncurry_injective _)
rw [MonoidalClosed.uncurry_natural_left]
simp [curryId, MonoidalClosed.uncurry_natural_right, MonoidalClosed.uncurry_curry]

/-- The uncurrying operation `Hom A (section X) → Hom ((star I).obj A) X`. -/
def sectionsUncurry {X : Over I} {A : C} (v : A ⟶ (sections I).obj X) :
(star I).obj A ⟶ X := by
let v₂ : A ⟶ (I ⟹ X.left) := v ≫ pullback.snd ..
have w : terminal.from A ≫ (curryId I) = v₂ ≫ (exp I).map X.hom := by
have w : terminal.from A ≫ (curryId I) = v₂ ≫ (ihom I).map X.hom := by
rw [IsTerminal.hom_ext terminalIsTerminal (terminal.from A ) (v ≫ (pullback.fst ..))]
simp [v₂, pullback.condition]
dsimp [curryId] at w
have w' := homEquiv_naturality_right_square (F := MonoidalCategory.tensorLeft I)
(adj := exp.adjunction I) _ _ _ _ w
simp [CartesianClosed.curry] at w'
refine Over.homMk ((prodIsoTensorObj I A).hom ≫ CartesianClosed.uncurry v₂) ?_
· dsimp [CartesianClosed.uncurry] at *
(adj := ihom.adjunction I) _ _ _ _ w
simp [MonoidalClosed.curry] at w'
refine Over.homMk ((prodIsoTensorObj I A).hom ≫ MonoidalClosed.uncurry v₂) ?_
· dsimp [MonoidalClosed.uncurry] at *
rw [Category.assoc, ← w']
simp [star_obj_hom]

Expand DownExpand Up@@ -188,13 +189,13 @@ def coreHomEquiv : CoreHomEquiv (star I) (sections I) where
simp only [star_map]
rw [← Over.homMk_comp] -- note: in a newer version of mathlib this is `Over.homMk_eta`
congr 1
simp [CartesianClosed.uncurry_natural_left]
simp [MonoidalClosed.uncurry_natural_left]
homEquiv_naturality_right := by
intro A X' X u g
dsimp [sectionsCurry, sectionsUncurry, curryId]
apply pullback.hom_ext (IsTerminal.hom_ext terminalIsTerminal _ _)
simp [sectionsMap, curryId]
rw [← CartesianClosed.curry_natural_right, Category.assoc]
rw [← MonoidalClosed.curry_natural_right, Category.assoc]

variable (I)

Expand Down
2 changes: 1 addition & 1 deletion ...Theory/Limits/Shapes/Pullback/CommSq.lean → ...its/Shapes/Pullback/IsPullback/Basic.lean
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Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Poly.ForMathlib.CategoryTheory.CommSq

namespace CategoryTheory.Functor
Expand Down
21 changes: 11 additions & 10 deletions Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Basic.lean
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Expand Up@@ -67,7 +67,7 @@ open CategoryTheory Category MonoidalCategory CartesianMonoidalCategory Limits F

variable {C : Type u} [Category.{v} C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

/-- A morphism `f : I ⟶ J` is exponentiable if the pullback functor `Over J ⥤ Over I`
has a right adjoint. -/
Expand DownExpand Up@@ -179,7 +179,7 @@ instance isMultiplicative : (ExponentiableMorphism (C:= C)).IsMultiplicative whe
/-- A morphism with a pushforward is an exponentiable object in the slice category. -/
def exponentiableOverMk [HasFiniteWidePullbacks C] {X I : C} (f : X ⟶ I)
[ExponentiableMorphism f] :
Exponentiable (Over.mk f) where
Closed (Over.mk f) where
rightAdj := pullback f ⋙ pushforward f
adj := by
apply ofNatIsoLeft _ _
Expand All@@ -192,7 +192,7 @@ morphism `X.hom`.
Here the pushforward functor along a morphism `f : I ⟶ J` is defined using the section functor
`Over (Over.mk f) ⥤ Over J`.
-/
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Exponentiable X] :
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Closed X] :
ExponentiableMorphism X.hom :=
⟨X.iteratedSliceEquiv.inverse ⋙ sections X, ⟨by
refine ofNatIsoLeft (Adjunction.comp ?_ ?_) (starIteratedSliceForwardIsoPullback X.hom)
Expand All@@ -217,7 +217,7 @@ variable {C} [HasFiniteWidePullbacks C] [HasPushforwards C]
/-- In a category where pushforwards exists along all morphisms, every slice category `Over I` is
cartesian closed. -/
instance cartesianClosedOver (I : C) :
CartesianClosed (Over I) where
MonoidalClosed (Over I) where
closed X := @exponentiableOverMk _ _ _ _ _ _ X.hom (HasPushforwards.exponentiable X.hom)

end HasPushforwards
Expand All@@ -226,13 +226,13 @@ namespace CartesianClosedOver

open Over Reindex IsIso CartesianClosed HasPushforwards ExponentiableMorphism

variable {C} [HasFiniteWidePullbacks C] {I J : C} [CartesianClosed (Over J)]
variable {C} [HasFiniteWidePullbacks C] {I J : C} [MonoidalClosed (Over J)]

instance (f : I ⟶ J) : ExponentiableMorphism f :=
ExponentiableMorphism.ofOverExponentiable (Over.mk f)

/-- A category with cartesian closed slices has pushforwards along all morphisms. -/
instance hasPushforwards [Π (I : C), CartesianClosed (Over I)] : HasPushforwards C where
instance hasPushforwards [Π (I : C), MonoidalClosed (Over I)] : HasPushforwards C where
exponentiable f := ExponentiableMorphism.ofOverExponentiable (Over.mk f)

end CartesianClosedOver
Expand All@@ -242,7 +242,7 @@ is exponentiable and all the slices are cartesian closed. -/
class LocallyCartesianClosed [HasFiniteWidePullbacks C] extends
HasPushforwards C where
/-- every slice category `Over I` is cartesian closed. This is filled in by default. -/
cartesianClosedOver : Π (I : C), CartesianClosed (Over I) := HasPushforwards.cartesianClosedOver
cartesianClosedOver : Π (I : C), MonoidalClosed (Over I) := HasPushforwards.cartesianClosedOver

namespace LocallyCartesianClosed

Expand All@@ -256,7 +256,7 @@ attribute [scoped instance] hasFiniteLimits_of_hasTerminal_and_pullbacks
instance mkOfHasPushforwards [HasPushforwards C] : LocallyCartesianClosed C where

/-- A category with cartesian closed slices is locally cartesian closed. -/
instance mkOfCartesianClosedOver [Π (I : C), CartesianClosed (Over I)] :
instance mkOfCartesianClosedOver [Π (I : C), MonoidalClosed (Over I)] :
LocallyCartesianClosed C where

variable [LocallyCartesianClosed C]
Expand All@@ -282,15 +282,16 @@ abbrev ev' {I : C} (X : Over I) (Y : Over X.left) : Reindex X (Pi X Y) ⟶ Y :=
adj X.hom |>.counit.app Y

/-- A locally cartesian closed category with a terminal object is cartesian closed. -/
def cartesianClosed [HasTerminal C] :
CartesianClosed C := cartesianClosedOfEquiv <| equivOverTerminal C
def monoidalClosed [HasTerminal C] :
MonoidalClosed C := cartesianClosedOfEquiv <| equivOverTerminal C

/-- The slices of a locally cartesian closed category are locally cartesian closed. -/
def overLocallyCartesianClosed (I : C) : LocallyCartesianClosed (Over I) := by
apply (config := { allowSynthFailures:= true}) mkOfCartesianClosedOver
intro X
exact cartesianClosedOfEquiv (C := Over (X.left)) X.iteratedSliceEquiv.symm

open CartesianClosed in
/-- The exponential `X^^A` in the slice category `Over I` is isomorphic to the pushforward of the
pullback of `X` along `A`. -/
def expIso {I : C} (A X : Over I) : Pi A (Reindex A X) ≅ A ⟹ X := Iso.refl _
Expand Down
2 changes: 1 addition & 1 deletion Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/BeckChevalley.lean
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Expand Up@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour, Emily Riehl
-/
import Poly.ForMathlib.CategoryTheory.LocallyCartesianClosed.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

/-!
# Beck-Chevalley natural transformations and natural isomorphisms
Expand Down
6 changes: 3 additions & 3 deletions Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Presheaf.lean
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Expand Up@@ -22,10 +22,10 @@ abbrev Psh (C : Type u) [Category.{v} C] : Type (max u (v + 1)) := Cᵒᵖ ⥤ T

variable {C : Type*} [SmallCategory C] [HasTerminal C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

instance cartesianClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
CartesianClosed (Over P) :=
instance monoidalClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
MonoidalClosed (Over P) :=
cartesianClosedOfEquiv (overEquivPresheafCostructuredArrow P).symm

instance locallyCartesianClosed : LocallyCartesianClosed (Psh C) := by
Expand Down
2 changes: 1 addition & 1 deletion Poly/ForMathlib/CategoryTheory/NatTrans.lean
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Expand Up@@ -6,7 +6,7 @@ Authors: Sina Hazratpour

import Mathlib.CategoryTheory.NatTrans
import Mathlib.CategoryTheory.Functor.TwoSquare
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

open CategoryTheory Limits IsPullback

Expand Down
4 changes: 3 additions & 1 deletion Poly/ForMathlib/CategoryTheory/PartialProduct.lean
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Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Mathlib.CategoryTheory.Comma.Over.Pullback
import Poly.ForMathlib.CategoryTheory.Comma.Over.Pullback
import Mathlib.CategoryTheory.Monoidal.Closed.Cartesian
Expand DownExpand Up@@ -100,6 +100,8 @@ structure Fan.Hom (c c' : Fan s X) where

attribute [reassoc (attr := simp)] Fan.Hom.w_left Fan.Hom.w_right

-- TODO: this is taking ages to check since 4.28.0-rc1.
set_option maxHeartbeats 0 in
@[simps]
instance : Category (Fan s X) where
Hom := Fan.Hom
Expand Down
2 changes: 1 addition & 1 deletion Poly/Type/Univariate.lean
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Expand Up@@ -189,7 +189,7 @@ def Obj.iget [DecidableEq P.B] {X} [Inhabited X] (x : P X) (i : P.Total) : X :=
@[simp]
theorem iget_map [DecidableEq P.B] [Inhabited X] [Inhabited Y] (x : P X)
(f : X → Y) (i : P.Total) (h : i.1 = x.1) : (P.map f x).iget i = f (x.iget i) := by
simp only [Obj.iget, fst_map, *, dif_pos, eq_self_iff_true]
simp only [Obj.iget, fst_map, *, dif_pos]
cases x
rfl

Expand Down
20 changes: 10 additions & 10 deletions lake-manifest.json
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Expand Up@@ -15,7 +15,7 @@
"type": "git",
"subDir": null,
"scope": "",
"rev": "dd5e5d97469dec395f29661366030566355ad9be",
"rev": "b8dad038b1b3a05b77d6884b15b8db03ec01dca1",
"name": "mathlib",
"manifestFile": "lake-manifest.json",
"inputRev": null,
Expand All@@ -25,7 +25,7 @@
"type": "git",
"subDir": null,
"scope": "leanprover-community",
"rev": "b3dd6c3ebc0a71685e86bea9223be39ea4c299fb",
"rev": "7311586e1a56af887b1081d05e80c11b6c41d212",
"name": "plausible",
"manifestFile": "lake-manifest.json",
"inputRev": "main",
Expand All@@ -45,7 +45,7 @@
"type": "git",
"subDir": null,
"scope": "leanprover-community",
"rev": "cff9dd30f2c161b9efd7c657cafed1f967645890",
"rev": "b5908dbac486279f1133cb937648c63c30b455af",
"name": "importGraph",
"manifestFile": "lake-manifest.json",
"inputRev": "main",
Expand All@@ -55,17 +55,17 @@
"type": "git",
"subDir": null,
"scope": "leanprover-community",
"rev": "ef8377f31b5535430b6753a974d685b0019d0681",
"rev": "6d65c6e0a25b8a52c13c3adeb63ecde3bfbb6294",
"name": "proofwidgets",
"manifestFile": "lake-manifest.json",
"inputRev": "v0.0.84",
"inputRev": "v0.0.86",
"inherited": true,
"configFile": "lakefile.lean"},
{"url": "https://github.com/leanprover-community/aesop",
"type": "git",
"subDir": null,
"scope": "leanprover-community",
"rev": "fa78cf032194308a950a264ed87b422a2a7c1c6c",
"rev": "f08e838d4f9aea519f3cde06260cfb686fd4bab0",
"name": "aesop",
"manifestFile": "lake-manifest.json",
"inputRev": "master",
Expand All@@ -75,7 +75,7 @@
"type": "git",
"subDir": null,
"scope": "leanprover-community",
"rev": "8920dcbb96a4e8bf641fc399ac9c0888e4a6be72",
"rev": "23324752757bf28124a518ec284044c8db79fee5",
"name": "Qq",
"manifestFile": "lake-manifest.json",
"inputRev": "master",
Expand All@@ -85,7 +85,7 @@
"type": "git",
"subDir": null,
"scope": "leanprover-community",
"rev": "dff865b7ee7011518d59abfc101c368293173150",
"rev": "100083c18750b6a9b7553c65f6b052c0a2f6bcb4",
"name": "batteries",
"manifestFile": "lake-manifest.json",
"inputRev": "main",
Expand All@@ -95,10 +95,10 @@
"type": "git",
"subDir": null,
"scope": "leanprover",
"rev": "726b98c53e2da249c1de768fbbbb5e67bc9cef60",
"rev": "28e0856d4424863a85b18f38868c5420c55f9bae",
"name": "Cli",
"manifestFile": "lake-manifest.json",
"inputRev": "v4.27.0-rc1",
"inputRev": "v4.28.0-rc1",
"inherited": true,
"configFile": "lakefile.toml"}],
"name": "Poly",
Expand Down
2 changes: 1 addition & 1 deletion lean-toolchain
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Original file line numberDiff line numberDiff line change
@@ -1 +1 @@
leanprover/lean4:v4.27.0-rc1
leanprover/lean4:v4.28.0-rc1
, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Add copy buttons to all 
 blocks\n(function() {\n function addCopyButtons() {\n document.querySelectorAll('pre code').forEach(function(codeBlock) {\n if (codeBlock.parentElement.hasAttribute('data-copy-added')) return;\n codeBlock.parentElement.setAttribute('data-copy-added', 'true');\n \n var btn = document.createElement('button');\n btn.textContent = 'Copy';\n btn.style.cssText = 'position:absolute;top:4px;right:4px;padding:2px 8px;font-size:11px;background:#4ecdc4;border:none;border-radius:4px;color:#1a1a2e;cursor:pointer;opacity:0.7;transition:opacity 0.2s;';\n btn.onmouseover = function() { this.style.opacity = '1'; };\n btn.onmouseout = function() { this.style.opacity = '0.7'; };\n btn.onclick = function() {\n navigator.clipboard.writeText(codeBlock.textContent).then(function() {\n btn.textContent = 'Copied!';\n setTimeout(function() { btn.textContent = 'Copy'; }, 1500);\n });\n };\n codeBlock.parentElement.style.position = 'relative';\n codeBlock.parentElement.appendChild(btn);\n });\n }\n \n addCopyButtons();\n \n // Re-run on dynamic content\n var observer = new MutationObserver(addCopyButtons);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Add Copy Buttons to Code Blocks");
}
} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '

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Vtec234
merged 1 commit into

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Jul 10, 2026
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feat: bump to Lean v4.28.0-rc1
#36
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4 changes: 0 additions & 4 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -35,10 +35,6 @@ lemma homMk_comp'_assoc {X Y Z W : T} (f : X ⟶ Y) (g : Y ⟶ Z) (h : Z ⟶ W)
lemma homMk_id {X B : T} (f : X ⟶ B) (h : 𝟙 X ≫ f = f) : homMk (𝟙 X) h = 𝟙 (mk f) :=
 rfl

@[simp]
theorem mkIdTerminal_from_left {B : T} (U : Over B) : (mkIdTerminal.from U).left = U.hom := by
 simp [mkIdTerminal, CostructuredArrow.mkIdTerminal, Limits.IsTerminal.from, Functor.preimage]

/-- `Over.Sigma Y U` is a shorthand for `(Over.map Y.hom).obj U`.
This is a category-theoretic analogue of `Sigma` for types. -/
abbrev Sigma {X : T} (Y : Over X) (U : Over (Y.left)) : Over X :=
Expand Down

12 changes: 3 additions & 9 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Pullback.lean

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Expand Up@@ -9,7 +9,7 @@ import Mathlib.CategoryTheory.Limits.Constructions.Over.Basic
import Mathlib.CategoryTheory.Monad.Products
import Poly.ForMathlib.CategoryTheory.Comma.Over.Basic
import Poly.ForMathlib.CategoryTheory.NatTrans
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

noncomputable section

Expand All@@ -19,7 +19,7 @@ namespace CategoryTheory

open Category Limits Comonad MonoidalCategory CartesianMonoidalCategory

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

variable {C : Type u₁} [Category.{v₁} C]

Expand DownExpand Up@@ -211,7 +211,7 @@ lemma star_map [HasBinaryProducts C] {X : C} {Y Z : C} (f : Y ⟶ Z) :
instance [HasBinaryProducts C] (X : C) : (forget X).IsLeftAdjoint :=
 ⟨_, ⟨forgetAdjStar X⟩⟩

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

lemma whiskerLeftProdMapId [HasFiniteLimits C] {X : C} {A A' : C} {g : A ⟶ A'} :
 X ◁ g = prod.map (𝟙 X) g := by
Expand DownExpand Up@@ -298,12 +298,6 @@ def starIsoToOverTerminal [HasTerminal C] [HasBinaryProducts C] :

variable {C}

/-- A natural isomorphism between the functors `star X` and `star Y ⋙ pullback f`
for any morphism `f : X ⟶ Y`. -/
def starPullbackIsoStar [HasBinaryProducts C] [HasPullbacks C] {X Y : C} (f : X ⟶ Y) :
 star Y ⋙ pullback f ≅ star X :=
 conjugateIsoEquiv ((mapPullbackAdj f).comp (forgetAdjStar Y)) (forgetAdjStar X) (mapForget f)

/-- The functor `Over.pullback f : Over Y ⥤ Over X` is naturally isomorphic to
`Over.star : Over Y ⥤ Over (Over.mk f)` post-composed with the
iterated slice equivlanece `Over (Over.mk f) ⥤ Over X`. -/
Expand Down

33 changes: 17 additions & 16 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Sections.lean

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Expand Up@@ -28,7 +28,7 @@ variable {C : Type u₁} [Category.{v₁} C]

attribute [local instance] hasBinaryProducts_of_hasTerminal_and_pullbacks
attribute [local instance] hasFiniteProducts_of_has_binary_and_terminal
attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

section

Expand DownExpand Up@@ -69,11 +69,11 @@ end

variable [HasTerminal C] [HasPullbacks C]

variable (I : C) [Exponentiable I]
variable (I : C) [Closed I]

/-- The first leg of a cospan constructing a pullback diagram in `C` used to define `sections` . -/
def curryId : ⊤_ C ⟶ (I ⟹ I) :=
CartesianClosed.curry (fst I (⊤_ C))
MonoidalClosed.curry (fst I (⊤_ C))

variable {I}

Expand All@@ -90,14 +90,14 @@ pullback diagram:
 ⊤_ C ----> I ⟹ I
```-/
abbrev sectionsObj (X : Over I) : C :=
 Limits.pullback (curryId I) ((exp I).map X.hom)
 Limits.pullback (curryId I) ((ihom I).map X.hom)

/-- The functoriality of `sectionsObj`. -/
def sectionsMap {X X' : Over I} (u : X ⟶ X') :
 sectionsObj X ⟶ sectionsObj X' := by
 fapply pullback.map
 · exact 𝟙 _
 · exact (exp I).map u.left
 · exact (ihom I).map u.left
 · exact 𝟙 _
 · simp only [comp_id, id_comp]
 · simp only [comp_id, ← Functor.map_comp, w]
Expand DownExpand Up@@ -130,29 +130,30 @@ variable {I}
in `C`. See `sectionsCurry`. -/
def sectionsCurryAux {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (I ⟹ X.left) :=
CartesianClosed.curry (u.left)
MonoidalClosed.curry (u.left)

/-- The currying operation `Hom ((star I).obj A) X → Hom A (I ⟹ X.left)`. -/
def sectionsCurry {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (sections I).obj X := by
 apply pullback.lift (terminal.from A)
 (CartesianClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left)) (uncurry_injective _)
 rw [uncurry_natural_left]
 simp [curryId, uncurry_natural_right, uncurry_curry]
 (MonoidalClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left))
 (MonoidalClosed.uncurry_injective _)
 rw [MonoidalClosed.uncurry_natural_left]
 simp [curryId, MonoidalClosed.uncurry_natural_right, MonoidalClosed.uncurry_curry]

/-- The uncurrying operation `Hom A (section X) → Hom ((star I).obj A) X`. -/
def sectionsUncurry {X : Over I} {A : C} (v : A ⟶ (sections I).obj X) :
 (star I).obj A ⟶ X := by
 let v₂ : A ⟶ (I ⟹ X.left) := v ≫ pullback.snd ..
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (exp I).map X.hom := by
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (ihom I).map X.hom := by
 rw [IsTerminal.hom_ext terminalIsTerminal (terminal.from A ) (v ≫ (pullback.fst ..))]
 simp [v₂, pullback.condition]
 dsimp [curryId] at w
 have w' := homEquiv_naturality_right_square (F := MonoidalCategory.tensorLeft I)
 (adj := exp.adjunction I) _ _ _ _ w
 simp [CartesianClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ CartesianClosed.uncurry v₂) ?_
 · dsimp [CartesianClosed.uncurry] at *
 (adj := ihom.adjunction I) _ _ _ _ w
 simp [MonoidalClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ MonoidalClosed.uncurry v₂) ?_
 · dsimp [MonoidalClosed.uncurry] at *
 rw [Category.assoc, ← w']
 simp [star_obj_hom]

Expand DownExpand Up@@ -188,13 +189,13 @@ def coreHomEquiv : CoreHomEquiv (star I) (sections I) where
 simp only [star_map]
 rw [← Over.homMk_comp] -- note: in a newer version of mathlib this is `Over.homMk_eta`
 congr 1
 simp [CartesianClosed.uncurry_natural_left]
 simp [MonoidalClosed.uncurry_natural_left]
 homEquiv_naturality_right := by
 intro A X' X u g
 dsimp [sectionsCurry, sectionsUncurry, curryId]
 apply pullback.hom_ext (IsTerminal.hom_ext terminalIsTerminal _ _)
 simp [sectionsMap, curryId]
 rw [← CartesianClosed.curry_natural_right, Category.assoc]
 rw [← MonoidalClosed.curry_natural_right, Category.assoc]

variable (I)

Expand Down

2 changes: 1 addition & 1 deletion
...Theory/Limits/Shapes/Pullback/CommSq.lean → ...its/Shapes/Pullback/IsPullback/Basic.lean

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Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Poly.ForMathlib.CategoryTheory.CommSq

namespace CategoryTheory.Functor
Expand Down

21 changes: 11 additions & 10 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Basic.lean

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Expand Up@@ -67,7 +67,7 @@ open CategoryTheory Category MonoidalCategory CartesianMonoidalCategory Limits F

variable {C : Type u} [Category.{v} C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

/-- A morphism `f : I ⟶ J` is exponentiable if the pullback functor `Over J ⥤ Over I`
has a right adjoint. -/
Expand DownExpand Up@@ -179,7 +179,7 @@ instance isMultiplicative : (ExponentiableMorphism (C:= C)).IsMultiplicative whe
/-- A morphism with a pushforward is an exponentiable object in the slice category. -/
def exponentiableOverMk [HasFiniteWidePullbacks C] {X I : C} (f : X ⟶ I)
 [ExponentiableMorphism f] :
Exponentiable (Over.mk f) where
Closed (Over.mk f) where
 rightAdj := pullback f ⋙ pushforward f
 adj := by
 apply ofNatIsoLeft _ _
Expand All@@ -192,7 +192,7 @@ morphism `X.hom`.
Here the pushforward functor along a morphism `f : I ⟶ J` is defined using the section functor
`Over (Over.mk f) ⥤ Over J`.
-/
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Exponentiable X] :
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Closed X] :
 ExponentiableMorphism X.hom :=
 ⟨X.iteratedSliceEquiv.inverse ⋙ sections X, ⟨by
 refine ofNatIsoLeft (Adjunction.comp ?_ ?_) (starIteratedSliceForwardIsoPullback X.hom)
Expand All@@ -217,7 +217,7 @@ variable {C} [HasFiniteWidePullbacks C] [HasPushforwards C]
/-- In a category where pushforwards exists along all morphisms, every slice category `Over I` is
cartesian closed. -/
instance cartesianClosedOver (I : C) :
CartesianClosed (Over I) where
MonoidalClosed (Over I) where
 closed X := @exponentiableOverMk _ _ _ _ _ _ X.hom (HasPushforwards.exponentiable X.hom)

end HasPushforwards
Expand All@@ -226,13 +226,13 @@ namespace CartesianClosedOver

open Over Reindex IsIso CartesianClosed HasPushforwards ExponentiableMorphism

variable {C} [HasFiniteWidePullbacks C] {I J : C} [CartesianClosed (Over J)]
variable {C} [HasFiniteWidePullbacks C] {I J : C} [MonoidalClosed (Over J)]

instance (f : I ⟶ J) : ExponentiableMorphism f :=
 ExponentiableMorphism.ofOverExponentiable (Over.mk f)

/-- A category with cartesian closed slices has pushforwards along all morphisms. -/
instance hasPushforwards [Π (I : C), CartesianClosed (Over I)] : HasPushforwards C where
instance hasPushforwards [Π (I : C), MonoidalClosed (Over I)] : HasPushforwards C where
 exponentiable f := ExponentiableMorphism.ofOverExponentiable (Over.mk f)

end CartesianClosedOver
Expand All@@ -242,7 +242,7 @@ is exponentiable and all the slices are cartesian closed. -/
class LocallyCartesianClosed [HasFiniteWidePullbacks C] extends
 HasPushforwards C where
 /-- every slice category `Over I` is cartesian closed. This is filled in by default. -/
 cartesianClosedOver : Π (I : C), CartesianClosed (Over I) := HasPushforwards.cartesianClosedOver
 cartesianClosedOver : Π (I : C), MonoidalClosed (Over I) := HasPushforwards.cartesianClosedOver

namespace LocallyCartesianClosed

Expand All@@ -256,7 +256,7 @@ attribute [scoped instance] hasFiniteLimits_of_hasTerminal_and_pullbacks
instance mkOfHasPushforwards [HasPushforwards C] : LocallyCartesianClosed C where

/-- A category with cartesian closed slices is locally cartesian closed. -/
instance mkOfCartesianClosedOver [Π (I : C), CartesianClosed (Over I)] :
instance mkOfCartesianClosedOver [Π (I : C), MonoidalClosed (Over I)] :
 LocallyCartesianClosed C where

variable [LocallyCartesianClosed C]
Expand All@@ -282,15 +282,16 @@ abbrev ev' {I : C} (X : Over I) (Y : Over X.left) : Reindex X (Pi X Y) ⟶ Y :=
 adj X.hom |>.counit.app Y

/-- A locally cartesian closed category with a terminal object is cartesian closed. -/
def cartesianClosed [HasTerminal C] :
CartesianClosed C := cartesianClosedOfEquiv <| equivOverTerminal C
def monoidalClosed [HasTerminal C] :
MonoidalClosed C := cartesianClosedOfEquiv <| equivOverTerminal C

/-- The slices of a locally cartesian closed category are locally cartesian closed. -/
def overLocallyCartesianClosed (I : C) : LocallyCartesianClosed (Over I) := by
 apply (config := { allowSynthFailures:= true}) mkOfCartesianClosedOver
 intro X
 exact cartesianClosedOfEquiv (C := Over (X.left)) X.iteratedSliceEquiv.symm

open CartesianClosed in
/-- The exponential `X^^A` in the slice category `Over I` is isomorphic to the pushforward of the
pullback of `X` along `A`. -/
def expIso {I : C} (A X : Over I) : Pi A (Reindex A X) ≅ A ⟹ X := Iso.refl _
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/BeckChevalley.lean

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Expand Up@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour, Emily Riehl
-/
import Poly.ForMathlib.CategoryTheory.LocallyCartesianClosed.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

/-!
# Beck-Chevalley natural transformations and natural isomorphisms
Expand Down

6 changes: 3 additions & 3 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Presheaf.lean

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Expand Up@@ -22,10 +22,10 @@ abbrev Psh (C : Type u) [Category.{v} C] : Type (max u (v + 1)) := Cᵒᵖ ⥤ T

variable {C : Type*} [SmallCategory C] [HasTerminal C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

instance cartesianClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
CartesianClosed (Over P) :=
instance monoidalClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
MonoidalClosed (Over P) :=
 cartesianClosedOfEquiv (overEquivPresheafCostructuredArrow P).symm

instance locallyCartesianClosed : LocallyCartesianClosed (Psh C) := by
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/NatTrans.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -6,7 +6,7 @@ Authors: Sina Hazratpour

import Mathlib.CategoryTheory.NatTrans
import Mathlib.CategoryTheory.Functor.TwoSquare
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

open CategoryTheory Limits IsPullback

Expand Down

4 changes: 3 additions & 1 deletion
Poly/ForMathlib/CategoryTheory/PartialProduct.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Mathlib.CategoryTheory.Comma.Over.Pullback
import Poly.ForMathlib.CategoryTheory.Comma.Over.Pullback
import Mathlib.CategoryTheory.Monoidal.Closed.Cartesian
Expand DownExpand Up@@ -100,6 +100,8 @@ structure Fan.Hom (c c' : Fan s X) where

attribute [reassoc (attr := simp)] Fan.Hom.w_left Fan.Hom.w_right

-- TODO: this is taking ages to check since 4.28.0-rc1.
set_option maxHeartbeats 0 in
@[simps]
instance : Category (Fan s X) where
 Hom := Fan.Hom
Expand Down

2 changes: 1 addition & 1 deletion
Poly/Type/Univariate.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -189,7 +189,7 @@ def Obj.iget [DecidableEq P.B] {X} [Inhabited X] (x : P X) (i : P.Total) : X :=
@[simp]
theorem iget_map [DecidableEq P.B] [Inhabited X] [Inhabited Y] (x : P X)
 (f : X → Y) (i : P.Total) (h : i.1 = x.1) : (P.map f x).iget i = f (x.iget i) := by
 simp only [Obj.iget, fst_map, *, dif_pos, eq_self_iff_true]
 simp only [Obj.iget, fst_map, *, dif_pos]
 cases x
 rfl

Expand Down

20 changes: 10 additions & 10 deletions
lake-manifest.json

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Original file line numberDiff line numberDiff line change
Expand Up@@ -15,7 +15,7 @@
 "type": "git",
 "subDir": null,
 "scope": "",
 "rev": "dd5e5d97469dec395f29661366030566355ad9be",
 "rev": "b8dad038b1b3a05b77d6884b15b8db03ec01dca1",
 "name": "mathlib",
 "manifestFile": "lake-manifest.json",
 "inputRev": null,
Expand All@@ -25,7 +25,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "b3dd6c3ebc0a71685e86bea9223be39ea4c299fb",
 "rev": "7311586e1a56af887b1081d05e80c11b6c41d212",
 "name": "plausible",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -45,7 +45,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "cff9dd30f2c161b9efd7c657cafed1f967645890",
 "rev": "b5908dbac486279f1133cb937648c63c30b455af",
 "name": "importGraph",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -55,17 +55,17 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "ef8377f31b5535430b6753a974d685b0019d0681",
 "rev": "6d65c6e0a25b8a52c13c3adeb63ecde3bfbb6294",
 "name": "proofwidgets",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v0.0.84",
 "inputRev": "v0.0.86",
 "inherited": true,
 "configFile": "lakefile.lean"},
 {"url": "https://github.com/leanprover-community/aesop",
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "fa78cf032194308a950a264ed87b422a2a7c1c6c",
 "rev": "f08e838d4f9aea519f3cde06260cfb686fd4bab0",
 "name": "aesop",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -75,7 +75,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "8920dcbb96a4e8bf641fc399ac9c0888e4a6be72",
 "rev": "23324752757bf28124a518ec284044c8db79fee5",
 "name": "Qq",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -85,7 +85,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "dff865b7ee7011518d59abfc101c368293173150",
 "rev": "100083c18750b6a9b7553c65f6b052c0a2f6bcb4",
 "name": "batteries",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -95,10 +95,10 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover",
 "rev": "726b98c53e2da249c1de768fbbbb5e67bc9cef60",
 "rev": "28e0856d4424863a85b18f38868c5420c55f9bae",
 "name": "Cli",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v4.27.0-rc1",
 "inputRev": "v4.28.0-rc1",
 "inherited": true,
 "configFile": "lakefile.toml"}],
 "name": "Poly",
Expand Down

2 changes: 1 addition & 1 deletion
lean-toolchain

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Original file line numberDiff line numberDiff line change
@@ -1 +1 @@
leanprover/lean4:v4.27.0-rc1
leanprover/lean4:v4.28.0-rc1

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix");
}
} catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Jul 10, 2026
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feat: bump to Lean v4.28.0-rc1
#36
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4 changes: 0 additions & 4 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -35,10 +35,6 @@ lemma homMk_comp'_assoc {X Y Z W : T} (f : X ⟶ Y) (g : Y ⟶ Z) (h : Z ⟶ W)
lemma homMk_id {X B : T} (f : X ⟶ B) (h : 𝟙 X ≫ f = f) : homMk (𝟙 X) h = 𝟙 (mk f) :=
 rfl

@[simp]
theorem mkIdTerminal_from_left {B : T} (U : Over B) : (mkIdTerminal.from U).left = U.hom := by
 simp [mkIdTerminal, CostructuredArrow.mkIdTerminal, Limits.IsTerminal.from, Functor.preimage]

/-- `Over.Sigma Y U` is a shorthand for `(Over.map Y.hom).obj U`.
This is a category-theoretic analogue of `Sigma` for types. -/
abbrev Sigma {X : T} (Y : Over X) (U : Over (Y.left)) : Over X :=
Expand Down

12 changes: 3 additions & 9 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Pullback.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -9,7 +9,7 @@ import Mathlib.CategoryTheory.Limits.Constructions.Over.Basic
import Mathlib.CategoryTheory.Monad.Products
import Poly.ForMathlib.CategoryTheory.Comma.Over.Basic
import Poly.ForMathlib.CategoryTheory.NatTrans
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

noncomputable section

Expand All@@ -19,7 +19,7 @@ namespace CategoryTheory

open Category Limits Comonad MonoidalCategory CartesianMonoidalCategory

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

variable {C : Type u₁} [Category.{v₁} C]

Expand DownExpand Up@@ -211,7 +211,7 @@ lemma star_map [HasBinaryProducts C] {X : C} {Y Z : C} (f : Y ⟶ Z) :
instance [HasBinaryProducts C] (X : C) : (forget X).IsLeftAdjoint :=
 ⟨_, ⟨forgetAdjStar X⟩⟩

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

lemma whiskerLeftProdMapId [HasFiniteLimits C] {X : C} {A A' : C} {g : A ⟶ A'} :
 X ◁ g = prod.map (𝟙 X) g := by
Expand DownExpand Up@@ -298,12 +298,6 @@ def starIsoToOverTerminal [HasTerminal C] [HasBinaryProducts C] :

variable {C}

/-- A natural isomorphism between the functors `star X` and `star Y ⋙ pullback f`
for any morphism `f : X ⟶ Y`. -/
def starPullbackIsoStar [HasBinaryProducts C] [HasPullbacks C] {X Y : C} (f : X ⟶ Y) :
 star Y ⋙ pullback f ≅ star X :=
 conjugateIsoEquiv ((mapPullbackAdj f).comp (forgetAdjStar Y)) (forgetAdjStar X) (mapForget f)

/-- The functor `Over.pullback f : Over Y ⥤ Over X` is naturally isomorphic to
`Over.star : Over Y ⥤ Over (Over.mk f)` post-composed with the
iterated slice equivlanece `Over (Over.mk f) ⥤ Over X`. -/
Expand Down

33 changes: 17 additions & 16 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Sections.lean

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Expand Up@@ -28,7 +28,7 @@ variable {C : Type u₁} [Category.{v₁} C]

attribute [local instance] hasBinaryProducts_of_hasTerminal_and_pullbacks
attribute [local instance] hasFiniteProducts_of_has_binary_and_terminal
attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

section

Expand DownExpand Up@@ -69,11 +69,11 @@ end

variable [HasTerminal C] [HasPullbacks C]

variable (I : C) [Exponentiable I]
variable (I : C) [Closed I]

/-- The first leg of a cospan constructing a pullback diagram in `C` used to define `sections` . -/
def curryId : ⊤_ C ⟶ (I ⟹ I) :=
CartesianClosed.curry (fst I (⊤_ C))
MonoidalClosed.curry (fst I (⊤_ C))

variable {I}

Expand All@@ -90,14 +90,14 @@ pullback diagram:
 ⊤_ C ----> I ⟹ I
```-/
abbrev sectionsObj (X : Over I) : C :=
 Limits.pullback (curryId I) ((exp I).map X.hom)
 Limits.pullback (curryId I) ((ihom I).map X.hom)

/-- The functoriality of `sectionsObj`. -/
def sectionsMap {X X' : Over I} (u : X ⟶ X') :
 sectionsObj X ⟶ sectionsObj X' := by
 fapply pullback.map
 · exact 𝟙 _
 · exact (exp I).map u.left
 · exact (ihom I).map u.left
 · exact 𝟙 _
 · simp only [comp_id, id_comp]
 · simp only [comp_id, ← Functor.map_comp, w]
Expand DownExpand Up@@ -130,29 +130,30 @@ variable {I}
in `C`. See `sectionsCurry`. -/
def sectionsCurryAux {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (I ⟹ X.left) :=
CartesianClosed.curry (u.left)
MonoidalClosed.curry (u.left)

/-- The currying operation `Hom ((star I).obj A) X → Hom A (I ⟹ X.left)`. -/
def sectionsCurry {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (sections I).obj X := by
 apply pullback.lift (terminal.from A)
 (CartesianClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left)) (uncurry_injective _)
 rw [uncurry_natural_left]
 simp [curryId, uncurry_natural_right, uncurry_curry]
 (MonoidalClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left))
 (MonoidalClosed.uncurry_injective _)
 rw [MonoidalClosed.uncurry_natural_left]
 simp [curryId, MonoidalClosed.uncurry_natural_right, MonoidalClosed.uncurry_curry]

/-- The uncurrying operation `Hom A (section X) → Hom ((star I).obj A) X`. -/
def sectionsUncurry {X : Over I} {A : C} (v : A ⟶ (sections I).obj X) :
 (star I).obj A ⟶ X := by
 let v₂ : A ⟶ (I ⟹ X.left) := v ≫ pullback.snd ..
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (exp I).map X.hom := by
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (ihom I).map X.hom := by
 rw [IsTerminal.hom_ext terminalIsTerminal (terminal.from A ) (v ≫ (pullback.fst ..))]
 simp [v₂, pullback.condition]
 dsimp [curryId] at w
 have w' := homEquiv_naturality_right_square (F := MonoidalCategory.tensorLeft I)
 (adj := exp.adjunction I) _ _ _ _ w
 simp [CartesianClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ CartesianClosed.uncurry v₂) ?_
 · dsimp [CartesianClosed.uncurry] at *
 (adj := ihom.adjunction I) _ _ _ _ w
 simp [MonoidalClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ MonoidalClosed.uncurry v₂) ?_
 · dsimp [MonoidalClosed.uncurry] at *
 rw [Category.assoc, ← w']
 simp [star_obj_hom]

Expand DownExpand Up@@ -188,13 +189,13 @@ def coreHomEquiv : CoreHomEquiv (star I) (sections I) where
 simp only [star_map]
 rw [← Over.homMk_comp] -- note: in a newer version of mathlib this is `Over.homMk_eta`
 congr 1
 simp [CartesianClosed.uncurry_natural_left]
 simp [MonoidalClosed.uncurry_natural_left]
 homEquiv_naturality_right := by
 intro A X' X u g
 dsimp [sectionsCurry, sectionsUncurry, curryId]
 apply pullback.hom_ext (IsTerminal.hom_ext terminalIsTerminal _ _)
 simp [sectionsMap, curryId]
 rw [← CartesianClosed.curry_natural_right, Category.assoc]
 rw [← MonoidalClosed.curry_natural_right, Category.assoc]

variable (I)

Expand Down

2 changes: 1 addition & 1 deletion
...Theory/Limits/Shapes/Pullback/CommSq.lean → ...its/Shapes/Pullback/IsPullback/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Poly.ForMathlib.CategoryTheory.CommSq

namespace CategoryTheory.Functor
Expand Down

21 changes: 11 additions & 10 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -67,7 +67,7 @@ open CategoryTheory Category MonoidalCategory CartesianMonoidalCategory Limits F

variable {C : Type u} [Category.{v} C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

/-- A morphism `f : I ⟶ J` is exponentiable if the pullback functor `Over J ⥤ Over I`
has a right adjoint. -/
Expand DownExpand Up@@ -179,7 +179,7 @@ instance isMultiplicative : (ExponentiableMorphism (C:= C)).IsMultiplicative whe
/-- A morphism with a pushforward is an exponentiable object in the slice category. -/
def exponentiableOverMk [HasFiniteWidePullbacks C] {X I : C} (f : X ⟶ I)
 [ExponentiableMorphism f] :
Exponentiable (Over.mk f) where
Closed (Over.mk f) where
 rightAdj := pullback f ⋙ pushforward f
 adj := by
 apply ofNatIsoLeft _ _
Expand All@@ -192,7 +192,7 @@ morphism `X.hom`.
Here the pushforward functor along a morphism `f : I ⟶ J` is defined using the section functor
`Over (Over.mk f) ⥤ Over J`.
-/
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Exponentiable X] :
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Closed X] :
 ExponentiableMorphism X.hom :=
 ⟨X.iteratedSliceEquiv.inverse ⋙ sections X, ⟨by
 refine ofNatIsoLeft (Adjunction.comp ?_ ?_) (starIteratedSliceForwardIsoPullback X.hom)
Expand All@@ -217,7 +217,7 @@ variable {C} [HasFiniteWidePullbacks C] [HasPushforwards C]
/-- In a category where pushforwards exists along all morphisms, every slice category `Over I` is
cartesian closed. -/
instance cartesianClosedOver (I : C) :
CartesianClosed (Over I) where
MonoidalClosed (Over I) where
 closed X := @exponentiableOverMk _ _ _ _ _ _ X.hom (HasPushforwards.exponentiable X.hom)

end HasPushforwards
Expand All@@ -226,13 +226,13 @@ namespace CartesianClosedOver

open Over Reindex IsIso CartesianClosed HasPushforwards ExponentiableMorphism

variable {C} [HasFiniteWidePullbacks C] {I J : C} [CartesianClosed (Over J)]
variable {C} [HasFiniteWidePullbacks C] {I J : C} [MonoidalClosed (Over J)]

instance (f : I ⟶ J) : ExponentiableMorphism f :=
 ExponentiableMorphism.ofOverExponentiable (Over.mk f)

/-- A category with cartesian closed slices has pushforwards along all morphisms. -/
instance hasPushforwards [Π (I : C), CartesianClosed (Over I)] : HasPushforwards C where
instance hasPushforwards [Π (I : C), MonoidalClosed (Over I)] : HasPushforwards C where
 exponentiable f := ExponentiableMorphism.ofOverExponentiable (Over.mk f)

end CartesianClosedOver
Expand All@@ -242,7 +242,7 @@ is exponentiable and all the slices are cartesian closed. -/
class LocallyCartesianClosed [HasFiniteWidePullbacks C] extends
 HasPushforwards C where
 /-- every slice category `Over I` is cartesian closed. This is filled in by default. -/
 cartesianClosedOver : Π (I : C), CartesianClosed (Over I) := HasPushforwards.cartesianClosedOver
 cartesianClosedOver : Π (I : C), MonoidalClosed (Over I) := HasPushforwards.cartesianClosedOver

namespace LocallyCartesianClosed

Expand All@@ -256,7 +256,7 @@ attribute [scoped instance] hasFiniteLimits_of_hasTerminal_and_pullbacks
instance mkOfHasPushforwards [HasPushforwards C] : LocallyCartesianClosed C where

/-- A category with cartesian closed slices is locally cartesian closed. -/
instance mkOfCartesianClosedOver [Π (I : C), CartesianClosed (Over I)] :
instance mkOfCartesianClosedOver [Π (I : C), MonoidalClosed (Over I)] :
 LocallyCartesianClosed C where

variable [LocallyCartesianClosed C]
Expand All@@ -282,15 +282,16 @@ abbrev ev' {I : C} (X : Over I) (Y : Over X.left) : Reindex X (Pi X Y) ⟶ Y :=
 adj X.hom |>.counit.app Y

/-- A locally cartesian closed category with a terminal object is cartesian closed. -/
def cartesianClosed [HasTerminal C] :
CartesianClosed C := cartesianClosedOfEquiv <| equivOverTerminal C
def monoidalClosed [HasTerminal C] :
MonoidalClosed C := cartesianClosedOfEquiv <| equivOverTerminal C

/-- The slices of a locally cartesian closed category are locally cartesian closed. -/
def overLocallyCartesianClosed (I : C) : LocallyCartesianClosed (Over I) := by
 apply (config := { allowSynthFailures:= true}) mkOfCartesianClosedOver
 intro X
 exact cartesianClosedOfEquiv (C := Over (X.left)) X.iteratedSliceEquiv.symm

open CartesianClosed in
/-- The exponential `X^^A` in the slice category `Over I` is isomorphic to the pushforward of the
pullback of `X` along `A`. -/
def expIso {I : C} (A X : Over I) : Pi A (Reindex A X) ≅ A ⟹ X := Iso.refl _
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/BeckChevalley.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour, Emily Riehl
-/
import Poly.ForMathlib.CategoryTheory.LocallyCartesianClosed.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

/-!
# Beck-Chevalley natural transformations and natural isomorphisms
Expand Down

6 changes: 3 additions & 3 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Presheaf.lean

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Expand Up@@ -22,10 +22,10 @@ abbrev Psh (C : Type u) [Category.{v} C] : Type (max u (v + 1)) := Cᵒᵖ ⥤ T

variable {C : Type*} [SmallCategory C] [HasTerminal C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

instance cartesianClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
CartesianClosed (Over P) :=
instance monoidalClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
MonoidalClosed (Over P) :=
 cartesianClosedOfEquiv (overEquivPresheafCostructuredArrow P).symm

instance locallyCartesianClosed : LocallyCartesianClosed (Psh C) := by
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/NatTrans.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -6,7 +6,7 @@ Authors: Sina Hazratpour

import Mathlib.CategoryTheory.NatTrans
import Mathlib.CategoryTheory.Functor.TwoSquare
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

open CategoryTheory Limits IsPullback

Expand Down

4 changes: 3 additions & 1 deletion
Poly/ForMathlib/CategoryTheory/PartialProduct.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Mathlib.CategoryTheory.Comma.Over.Pullback
import Poly.ForMathlib.CategoryTheory.Comma.Over.Pullback
import Mathlib.CategoryTheory.Monoidal.Closed.Cartesian
Expand DownExpand Up@@ -100,6 +100,8 @@ structure Fan.Hom (c c' : Fan s X) where

attribute [reassoc (attr := simp)] Fan.Hom.w_left Fan.Hom.w_right

-- TODO: this is taking ages to check since 4.28.0-rc1.
set_option maxHeartbeats 0 in
@[simps]
instance : Category (Fan s X) where
 Hom := Fan.Hom
Expand Down

2 changes: 1 addition & 1 deletion
Poly/Type/Univariate.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -189,7 +189,7 @@ def Obj.iget [DecidableEq P.B] {X} [Inhabited X] (x : P X) (i : P.Total) : X :=
@[simp]
theorem iget_map [DecidableEq P.B] [Inhabited X] [Inhabited Y] (x : P X)
 (f : X → Y) (i : P.Total) (h : i.1 = x.1) : (P.map f x).iget i = f (x.iget i) := by
 simp only [Obj.iget, fst_map, *, dif_pos, eq_self_iff_true]
 simp only [Obj.iget, fst_map, *, dif_pos]
 cases x
 rfl

Expand Down

20 changes: 10 additions & 10 deletions
lake-manifest.json

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Original file line numberDiff line numberDiff line change
Expand Up@@ -15,7 +15,7 @@
 "type": "git",
 "subDir": null,
 "scope": "",
 "rev": "dd5e5d97469dec395f29661366030566355ad9be",
 "rev": "b8dad038b1b3a05b77d6884b15b8db03ec01dca1",
 "name": "mathlib",
 "manifestFile": "lake-manifest.json",
 "inputRev": null,
Expand All@@ -25,7 +25,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "b3dd6c3ebc0a71685e86bea9223be39ea4c299fb",
 "rev": "7311586e1a56af887b1081d05e80c11b6c41d212",
 "name": "plausible",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -45,7 +45,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "cff9dd30f2c161b9efd7c657cafed1f967645890",
 "rev": "b5908dbac486279f1133cb937648c63c30b455af",
 "name": "importGraph",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -55,17 +55,17 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "ef8377f31b5535430b6753a974d685b0019d0681",
 "rev": "6d65c6e0a25b8a52c13c3adeb63ecde3bfbb6294",
 "name": "proofwidgets",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v0.0.84",
 "inputRev": "v0.0.86",
 "inherited": true,
 "configFile": "lakefile.lean"},
 {"url": "https://github.com/leanprover-community/aesop",
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "fa78cf032194308a950a264ed87b422a2a7c1c6c",
 "rev": "f08e838d4f9aea519f3cde06260cfb686fd4bab0",
 "name": "aesop",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -75,7 +75,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "8920dcbb96a4e8bf641fc399ac9c0888e4a6be72",
 "rev": "23324752757bf28124a518ec284044c8db79fee5",
 "name": "Qq",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -85,7 +85,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "dff865b7ee7011518d59abfc101c368293173150",
 "rev": "100083c18750b6a9b7553c65f6b052c0a2f6bcb4",
 "name": "batteries",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -95,10 +95,10 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover",
 "rev": "726b98c53e2da249c1de768fbbbb5e67bc9cef60",
 "rev": "28e0856d4424863a85b18f38868c5420c55f9bae",
 "name": "Cli",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v4.27.0-rc1",
 "inputRev": "v4.28.0-rc1",
 "inherited": true,
 "configFile": "lakefile.toml"}],
 "name": "Poly",
Expand Down

2 changes: 1 addition & 1 deletion
lean-toolchain

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Original file line numberDiff line numberDiff line change
@@ -1 +1 @@
leanprover/lean4:v4.27.0-rc1
leanprover/lean4:v4.28.0-rc1

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms");
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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feat: bump to Lean v4.28.0-rc1#36

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Jul 10, 2026
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feat: bump to Lean v4.28.0-rc1
#36
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4 changes: 0 additions & 4 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -35,10 +35,6 @@ lemma homMk_comp'_assoc {X Y Z W : T} (f : X ⟶ Y) (g : Y ⟶ Z) (h : Z ⟶ W)
lemma homMk_id {X B : T} (f : X ⟶ B) (h : 𝟙 X ≫ f = f) : homMk (𝟙 X) h = 𝟙 (mk f) :=
 rfl

@[simp]
theorem mkIdTerminal_from_left {B : T} (U : Over B) : (mkIdTerminal.from U).left = U.hom := by
 simp [mkIdTerminal, CostructuredArrow.mkIdTerminal, Limits.IsTerminal.from, Functor.preimage]

/-- `Over.Sigma Y U` is a shorthand for `(Over.map Y.hom).obj U`.
This is a category-theoretic analogue of `Sigma` for types. -/
abbrev Sigma {X : T} (Y : Over X) (U : Over (Y.left)) : Over X :=
Expand Down

12 changes: 3 additions & 9 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Pullback.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -9,7 +9,7 @@ import Mathlib.CategoryTheory.Limits.Constructions.Over.Basic
import Mathlib.CategoryTheory.Monad.Products
import Poly.ForMathlib.CategoryTheory.Comma.Over.Basic
import Poly.ForMathlib.CategoryTheory.NatTrans
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

noncomputable section

Expand All@@ -19,7 +19,7 @@ namespace CategoryTheory

open Category Limits Comonad MonoidalCategory CartesianMonoidalCategory

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

variable {C : Type u₁} [Category.{v₁} C]

Expand DownExpand Up@@ -211,7 +211,7 @@ lemma star_map [HasBinaryProducts C] {X : C} {Y Z : C} (f : Y ⟶ Z) :
instance [HasBinaryProducts C] (X : C) : (forget X).IsLeftAdjoint :=
 ⟨_, ⟨forgetAdjStar X⟩⟩

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

lemma whiskerLeftProdMapId [HasFiniteLimits C] {X : C} {A A' : C} {g : A ⟶ A'} :
 X ◁ g = prod.map (𝟙 X) g := by
Expand DownExpand Up@@ -298,12 +298,6 @@ def starIsoToOverTerminal [HasTerminal C] [HasBinaryProducts C] :

variable {C}

/-- A natural isomorphism between the functors `star X` and `star Y ⋙ pullback f`
for any morphism `f : X ⟶ Y`. -/
def starPullbackIsoStar [HasBinaryProducts C] [HasPullbacks C] {X Y : C} (f : X ⟶ Y) :
 star Y ⋙ pullback f ≅ star X :=
 conjugateIsoEquiv ((mapPullbackAdj f).comp (forgetAdjStar Y)) (forgetAdjStar X) (mapForget f)

/-- The functor `Over.pullback f : Over Y ⥤ Over X` is naturally isomorphic to
`Over.star : Over Y ⥤ Over (Over.mk f)` post-composed with the
iterated slice equivlanece `Over (Over.mk f) ⥤ Over X`. -/
Expand Down

33 changes: 17 additions & 16 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Sections.lean

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Expand Up@@ -28,7 +28,7 @@ variable {C : Type u₁} [Category.{v₁} C]

attribute [local instance] hasBinaryProducts_of_hasTerminal_and_pullbacks
attribute [local instance] hasFiniteProducts_of_has_binary_and_terminal
attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

section

Expand DownExpand Up@@ -69,11 +69,11 @@ end

variable [HasTerminal C] [HasPullbacks C]

variable (I : C) [Exponentiable I]
variable (I : C) [Closed I]

/-- The first leg of a cospan constructing a pullback diagram in `C` used to define `sections` . -/
def curryId : ⊤_ C ⟶ (I ⟹ I) :=
CartesianClosed.curry (fst I (⊤_ C))
MonoidalClosed.curry (fst I (⊤_ C))

variable {I}

Expand All@@ -90,14 +90,14 @@ pullback diagram:
 ⊤_ C ----> I ⟹ I
```-/
abbrev sectionsObj (X : Over I) : C :=
 Limits.pullback (curryId I) ((exp I).map X.hom)
 Limits.pullback (curryId I) ((ihom I).map X.hom)

/-- The functoriality of `sectionsObj`. -/
def sectionsMap {X X' : Over I} (u : X ⟶ X') :
 sectionsObj X ⟶ sectionsObj X' := by
 fapply pullback.map
 · exact 𝟙 _
 · exact (exp I).map u.left
 · exact (ihom I).map u.left
 · exact 𝟙 _
 · simp only [comp_id, id_comp]
 · simp only [comp_id, ← Functor.map_comp, w]
Expand DownExpand Up@@ -130,29 +130,30 @@ variable {I}
in `C`. See `sectionsCurry`. -/
def sectionsCurryAux {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (I ⟹ X.left) :=
CartesianClosed.curry (u.left)
MonoidalClosed.curry (u.left)

/-- The currying operation `Hom ((star I).obj A) X → Hom A (I ⟹ X.left)`. -/
def sectionsCurry {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (sections I).obj X := by
 apply pullback.lift (terminal.from A)
 (CartesianClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left)) (uncurry_injective _)
 rw [uncurry_natural_left]
 simp [curryId, uncurry_natural_right, uncurry_curry]
 (MonoidalClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left))
 (MonoidalClosed.uncurry_injective _)
 rw [MonoidalClosed.uncurry_natural_left]
 simp [curryId, MonoidalClosed.uncurry_natural_right, MonoidalClosed.uncurry_curry]

/-- The uncurrying operation `Hom A (section X) → Hom ((star I).obj A) X`. -/
def sectionsUncurry {X : Over I} {A : C} (v : A ⟶ (sections I).obj X) :
 (star I).obj A ⟶ X := by
 let v₂ : A ⟶ (I ⟹ X.left) := v ≫ pullback.snd ..
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (exp I).map X.hom := by
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (ihom I).map X.hom := by
 rw [IsTerminal.hom_ext terminalIsTerminal (terminal.from A ) (v ≫ (pullback.fst ..))]
 simp [v₂, pullback.condition]
 dsimp [curryId] at w
 have w' := homEquiv_naturality_right_square (F := MonoidalCategory.tensorLeft I)
 (adj := exp.adjunction I) _ _ _ _ w
 simp [CartesianClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ CartesianClosed.uncurry v₂) ?_
 · dsimp [CartesianClosed.uncurry] at *
 (adj := ihom.adjunction I) _ _ _ _ w
 simp [MonoidalClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ MonoidalClosed.uncurry v₂) ?_
 · dsimp [MonoidalClosed.uncurry] at *
 rw [Category.assoc, ← w']
 simp [star_obj_hom]

Expand DownExpand Up@@ -188,13 +189,13 @@ def coreHomEquiv : CoreHomEquiv (star I) (sections I) where
 simp only [star_map]
 rw [← Over.homMk_comp] -- note: in a newer version of mathlib this is `Over.homMk_eta`
 congr 1
 simp [CartesianClosed.uncurry_natural_left]
 simp [MonoidalClosed.uncurry_natural_left]
 homEquiv_naturality_right := by
 intro A X' X u g
 dsimp [sectionsCurry, sectionsUncurry, curryId]
 apply pullback.hom_ext (IsTerminal.hom_ext terminalIsTerminal _ _)
 simp [sectionsMap, curryId]
 rw [← CartesianClosed.curry_natural_right, Category.assoc]
 rw [← MonoidalClosed.curry_natural_right, Category.assoc]

variable (I)

Expand Down

2 changes: 1 addition & 1 deletion
...Theory/Limits/Shapes/Pullback/CommSq.lean → ...its/Shapes/Pullback/IsPullback/Basic.lean

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Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Poly.ForMathlib.CategoryTheory.CommSq

namespace CategoryTheory.Functor
Expand Down

21 changes: 11 additions & 10 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Basic.lean

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Expand Up@@ -67,7 +67,7 @@ open CategoryTheory Category MonoidalCategory CartesianMonoidalCategory Limits F

variable {C : Type u} [Category.{v} C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

/-- A morphism `f : I ⟶ J` is exponentiable if the pullback functor `Over J ⥤ Over I`
has a right adjoint. -/
Expand DownExpand Up@@ -179,7 +179,7 @@ instance isMultiplicative : (ExponentiableMorphism (C:= C)).IsMultiplicative whe
/-- A morphism with a pushforward is an exponentiable object in the slice category. -/
def exponentiableOverMk [HasFiniteWidePullbacks C] {X I : C} (f : X ⟶ I)
 [ExponentiableMorphism f] :
Exponentiable (Over.mk f) where
Closed (Over.mk f) where
 rightAdj := pullback f ⋙ pushforward f
 adj := by
 apply ofNatIsoLeft _ _
Expand All@@ -192,7 +192,7 @@ morphism `X.hom`.
Here the pushforward functor along a morphism `f : I ⟶ J` is defined using the section functor
`Over (Over.mk f) ⥤ Over J`.
-/
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Exponentiable X] :
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Closed X] :
 ExponentiableMorphism X.hom :=
 ⟨X.iteratedSliceEquiv.inverse ⋙ sections X, ⟨by
 refine ofNatIsoLeft (Adjunction.comp ?_ ?_) (starIteratedSliceForwardIsoPullback X.hom)
Expand All@@ -217,7 +217,7 @@ variable {C} [HasFiniteWidePullbacks C] [HasPushforwards C]
/-- In a category where pushforwards exists along all morphisms, every slice category `Over I` is
cartesian closed. -/
instance cartesianClosedOver (I : C) :
CartesianClosed (Over I) where
MonoidalClosed (Over I) where
 closed X := @exponentiableOverMk _ _ _ _ _ _ X.hom (HasPushforwards.exponentiable X.hom)

end HasPushforwards
Expand All@@ -226,13 +226,13 @@ namespace CartesianClosedOver

open Over Reindex IsIso CartesianClosed HasPushforwards ExponentiableMorphism

variable {C} [HasFiniteWidePullbacks C] {I J : C} [CartesianClosed (Over J)]
variable {C} [HasFiniteWidePullbacks C] {I J : C} [MonoidalClosed (Over J)]

instance (f : I ⟶ J) : ExponentiableMorphism f :=
 ExponentiableMorphism.ofOverExponentiable (Over.mk f)

/-- A category with cartesian closed slices has pushforwards along all morphisms. -/
instance hasPushforwards [Π (I : C), CartesianClosed (Over I)] : HasPushforwards C where
instance hasPushforwards [Π (I : C), MonoidalClosed (Over I)] : HasPushforwards C where
 exponentiable f := ExponentiableMorphism.ofOverExponentiable (Over.mk f)

end CartesianClosedOver
Expand All@@ -242,7 +242,7 @@ is exponentiable and all the slices are cartesian closed. -/
class LocallyCartesianClosed [HasFiniteWidePullbacks C] extends
 HasPushforwards C where
 /-- every slice category `Over I` is cartesian closed. This is filled in by default. -/
 cartesianClosedOver : Π (I : C), CartesianClosed (Over I) := HasPushforwards.cartesianClosedOver
 cartesianClosedOver : Π (I : C), MonoidalClosed (Over I) := HasPushforwards.cartesianClosedOver

namespace LocallyCartesianClosed

Expand All@@ -256,7 +256,7 @@ attribute [scoped instance] hasFiniteLimits_of_hasTerminal_and_pullbacks
instance mkOfHasPushforwards [HasPushforwards C] : LocallyCartesianClosed C where

/-- A category with cartesian closed slices is locally cartesian closed. -/
instance mkOfCartesianClosedOver [Π (I : C), CartesianClosed (Over I)] :
instance mkOfCartesianClosedOver [Π (I : C), MonoidalClosed (Over I)] :
 LocallyCartesianClosed C where

variable [LocallyCartesianClosed C]
Expand All@@ -282,15 +282,16 @@ abbrev ev' {I : C} (X : Over I) (Y : Over X.left) : Reindex X (Pi X Y) ⟶ Y :=
 adj X.hom |>.counit.app Y

/-- A locally cartesian closed category with a terminal object is cartesian closed. -/
def cartesianClosed [HasTerminal C] :
CartesianClosed C := cartesianClosedOfEquiv <| equivOverTerminal C
def monoidalClosed [HasTerminal C] :
MonoidalClosed C := cartesianClosedOfEquiv <| equivOverTerminal C

/-- The slices of a locally cartesian closed category are locally cartesian closed. -/
def overLocallyCartesianClosed (I : C) : LocallyCartesianClosed (Over I) := by
 apply (config := { allowSynthFailures:= true}) mkOfCartesianClosedOver
 intro X
 exact cartesianClosedOfEquiv (C := Over (X.left)) X.iteratedSliceEquiv.symm

open CartesianClosed in
/-- The exponential `X^^A` in the slice category `Over I` is isomorphic to the pushforward of the
pullback of `X` along `A`. -/
def expIso {I : C} (A X : Over I) : Pi A (Reindex A X) ≅ A ⟹ X := Iso.refl _
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/BeckChevalley.lean

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Expand Up@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour, Emily Riehl
-/
import Poly.ForMathlib.CategoryTheory.LocallyCartesianClosed.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

/-!
# Beck-Chevalley natural transformations and natural isomorphisms
Expand Down

6 changes: 3 additions & 3 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Presheaf.lean

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Expand Up@@ -22,10 +22,10 @@ abbrev Psh (C : Type u) [Category.{v} C] : Type (max u (v + 1)) := Cᵒᵖ ⥤ T

variable {C : Type*} [SmallCategory C] [HasTerminal C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

instance cartesianClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
CartesianClosed (Over P) :=
instance monoidalClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
MonoidalClosed (Over P) :=
 cartesianClosedOfEquiv (overEquivPresheafCostructuredArrow P).symm

instance locallyCartesianClosed : LocallyCartesianClosed (Psh C) := by
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/NatTrans.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -6,7 +6,7 @@ Authors: Sina Hazratpour

import Mathlib.CategoryTheory.NatTrans
import Mathlib.CategoryTheory.Functor.TwoSquare
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

open CategoryTheory Limits IsPullback

Expand Down

4 changes: 3 additions & 1 deletion
Poly/ForMathlib/CategoryTheory/PartialProduct.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Mathlib.CategoryTheory.Comma.Over.Pullback
import Poly.ForMathlib.CategoryTheory.Comma.Over.Pullback
import Mathlib.CategoryTheory.Monoidal.Closed.Cartesian
Expand DownExpand Up@@ -100,6 +100,8 @@ structure Fan.Hom (c c' : Fan s X) where

attribute [reassoc (attr := simp)] Fan.Hom.w_left Fan.Hom.w_right

-- TODO: this is taking ages to check since 4.28.0-rc1.
set_option maxHeartbeats 0 in
@[simps]
instance : Category (Fan s X) where
 Hom := Fan.Hom
Expand Down

2 changes: 1 addition & 1 deletion
Poly/Type/Univariate.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -189,7 +189,7 @@ def Obj.iget [DecidableEq P.B] {X} [Inhabited X] (x : P X) (i : P.Total) : X :=
@[simp]
theorem iget_map [DecidableEq P.B] [Inhabited X] [Inhabited Y] (x : P X)
 (f : X → Y) (i : P.Total) (h : i.1 = x.1) : (P.map f x).iget i = f (x.iget i) := by
 simp only [Obj.iget, fst_map, *, dif_pos, eq_self_iff_true]
 simp only [Obj.iget, fst_map, *, dif_pos]
 cases x
 rfl

Expand Down

20 changes: 10 additions & 10 deletions
lake-manifest.json

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Original file line numberDiff line numberDiff line change
Expand Up@@ -15,7 +15,7 @@
 "type": "git",
 "subDir": null,
 "scope": "",
 "rev": "dd5e5d97469dec395f29661366030566355ad9be",
 "rev": "b8dad038b1b3a05b77d6884b15b8db03ec01dca1",
 "name": "mathlib",
 "manifestFile": "lake-manifest.json",
 "inputRev": null,
Expand All@@ -25,7 +25,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "b3dd6c3ebc0a71685e86bea9223be39ea4c299fb",
 "rev": "7311586e1a56af887b1081d05e80c11b6c41d212",
 "name": "plausible",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -45,7 +45,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "cff9dd30f2c161b9efd7c657cafed1f967645890",
 "rev": "b5908dbac486279f1133cb937648c63c30b455af",
 "name": "importGraph",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -55,17 +55,17 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "ef8377f31b5535430b6753a974d685b0019d0681",
 "rev": "6d65c6e0a25b8a52c13c3adeb63ecde3bfbb6294",
 "name": "proofwidgets",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v0.0.84",
 "inputRev": "v0.0.86",
 "inherited": true,
 "configFile": "lakefile.lean"},
 {"url": "https://github.com/leanprover-community/aesop",
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "fa78cf032194308a950a264ed87b422a2a7c1c6c",
 "rev": "f08e838d4f9aea519f3cde06260cfb686fd4bab0",
 "name": "aesop",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -75,7 +75,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "8920dcbb96a4e8bf641fc399ac9c0888e4a6be72",
 "rev": "23324752757bf28124a518ec284044c8db79fee5",
 "name": "Qq",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -85,7 +85,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "dff865b7ee7011518d59abfc101c368293173150",
 "rev": "100083c18750b6a9b7553c65f6b052c0a2f6bcb4",
 "name": "batteries",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -95,10 +95,10 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover",
 "rev": "726b98c53e2da249c1de768fbbbb5e67bc9cef60",
 "rev": "28e0856d4424863a85b18f38868c5420c55f9bae",
 "name": "Cli",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v4.27.0-rc1",
 "inputRev": "v4.28.0-rc1",
 "inherited": true,
 "configFile": "lakefile.toml"}],
 "name": "Poly",
Expand Down

2 changes: 1 addition & 1 deletion
lean-toolchain

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Original file line numberDiff line numberDiff line change
@@ -1 +1 @@
leanprover/lean4:v4.27.0-rc1
leanprover/lean4:v4.28.0-rc1

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links");
}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

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feat: bump to Lean v4.28.0-rc1#36

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Jul 10, 2026
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feat: bump to Lean v4.28.0-rc1
#36
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4 changes: 0 additions & 4 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -35,10 +35,6 @@ lemma homMk_comp'_assoc {X Y Z W : T} (f : X ⟶ Y) (g : Y ⟶ Z) (h : Z ⟶ W)
lemma homMk_id {X B : T} (f : X ⟶ B) (h : 𝟙 X ≫ f = f) : homMk (𝟙 X) h = 𝟙 (mk f) :=
 rfl

@[simp]
theorem mkIdTerminal_from_left {B : T} (U : Over B) : (mkIdTerminal.from U).left = U.hom := by
 simp [mkIdTerminal, CostructuredArrow.mkIdTerminal, Limits.IsTerminal.from, Functor.preimage]

/-- `Over.Sigma Y U` is a shorthand for `(Over.map Y.hom).obj U`.
This is a category-theoretic analogue of `Sigma` for types. -/
abbrev Sigma {X : T} (Y : Over X) (U : Over (Y.left)) : Over X :=
Expand Down

12 changes: 3 additions & 9 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Pullback.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -9,7 +9,7 @@ import Mathlib.CategoryTheory.Limits.Constructions.Over.Basic
import Mathlib.CategoryTheory.Monad.Products
import Poly.ForMathlib.CategoryTheory.Comma.Over.Basic
import Poly.ForMathlib.CategoryTheory.NatTrans
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

noncomputable section

Expand All@@ -19,7 +19,7 @@ namespace CategoryTheory

open Category Limits Comonad MonoidalCategory CartesianMonoidalCategory

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

variable {C : Type u₁} [Category.{v₁} C]

Expand DownExpand Up@@ -211,7 +211,7 @@ lemma star_map [HasBinaryProducts C] {X : C} {Y Z : C} (f : Y ⟶ Z) :
instance [HasBinaryProducts C] (X : C) : (forget X).IsLeftAdjoint :=
 ⟨_, ⟨forgetAdjStar X⟩⟩

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

lemma whiskerLeftProdMapId [HasFiniteLimits C] {X : C} {A A' : C} {g : A ⟶ A'} :
 X ◁ g = prod.map (𝟙 X) g := by
Expand DownExpand Up@@ -298,12 +298,6 @@ def starIsoToOverTerminal [HasTerminal C] [HasBinaryProducts C] :

variable {C}

/-- A natural isomorphism between the functors `star X` and `star Y ⋙ pullback f`
for any morphism `f : X ⟶ Y`. -/
def starPullbackIsoStar [HasBinaryProducts C] [HasPullbacks C] {X Y : C} (f : X ⟶ Y) :
 star Y ⋙ pullback f ≅ star X :=
 conjugateIsoEquiv ((mapPullbackAdj f).comp (forgetAdjStar Y)) (forgetAdjStar X) (mapForget f)

/-- The functor `Over.pullback f : Over Y ⥤ Over X` is naturally isomorphic to
`Over.star : Over Y ⥤ Over (Over.mk f)` post-composed with the
iterated slice equivlanece `Over (Over.mk f) ⥤ Over X`. -/
Expand Down

33 changes: 17 additions & 16 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Sections.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -28,7 +28,7 @@ variable {C : Type u₁} [Category.{v₁} C]

attribute [local instance] hasBinaryProducts_of_hasTerminal_and_pullbacks
attribute [local instance] hasFiniteProducts_of_has_binary_and_terminal
attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

section

Expand DownExpand Up@@ -69,11 +69,11 @@ end

variable [HasTerminal C] [HasPullbacks C]

variable (I : C) [Exponentiable I]
variable (I : C) [Closed I]

/-- The first leg of a cospan constructing a pullback diagram in `C` used to define `sections` . -/
def curryId : ⊤_ C ⟶ (I ⟹ I) :=
CartesianClosed.curry (fst I (⊤_ C))
MonoidalClosed.curry (fst I (⊤_ C))

variable {I}

Expand All@@ -90,14 +90,14 @@ pullback diagram:
 ⊤_ C ----> I ⟹ I
```-/
abbrev sectionsObj (X : Over I) : C :=
 Limits.pullback (curryId I) ((exp I).map X.hom)
 Limits.pullback (curryId I) ((ihom I).map X.hom)

/-- The functoriality of `sectionsObj`. -/
def sectionsMap {X X' : Over I} (u : X ⟶ X') :
 sectionsObj X ⟶ sectionsObj X' := by
 fapply pullback.map
 · exact 𝟙 _
 · exact (exp I).map u.left
 · exact (ihom I).map u.left
 · exact 𝟙 _
 · simp only [comp_id, id_comp]
 · simp only [comp_id, ← Functor.map_comp, w]
Expand DownExpand Up@@ -130,29 +130,30 @@ variable {I}
in `C`. See `sectionsCurry`. -/
def sectionsCurryAux {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (I ⟹ X.left) :=
CartesianClosed.curry (u.left)
MonoidalClosed.curry (u.left)

/-- The currying operation `Hom ((star I).obj A) X → Hom A (I ⟹ X.left)`. -/
def sectionsCurry {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (sections I).obj X := by
 apply pullback.lift (terminal.from A)
 (CartesianClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left)) (uncurry_injective _)
 rw [uncurry_natural_left]
 simp [curryId, uncurry_natural_right, uncurry_curry]
 (MonoidalClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left))
 (MonoidalClosed.uncurry_injective _)
 rw [MonoidalClosed.uncurry_natural_left]
 simp [curryId, MonoidalClosed.uncurry_natural_right, MonoidalClosed.uncurry_curry]

/-- The uncurrying operation `Hom A (section X) → Hom ((star I).obj A) X`. -/
def sectionsUncurry {X : Over I} {A : C} (v : A ⟶ (sections I).obj X) :
 (star I).obj A ⟶ X := by
 let v₂ : A ⟶ (I ⟹ X.left) := v ≫ pullback.snd ..
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (exp I).map X.hom := by
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (ihom I).map X.hom := by
 rw [IsTerminal.hom_ext terminalIsTerminal (terminal.from A ) (v ≫ (pullback.fst ..))]
 simp [v₂, pullback.condition]
 dsimp [curryId] at w
 have w' := homEquiv_naturality_right_square (F := MonoidalCategory.tensorLeft I)
 (adj := exp.adjunction I) _ _ _ _ w
 simp [CartesianClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ CartesianClosed.uncurry v₂) ?_
 · dsimp [CartesianClosed.uncurry] at *
 (adj := ihom.adjunction I) _ _ _ _ w
 simp [MonoidalClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ MonoidalClosed.uncurry v₂) ?_
 · dsimp [MonoidalClosed.uncurry] at *
 rw [Category.assoc, ← w']
 simp [star_obj_hom]

Expand DownExpand Up@@ -188,13 +189,13 @@ def coreHomEquiv : CoreHomEquiv (star I) (sections I) where
 simp only [star_map]
 rw [← Over.homMk_comp] -- note: in a newer version of mathlib this is `Over.homMk_eta`
 congr 1
 simp [CartesianClosed.uncurry_natural_left]
 simp [MonoidalClosed.uncurry_natural_left]
 homEquiv_naturality_right := by
 intro A X' X u g
 dsimp [sectionsCurry, sectionsUncurry, curryId]
 apply pullback.hom_ext (IsTerminal.hom_ext terminalIsTerminal _ _)
 simp [sectionsMap, curryId]
 rw [← CartesianClosed.curry_natural_right, Category.assoc]
 rw [← MonoidalClosed.curry_natural_right, Category.assoc]

variable (I)

Expand Down

2 changes: 1 addition & 1 deletion
...Theory/Limits/Shapes/Pullback/CommSq.lean → ...its/Shapes/Pullback/IsPullback/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Poly.ForMathlib.CategoryTheory.CommSq

namespace CategoryTheory.Functor
Expand Down

21 changes: 11 additions & 10 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -67,7 +67,7 @@ open CategoryTheory Category MonoidalCategory CartesianMonoidalCategory Limits F

variable {C : Type u} [Category.{v} C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

/-- A morphism `f : I ⟶ J` is exponentiable if the pullback functor `Over J ⥤ Over I`
has a right adjoint. -/
Expand DownExpand Up@@ -179,7 +179,7 @@ instance isMultiplicative : (ExponentiableMorphism (C:= C)).IsMultiplicative whe
/-- A morphism with a pushforward is an exponentiable object in the slice category. -/
def exponentiableOverMk [HasFiniteWidePullbacks C] {X I : C} (f : X ⟶ I)
 [ExponentiableMorphism f] :
Exponentiable (Over.mk f) where
Closed (Over.mk f) where
 rightAdj := pullback f ⋙ pushforward f
 adj := by
 apply ofNatIsoLeft _ _
Expand All@@ -192,7 +192,7 @@ morphism `X.hom`.
Here the pushforward functor along a morphism `f : I ⟶ J` is defined using the section functor
`Over (Over.mk f) ⥤ Over J`.
-/
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Exponentiable X] :
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Closed X] :
 ExponentiableMorphism X.hom :=
 ⟨X.iteratedSliceEquiv.inverse ⋙ sections X, ⟨by
 refine ofNatIsoLeft (Adjunction.comp ?_ ?_) (starIteratedSliceForwardIsoPullback X.hom)
Expand All@@ -217,7 +217,7 @@ variable {C} [HasFiniteWidePullbacks C] [HasPushforwards C]
/-- In a category where pushforwards exists along all morphisms, every slice category `Over I` is
cartesian closed. -/
instance cartesianClosedOver (I : C) :
CartesianClosed (Over I) where
MonoidalClosed (Over I) where
 closed X := @exponentiableOverMk _ _ _ _ _ _ X.hom (HasPushforwards.exponentiable X.hom)

end HasPushforwards
Expand All@@ -226,13 +226,13 @@ namespace CartesianClosedOver

open Over Reindex IsIso CartesianClosed HasPushforwards ExponentiableMorphism

variable {C} [HasFiniteWidePullbacks C] {I J : C} [CartesianClosed (Over J)]
variable {C} [HasFiniteWidePullbacks C] {I J : C} [MonoidalClosed (Over J)]

instance (f : I ⟶ J) : ExponentiableMorphism f :=
 ExponentiableMorphism.ofOverExponentiable (Over.mk f)

/-- A category with cartesian closed slices has pushforwards along all morphisms. -/
instance hasPushforwards [Π (I : C), CartesianClosed (Over I)] : HasPushforwards C where
instance hasPushforwards [Π (I : C), MonoidalClosed (Over I)] : HasPushforwards C where
 exponentiable f := ExponentiableMorphism.ofOverExponentiable (Over.mk f)

end CartesianClosedOver
Expand All@@ -242,7 +242,7 @@ is exponentiable and all the slices are cartesian closed. -/
class LocallyCartesianClosed [HasFiniteWidePullbacks C] extends
 HasPushforwards C where
 /-- every slice category `Over I` is cartesian closed. This is filled in by default. -/
 cartesianClosedOver : Π (I : C), CartesianClosed (Over I) := HasPushforwards.cartesianClosedOver
 cartesianClosedOver : Π (I : C), MonoidalClosed (Over I) := HasPushforwards.cartesianClosedOver

namespace LocallyCartesianClosed

Expand All@@ -256,7 +256,7 @@ attribute [scoped instance] hasFiniteLimits_of_hasTerminal_and_pullbacks
instance mkOfHasPushforwards [HasPushforwards C] : LocallyCartesianClosed C where

/-- A category with cartesian closed slices is locally cartesian closed. -/
instance mkOfCartesianClosedOver [Π (I : C), CartesianClosed (Over I)] :
instance mkOfCartesianClosedOver [Π (I : C), MonoidalClosed (Over I)] :
 LocallyCartesianClosed C where

variable [LocallyCartesianClosed C]
Expand All@@ -282,15 +282,16 @@ abbrev ev' {I : C} (X : Over I) (Y : Over X.left) : Reindex X (Pi X Y) ⟶ Y :=
 adj X.hom |>.counit.app Y

/-- A locally cartesian closed category with a terminal object is cartesian closed. -/
def cartesianClosed [HasTerminal C] :
CartesianClosed C := cartesianClosedOfEquiv <| equivOverTerminal C
def monoidalClosed [HasTerminal C] :
MonoidalClosed C := cartesianClosedOfEquiv <| equivOverTerminal C

/-- The slices of a locally cartesian closed category are locally cartesian closed. -/
def overLocallyCartesianClosed (I : C) : LocallyCartesianClosed (Over I) := by
 apply (config := { allowSynthFailures:= true}) mkOfCartesianClosedOver
 intro X
 exact cartesianClosedOfEquiv (C := Over (X.left)) X.iteratedSliceEquiv.symm

open CartesianClosed in
/-- The exponential `X^^A` in the slice category `Over I` is isomorphic to the pushforward of the
pullback of `X` along `A`. -/
def expIso {I : C} (A X : Over I) : Pi A (Reindex A X) ≅ A ⟹ X := Iso.refl _
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/BeckChevalley.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour, Emily Riehl
-/
import Poly.ForMathlib.CategoryTheory.LocallyCartesianClosed.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

/-!
# Beck-Chevalley natural transformations and natural isomorphisms
Expand Down

6 changes: 3 additions & 3 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Presheaf.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -22,10 +22,10 @@ abbrev Psh (C : Type u) [Category.{v} C] : Type (max u (v + 1)) := Cᵒᵖ ⥤ T

variable {C : Type*} [SmallCategory C] [HasTerminal C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

instance cartesianClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
CartesianClosed (Over P) :=
instance monoidalClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
MonoidalClosed (Over P) :=
 cartesianClosedOfEquiv (overEquivPresheafCostructuredArrow P).symm

instance locallyCartesianClosed : LocallyCartesianClosed (Psh C) := by
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/NatTrans.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -6,7 +6,7 @@ Authors: Sina Hazratpour

import Mathlib.CategoryTheory.NatTrans
import Mathlib.CategoryTheory.Functor.TwoSquare
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

open CategoryTheory Limits IsPullback

Expand Down

4 changes: 3 additions & 1 deletion
Poly/ForMathlib/CategoryTheory/PartialProduct.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Mathlib.CategoryTheory.Comma.Over.Pullback
import Poly.ForMathlib.CategoryTheory.Comma.Over.Pullback
import Mathlib.CategoryTheory.Monoidal.Closed.Cartesian
Expand DownExpand Up@@ -100,6 +100,8 @@ structure Fan.Hom (c c' : Fan s X) where

attribute [reassoc (attr := simp)] Fan.Hom.w_left Fan.Hom.w_right

-- TODO: this is taking ages to check since 4.28.0-rc1.
set_option maxHeartbeats 0 in
@[simps]
instance : Category (Fan s X) where
 Hom := Fan.Hom
Expand Down

2 changes: 1 addition & 1 deletion
Poly/Type/Univariate.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -189,7 +189,7 @@ def Obj.iget [DecidableEq P.B] {X} [Inhabited X] (x : P X) (i : P.Total) : X :=
@[simp]
theorem iget_map [DecidableEq P.B] [Inhabited X] [Inhabited Y] (x : P X)
 (f : X → Y) (i : P.Total) (h : i.1 = x.1) : (P.map f x).iget i = f (x.iget i) := by
 simp only [Obj.iget, fst_map, *, dif_pos, eq_self_iff_true]
 simp only [Obj.iget, fst_map, *, dif_pos]
 cases x
 rfl

Expand Down

20 changes: 10 additions & 10 deletions
lake-manifest.json

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Original file line numberDiff line numberDiff line change
Expand Up@@ -15,7 +15,7 @@
 "type": "git",
 "subDir": null,
 "scope": "",
 "rev": "dd5e5d97469dec395f29661366030566355ad9be",
 "rev": "b8dad038b1b3a05b77d6884b15b8db03ec01dca1",
 "name": "mathlib",
 "manifestFile": "lake-manifest.json",
 "inputRev": null,
Expand All@@ -25,7 +25,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "b3dd6c3ebc0a71685e86bea9223be39ea4c299fb",
 "rev": "7311586e1a56af887b1081d05e80c11b6c41d212",
 "name": "plausible",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -45,7 +45,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "cff9dd30f2c161b9efd7c657cafed1f967645890",
 "rev": "b5908dbac486279f1133cb937648c63c30b455af",
 "name": "importGraph",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -55,17 +55,17 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "ef8377f31b5535430b6753a974d685b0019d0681",
 "rev": "6d65c6e0a25b8a52c13c3adeb63ecde3bfbb6294",
 "name": "proofwidgets",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v0.0.84",
 "inputRev": "v0.0.86",
 "inherited": true,
 "configFile": "lakefile.lean"},
 {"url": "https://github.com/leanprover-community/aesop",
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "fa78cf032194308a950a264ed87b422a2a7c1c6c",
 "rev": "f08e838d4f9aea519f3cde06260cfb686fd4bab0",
 "name": "aesop",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -75,7 +75,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "8920dcbb96a4e8bf641fc399ac9c0888e4a6be72",
 "rev": "23324752757bf28124a518ec284044c8db79fee5",
 "name": "Qq",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -85,7 +85,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "dff865b7ee7011518d59abfc101c368293173150",
 "rev": "100083c18750b6a9b7553c65f6b052c0a2f6bcb4",
 "name": "batteries",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -95,10 +95,10 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover",
 "rev": "726b98c53e2da249c1de768fbbbb5e67bc9cef60",
 "rev": "28e0856d4424863a85b18f38868c5420c55f9bae",
 "name": "Cli",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v4.27.0-rc1",
 "inputRev": "v4.28.0-rc1",
 "inherited": true,
 "configFile": "lakefile.toml"}],
 "name": "Poly",
Expand Down

2 changes: 1 addition & 1 deletion
lean-toolchain

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Original file line numberDiff line numberDiff line change
@@ -1 +1 @@
leanprover/lean4:v4.27.0-rc1
leanprover/lean4:v4.28.0-rc1

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default");
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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feat: bump to Lean v4.28.0-rc1#36

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Jul 10, 2026
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feat: bump to Lean v4.28.0-rc1
#36
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4 changes: 0 additions & 4 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -35,10 +35,6 @@ lemma homMk_comp'_assoc {X Y Z W : T} (f : X ⟶ Y) (g : Y ⟶ Z) (h : Z ⟶ W)
lemma homMk_id {X B : T} (f : X ⟶ B) (h : 𝟙 X ≫ f = f) : homMk (𝟙 X) h = 𝟙 (mk f) :=
 rfl

@[simp]
theorem mkIdTerminal_from_left {B : T} (U : Over B) : (mkIdTerminal.from U).left = U.hom := by
 simp [mkIdTerminal, CostructuredArrow.mkIdTerminal, Limits.IsTerminal.from, Functor.preimage]

/-- `Over.Sigma Y U` is a shorthand for `(Over.map Y.hom).obj U`.
This is a category-theoretic analogue of `Sigma` for types. -/
abbrev Sigma {X : T} (Y : Over X) (U : Over (Y.left)) : Over X :=
Expand Down

12 changes: 3 additions & 9 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Pullback.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -9,7 +9,7 @@ import Mathlib.CategoryTheory.Limits.Constructions.Over.Basic
import Mathlib.CategoryTheory.Monad.Products
import Poly.ForMathlib.CategoryTheory.Comma.Over.Basic
import Poly.ForMathlib.CategoryTheory.NatTrans
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

noncomputable section

Expand All@@ -19,7 +19,7 @@ namespace CategoryTheory

open Category Limits Comonad MonoidalCategory CartesianMonoidalCategory

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

variable {C : Type u₁} [Category.{v₁} C]

Expand DownExpand Up@@ -211,7 +211,7 @@ lemma star_map [HasBinaryProducts C] {X : C} {Y Z : C} (f : Y ⟶ Z) :
instance [HasBinaryProducts C] (X : C) : (forget X).IsLeftAdjoint :=
 ⟨_, ⟨forgetAdjStar X⟩⟩

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

lemma whiskerLeftProdMapId [HasFiniteLimits C] {X : C} {A A' : C} {g : A ⟶ A'} :
 X ◁ g = prod.map (𝟙 X) g := by
Expand DownExpand Up@@ -298,12 +298,6 @@ def starIsoToOverTerminal [HasTerminal C] [HasBinaryProducts C] :

variable {C}

/-- A natural isomorphism between the functors `star X` and `star Y ⋙ pullback f`
for any morphism `f : X ⟶ Y`. -/
def starPullbackIsoStar [HasBinaryProducts C] [HasPullbacks C] {X Y : C} (f : X ⟶ Y) :
 star Y ⋙ pullback f ≅ star X :=
 conjugateIsoEquiv ((mapPullbackAdj f).comp (forgetAdjStar Y)) (forgetAdjStar X) (mapForget f)

/-- The functor `Over.pullback f : Over Y ⥤ Over X` is naturally isomorphic to
`Over.star : Over Y ⥤ Over (Over.mk f)` post-composed with the
iterated slice equivlanece `Over (Over.mk f) ⥤ Over X`. -/
Expand Down

33 changes: 17 additions & 16 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Sections.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -28,7 +28,7 @@ variable {C : Type u₁} [Category.{v₁} C]

attribute [local instance] hasBinaryProducts_of_hasTerminal_and_pullbacks
attribute [local instance] hasFiniteProducts_of_has_binary_and_terminal
attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

section

Expand DownExpand Up@@ -69,11 +69,11 @@ end

variable [HasTerminal C] [HasPullbacks C]

variable (I : C) [Exponentiable I]
variable (I : C) [Closed I]

/-- The first leg of a cospan constructing a pullback diagram in `C` used to define `sections` . -/
def curryId : ⊤_ C ⟶ (I ⟹ I) :=
CartesianClosed.curry (fst I (⊤_ C))
MonoidalClosed.curry (fst I (⊤_ C))

variable {I}

Expand All@@ -90,14 +90,14 @@ pullback diagram:
 ⊤_ C ----> I ⟹ I
```-/
abbrev sectionsObj (X : Over I) : C :=
 Limits.pullback (curryId I) ((exp I).map X.hom)
 Limits.pullback (curryId I) ((ihom I).map X.hom)

/-- The functoriality of `sectionsObj`. -/
def sectionsMap {X X' : Over I} (u : X ⟶ X') :
 sectionsObj X ⟶ sectionsObj X' := by
 fapply pullback.map
 · exact 𝟙 _
 · exact (exp I).map u.left
 · exact (ihom I).map u.left
 · exact 𝟙 _
 · simp only [comp_id, id_comp]
 · simp only [comp_id, ← Functor.map_comp, w]
Expand DownExpand Up@@ -130,29 +130,30 @@ variable {I}
in `C`. See `sectionsCurry`. -/
def sectionsCurryAux {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (I ⟹ X.left) :=
CartesianClosed.curry (u.left)
MonoidalClosed.curry (u.left)

/-- The currying operation `Hom ((star I).obj A) X → Hom A (I ⟹ X.left)`. -/
def sectionsCurry {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (sections I).obj X := by
 apply pullback.lift (terminal.from A)
 (CartesianClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left)) (uncurry_injective _)
 rw [uncurry_natural_left]
 simp [curryId, uncurry_natural_right, uncurry_curry]
 (MonoidalClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left))
 (MonoidalClosed.uncurry_injective _)
 rw [MonoidalClosed.uncurry_natural_left]
 simp [curryId, MonoidalClosed.uncurry_natural_right, MonoidalClosed.uncurry_curry]

/-- The uncurrying operation `Hom A (section X) → Hom ((star I).obj A) X`. -/
def sectionsUncurry {X : Over I} {A : C} (v : A ⟶ (sections I).obj X) :
 (star I).obj A ⟶ X := by
 let v₂ : A ⟶ (I ⟹ X.left) := v ≫ pullback.snd ..
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (exp I).map X.hom := by
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (ihom I).map X.hom := by
 rw [IsTerminal.hom_ext terminalIsTerminal (terminal.from A ) (v ≫ (pullback.fst ..))]
 simp [v₂, pullback.condition]
 dsimp [curryId] at w
 have w' := homEquiv_naturality_right_square (F := MonoidalCategory.tensorLeft I)
 (adj := exp.adjunction I) _ _ _ _ w
 simp [CartesianClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ CartesianClosed.uncurry v₂) ?_
 · dsimp [CartesianClosed.uncurry] at *
 (adj := ihom.adjunction I) _ _ _ _ w
 simp [MonoidalClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ MonoidalClosed.uncurry v₂) ?_
 · dsimp [MonoidalClosed.uncurry] at *
 rw [Category.assoc, ← w']
 simp [star_obj_hom]

Expand DownExpand Up@@ -188,13 +189,13 @@ def coreHomEquiv : CoreHomEquiv (star I) (sections I) where
 simp only [star_map]
 rw [← Over.homMk_comp] -- note: in a newer version of mathlib this is `Over.homMk_eta`
 congr 1
 simp [CartesianClosed.uncurry_natural_left]
 simp [MonoidalClosed.uncurry_natural_left]
 homEquiv_naturality_right := by
 intro A X' X u g
 dsimp [sectionsCurry, sectionsUncurry, curryId]
 apply pullback.hom_ext (IsTerminal.hom_ext terminalIsTerminal _ _)
 simp [sectionsMap, curryId]
 rw [← CartesianClosed.curry_natural_right, Category.assoc]
 rw [← MonoidalClosed.curry_natural_right, Category.assoc]

variable (I)

Expand Down

2 changes: 1 addition & 1 deletion
...Theory/Limits/Shapes/Pullback/CommSq.lean → ...its/Shapes/Pullback/IsPullback/Basic.lean

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Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Poly.ForMathlib.CategoryTheory.CommSq

namespace CategoryTheory.Functor
Expand Down

21 changes: 11 additions & 10 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -67,7 +67,7 @@ open CategoryTheory Category MonoidalCategory CartesianMonoidalCategory Limits F

variable {C : Type u} [Category.{v} C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

/-- A morphism `f : I ⟶ J` is exponentiable if the pullback functor `Over J ⥤ Over I`
has a right adjoint. -/
Expand DownExpand Up@@ -179,7 +179,7 @@ instance isMultiplicative : (ExponentiableMorphism (C:= C)).IsMultiplicative whe
/-- A morphism with a pushforward is an exponentiable object in the slice category. -/
def exponentiableOverMk [HasFiniteWidePullbacks C] {X I : C} (f : X ⟶ I)
 [ExponentiableMorphism f] :
Exponentiable (Over.mk f) where
Closed (Over.mk f) where
 rightAdj := pullback f ⋙ pushforward f
 adj := by
 apply ofNatIsoLeft _ _
Expand All@@ -192,7 +192,7 @@ morphism `X.hom`.
Here the pushforward functor along a morphism `f : I ⟶ J` is defined using the section functor
`Over (Over.mk f) ⥤ Over J`.
-/
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Exponentiable X] :
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Closed X] :
 ExponentiableMorphism X.hom :=
 ⟨X.iteratedSliceEquiv.inverse ⋙ sections X, ⟨by
 refine ofNatIsoLeft (Adjunction.comp ?_ ?_) (starIteratedSliceForwardIsoPullback X.hom)
Expand All@@ -217,7 +217,7 @@ variable {C} [HasFiniteWidePullbacks C] [HasPushforwards C]
/-- In a category where pushforwards exists along all morphisms, every slice category `Over I` is
cartesian closed. -/
instance cartesianClosedOver (I : C) :
CartesianClosed (Over I) where
MonoidalClosed (Over I) where
 closed X := @exponentiableOverMk _ _ _ _ _ _ X.hom (HasPushforwards.exponentiable X.hom)

end HasPushforwards
Expand All@@ -226,13 +226,13 @@ namespace CartesianClosedOver

open Over Reindex IsIso CartesianClosed HasPushforwards ExponentiableMorphism

variable {C} [HasFiniteWidePullbacks C] {I J : C} [CartesianClosed (Over J)]
variable {C} [HasFiniteWidePullbacks C] {I J : C} [MonoidalClosed (Over J)]

instance (f : I ⟶ J) : ExponentiableMorphism f :=
 ExponentiableMorphism.ofOverExponentiable (Over.mk f)

/-- A category with cartesian closed slices has pushforwards along all morphisms. -/
instance hasPushforwards [Π (I : C), CartesianClosed (Over I)] : HasPushforwards C where
instance hasPushforwards [Π (I : C), MonoidalClosed (Over I)] : HasPushforwards C where
 exponentiable f := ExponentiableMorphism.ofOverExponentiable (Over.mk f)

end CartesianClosedOver
Expand All@@ -242,7 +242,7 @@ is exponentiable and all the slices are cartesian closed. -/
class LocallyCartesianClosed [HasFiniteWidePullbacks C] extends
 HasPushforwards C where
 /-- every slice category `Over I` is cartesian closed. This is filled in by default. -/
 cartesianClosedOver : Π (I : C), CartesianClosed (Over I) := HasPushforwards.cartesianClosedOver
 cartesianClosedOver : Π (I : C), MonoidalClosed (Over I) := HasPushforwards.cartesianClosedOver

namespace LocallyCartesianClosed

Expand All@@ -256,7 +256,7 @@ attribute [scoped instance] hasFiniteLimits_of_hasTerminal_and_pullbacks
instance mkOfHasPushforwards [HasPushforwards C] : LocallyCartesianClosed C where

/-- A category with cartesian closed slices is locally cartesian closed. -/
instance mkOfCartesianClosedOver [Π (I : C), CartesianClosed (Over I)] :
instance mkOfCartesianClosedOver [Π (I : C), MonoidalClosed (Over I)] :
 LocallyCartesianClosed C where

variable [LocallyCartesianClosed C]
Expand All@@ -282,15 +282,16 @@ abbrev ev' {I : C} (X : Over I) (Y : Over X.left) : Reindex X (Pi X Y) ⟶ Y :=
 adj X.hom |>.counit.app Y

/-- A locally cartesian closed category with a terminal object is cartesian closed. -/
def cartesianClosed [HasTerminal C] :
CartesianClosed C := cartesianClosedOfEquiv <| equivOverTerminal C
def monoidalClosed [HasTerminal C] :
MonoidalClosed C := cartesianClosedOfEquiv <| equivOverTerminal C

/-- The slices of a locally cartesian closed category are locally cartesian closed. -/
def overLocallyCartesianClosed (I : C) : LocallyCartesianClosed (Over I) := by
 apply (config := { allowSynthFailures:= true}) mkOfCartesianClosedOver
 intro X
 exact cartesianClosedOfEquiv (C := Over (X.left)) X.iteratedSliceEquiv.symm

open CartesianClosed in
/-- The exponential `X^^A` in the slice category `Over I` is isomorphic to the pushforward of the
pullback of `X` along `A`. -/
def expIso {I : C} (A X : Over I) : Pi A (Reindex A X) ≅ A ⟹ X := Iso.refl _
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/BeckChevalley.lean

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Expand Up@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour, Emily Riehl
-/
import Poly.ForMathlib.CategoryTheory.LocallyCartesianClosed.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

/-!
# Beck-Chevalley natural transformations and natural isomorphisms
Expand Down

6 changes: 3 additions & 3 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Presheaf.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -22,10 +22,10 @@ abbrev Psh (C : Type u) [Category.{v} C] : Type (max u (v + 1)) := Cᵒᵖ ⥤ T

variable {C : Type*} [SmallCategory C] [HasTerminal C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

instance cartesianClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
CartesianClosed (Over P) :=
instance monoidalClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
MonoidalClosed (Over P) :=
 cartesianClosedOfEquiv (overEquivPresheafCostructuredArrow P).symm

instance locallyCartesianClosed : LocallyCartesianClosed (Psh C) := by
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/NatTrans.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -6,7 +6,7 @@ Authors: Sina Hazratpour

import Mathlib.CategoryTheory.NatTrans
import Mathlib.CategoryTheory.Functor.TwoSquare
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

open CategoryTheory Limits IsPullback

Expand Down

4 changes: 3 additions & 1 deletion
Poly/ForMathlib/CategoryTheory/PartialProduct.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Mathlib.CategoryTheory.Comma.Over.Pullback
import Poly.ForMathlib.CategoryTheory.Comma.Over.Pullback
import Mathlib.CategoryTheory.Monoidal.Closed.Cartesian
Expand DownExpand Up@@ -100,6 +100,8 @@ structure Fan.Hom (c c' : Fan s X) where

attribute [reassoc (attr := simp)] Fan.Hom.w_left Fan.Hom.w_right

-- TODO: this is taking ages to check since 4.28.0-rc1.
set_option maxHeartbeats 0 in
@[simps]
instance : Category (Fan s X) where
 Hom := Fan.Hom
Expand Down

2 changes: 1 addition & 1 deletion
Poly/Type/Univariate.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -189,7 +189,7 @@ def Obj.iget [DecidableEq P.B] {X} [Inhabited X] (x : P X) (i : P.Total) : X :=
@[simp]
theorem iget_map [DecidableEq P.B] [Inhabited X] [Inhabited Y] (x : P X)
 (f : X → Y) (i : P.Total) (h : i.1 = x.1) : (P.map f x).iget i = f (x.iget i) := by
 simp only [Obj.iget, fst_map, *, dif_pos, eq_self_iff_true]
 simp only [Obj.iget, fst_map, *, dif_pos]
 cases x
 rfl

Expand Down

20 changes: 10 additions & 10 deletions
lake-manifest.json

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Original file line numberDiff line numberDiff line change
Expand Up@@ -15,7 +15,7 @@
 "type": "git",
 "subDir": null,
 "scope": "",
 "rev": "dd5e5d97469dec395f29661366030566355ad9be",
 "rev": "b8dad038b1b3a05b77d6884b15b8db03ec01dca1",
 "name": "mathlib",
 "manifestFile": "lake-manifest.json",
 "inputRev": null,
Expand All@@ -25,7 +25,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "b3dd6c3ebc0a71685e86bea9223be39ea4c299fb",
 "rev": "7311586e1a56af887b1081d05e80c11b6c41d212",
 "name": "plausible",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -45,7 +45,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "cff9dd30f2c161b9efd7c657cafed1f967645890",
 "rev": "b5908dbac486279f1133cb937648c63c30b455af",
 "name": "importGraph",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -55,17 +55,17 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "ef8377f31b5535430b6753a974d685b0019d0681",
 "rev": "6d65c6e0a25b8a52c13c3adeb63ecde3bfbb6294",
 "name": "proofwidgets",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v0.0.84",
 "inputRev": "v0.0.86",
 "inherited": true,
 "configFile": "lakefile.lean"},
 {"url": "https://github.com/leanprover-community/aesop",
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "fa78cf032194308a950a264ed87b422a2a7c1c6c",
 "rev": "f08e838d4f9aea519f3cde06260cfb686fd4bab0",
 "name": "aesop",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -75,7 +75,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "8920dcbb96a4e8bf641fc399ac9c0888e4a6be72",
 "rev": "23324752757bf28124a518ec284044c8db79fee5",
 "name": "Qq",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -85,7 +85,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "dff865b7ee7011518d59abfc101c368293173150",
 "rev": "100083c18750b6a9b7553c65f6b052c0a2f6bcb4",
 "name": "batteries",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -95,10 +95,10 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover",
 "rev": "726b98c53e2da249c1de768fbbbb5e67bc9cef60",
 "rev": "28e0856d4424863a85b18f38868c5420c55f9bae",
 "name": "Cli",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v4.27.0-rc1",
 "inputRev": "v4.28.0-rc1",
 "inherited": true,
 "configFile": "lakefile.toml"}],
 "name": "Poly",
Expand Down

2 changes: 1 addition & 1 deletion
lean-toolchain

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Original file line numberDiff line numberDiff line change
@@ -1 +1 @@
leanprover/lean4:v4.27.0-rc1
leanprover/lean4:v4.28.0-rc1

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers");
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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feat: bump to Lean v4.28.0-rc1#36

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Jul 10, 2026
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feat: bump to Lean v4.28.0-rc1
#36
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4 changes: 0 additions & 4 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -35,10 +35,6 @@ lemma homMk_comp'_assoc {X Y Z W : T} (f : X ⟶ Y) (g : Y ⟶ Z) (h : Z ⟶ W)
lemma homMk_id {X B : T} (f : X ⟶ B) (h : 𝟙 X ≫ f = f) : homMk (𝟙 X) h = 𝟙 (mk f) :=
 rfl

@[simp]
theorem mkIdTerminal_from_left {B : T} (U : Over B) : (mkIdTerminal.from U).left = U.hom := by
 simp [mkIdTerminal, CostructuredArrow.mkIdTerminal, Limits.IsTerminal.from, Functor.preimage]

/-- `Over.Sigma Y U` is a shorthand for `(Over.map Y.hom).obj U`.
This is a category-theoretic analogue of `Sigma` for types. -/
abbrev Sigma {X : T} (Y : Over X) (U : Over (Y.left)) : Over X :=
Expand Down

12 changes: 3 additions & 9 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Pullback.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -9,7 +9,7 @@ import Mathlib.CategoryTheory.Limits.Constructions.Over.Basic
import Mathlib.CategoryTheory.Monad.Products
import Poly.ForMathlib.CategoryTheory.Comma.Over.Basic
import Poly.ForMathlib.CategoryTheory.NatTrans
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

noncomputable section

Expand All@@ -19,7 +19,7 @@ namespace CategoryTheory

open Category Limits Comonad MonoidalCategory CartesianMonoidalCategory

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

variable {C : Type u₁} [Category.{v₁} C]

Expand DownExpand Up@@ -211,7 +211,7 @@ lemma star_map [HasBinaryProducts C] {X : C} {Y Z : C} (f : Y ⟶ Z) :
instance [HasBinaryProducts C] (X : C) : (forget X).IsLeftAdjoint :=
 ⟨_, ⟨forgetAdjStar X⟩⟩

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

lemma whiskerLeftProdMapId [HasFiniteLimits C] {X : C} {A A' : C} {g : A ⟶ A'} :
 X ◁ g = prod.map (𝟙 X) g := by
Expand DownExpand Up@@ -298,12 +298,6 @@ def starIsoToOverTerminal [HasTerminal C] [HasBinaryProducts C] :

variable {C}

/-- A natural isomorphism between the functors `star X` and `star Y ⋙ pullback f`
for any morphism `f : X ⟶ Y`. -/
def starPullbackIsoStar [HasBinaryProducts C] [HasPullbacks C] {X Y : C} (f : X ⟶ Y) :
 star Y ⋙ pullback f ≅ star X :=
 conjugateIsoEquiv ((mapPullbackAdj f).comp (forgetAdjStar Y)) (forgetAdjStar X) (mapForget f)

/-- The functor `Over.pullback f : Over Y ⥤ Over X` is naturally isomorphic to
`Over.star : Over Y ⥤ Over (Over.mk f)` post-composed with the
iterated slice equivlanece `Over (Over.mk f) ⥤ Over X`. -/
Expand Down

33 changes: 17 additions & 16 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Sections.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -28,7 +28,7 @@ variable {C : Type u₁} [Category.{v₁} C]

attribute [local instance] hasBinaryProducts_of_hasTerminal_and_pullbacks
attribute [local instance] hasFiniteProducts_of_has_binary_and_terminal
attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

section

Expand DownExpand Up@@ -69,11 +69,11 @@ end

variable [HasTerminal C] [HasPullbacks C]

variable (I : C) [Exponentiable I]
variable (I : C) [Closed I]

/-- The first leg of a cospan constructing a pullback diagram in `C` used to define `sections` . -/
def curryId : ⊤_ C ⟶ (I ⟹ I) :=
CartesianClosed.curry (fst I (⊤_ C))
MonoidalClosed.curry (fst I (⊤_ C))

variable {I}

Expand All@@ -90,14 +90,14 @@ pullback diagram:
 ⊤_ C ----> I ⟹ I
```-/
abbrev sectionsObj (X : Over I) : C :=
 Limits.pullback (curryId I) ((exp I).map X.hom)
 Limits.pullback (curryId I) ((ihom I).map X.hom)

/-- The functoriality of `sectionsObj`. -/
def sectionsMap {X X' : Over I} (u : X ⟶ X') :
 sectionsObj X ⟶ sectionsObj X' := by
 fapply pullback.map
 · exact 𝟙 _
 · exact (exp I).map u.left
 · exact (ihom I).map u.left
 · exact 𝟙 _
 · simp only [comp_id, id_comp]
 · simp only [comp_id, ← Functor.map_comp, w]
Expand DownExpand Up@@ -130,29 +130,30 @@ variable {I}
in `C`. See `sectionsCurry`. -/
def sectionsCurryAux {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (I ⟹ X.left) :=
CartesianClosed.curry (u.left)
MonoidalClosed.curry (u.left)

/-- The currying operation `Hom ((star I).obj A) X → Hom A (I ⟹ X.left)`. -/
def sectionsCurry {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (sections I).obj X := by
 apply pullback.lift (terminal.from A)
 (CartesianClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left)) (uncurry_injective _)
 rw [uncurry_natural_left]
 simp [curryId, uncurry_natural_right, uncurry_curry]
 (MonoidalClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left))
 (MonoidalClosed.uncurry_injective _)
 rw [MonoidalClosed.uncurry_natural_left]
 simp [curryId, MonoidalClosed.uncurry_natural_right, MonoidalClosed.uncurry_curry]

/-- The uncurrying operation `Hom A (section X) → Hom ((star I).obj A) X`. -/
def sectionsUncurry {X : Over I} {A : C} (v : A ⟶ (sections I).obj X) :
 (star I).obj A ⟶ X := by
 let v₂ : A ⟶ (I ⟹ X.left) := v ≫ pullback.snd ..
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (exp I).map X.hom := by
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (ihom I).map X.hom := by
 rw [IsTerminal.hom_ext terminalIsTerminal (terminal.from A ) (v ≫ (pullback.fst ..))]
 simp [v₂, pullback.condition]
 dsimp [curryId] at w
 have w' := homEquiv_naturality_right_square (F := MonoidalCategory.tensorLeft I)
 (adj := exp.adjunction I) _ _ _ _ w
 simp [CartesianClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ CartesianClosed.uncurry v₂) ?_
 · dsimp [CartesianClosed.uncurry] at *
 (adj := ihom.adjunction I) _ _ _ _ w
 simp [MonoidalClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ MonoidalClosed.uncurry v₂) ?_
 · dsimp [MonoidalClosed.uncurry] at *
 rw [Category.assoc, ← w']
 simp [star_obj_hom]

Expand DownExpand Up@@ -188,13 +189,13 @@ def coreHomEquiv : CoreHomEquiv (star I) (sections I) where
 simp only [star_map]
 rw [← Over.homMk_comp] -- note: in a newer version of mathlib this is `Over.homMk_eta`
 congr 1
 simp [CartesianClosed.uncurry_natural_left]
 simp [MonoidalClosed.uncurry_natural_left]
 homEquiv_naturality_right := by
 intro A X' X u g
 dsimp [sectionsCurry, sectionsUncurry, curryId]
 apply pullback.hom_ext (IsTerminal.hom_ext terminalIsTerminal _ _)
 simp [sectionsMap, curryId]
 rw [← CartesianClosed.curry_natural_right, Category.assoc]
 rw [← MonoidalClosed.curry_natural_right, Category.assoc]

variable (I)

Expand Down

2 changes: 1 addition & 1 deletion
...Theory/Limits/Shapes/Pullback/CommSq.lean → ...its/Shapes/Pullback/IsPullback/Basic.lean

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Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Poly.ForMathlib.CategoryTheory.CommSq

namespace CategoryTheory.Functor
Expand Down

21 changes: 11 additions & 10 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -67,7 +67,7 @@ open CategoryTheory Category MonoidalCategory CartesianMonoidalCategory Limits F

variable {C : Type u} [Category.{v} C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

/-- A morphism `f : I ⟶ J` is exponentiable if the pullback functor `Over J ⥤ Over I`
has a right adjoint. -/
Expand DownExpand Up@@ -179,7 +179,7 @@ instance isMultiplicative : (ExponentiableMorphism (C:= C)).IsMultiplicative whe
/-- A morphism with a pushforward is an exponentiable object in the slice category. -/
def exponentiableOverMk [HasFiniteWidePullbacks C] {X I : C} (f : X ⟶ I)
 [ExponentiableMorphism f] :
Exponentiable (Over.mk f) where
Closed (Over.mk f) where
 rightAdj := pullback f ⋙ pushforward f
 adj := by
 apply ofNatIsoLeft _ _
Expand All@@ -192,7 +192,7 @@ morphism `X.hom`.
Here the pushforward functor along a morphism `f : I ⟶ J` is defined using the section functor
`Over (Over.mk f) ⥤ Over J`.
-/
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Exponentiable X] :
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Closed X] :
 ExponentiableMorphism X.hom :=
 ⟨X.iteratedSliceEquiv.inverse ⋙ sections X, ⟨by
 refine ofNatIsoLeft (Adjunction.comp ?_ ?_) (starIteratedSliceForwardIsoPullback X.hom)
Expand All@@ -217,7 +217,7 @@ variable {C} [HasFiniteWidePullbacks C] [HasPushforwards C]
/-- In a category where pushforwards exists along all morphisms, every slice category `Over I` is
cartesian closed. -/
instance cartesianClosedOver (I : C) :
CartesianClosed (Over I) where
MonoidalClosed (Over I) where
 closed X := @exponentiableOverMk _ _ _ _ _ _ X.hom (HasPushforwards.exponentiable X.hom)

end HasPushforwards
Expand All@@ -226,13 +226,13 @@ namespace CartesianClosedOver

open Over Reindex IsIso CartesianClosed HasPushforwards ExponentiableMorphism

variable {C} [HasFiniteWidePullbacks C] {I J : C} [CartesianClosed (Over J)]
variable {C} [HasFiniteWidePullbacks C] {I J : C} [MonoidalClosed (Over J)]

instance (f : I ⟶ J) : ExponentiableMorphism f :=
 ExponentiableMorphism.ofOverExponentiable (Over.mk f)

/-- A category with cartesian closed slices has pushforwards along all morphisms. -/
instance hasPushforwards [Π (I : C), CartesianClosed (Over I)] : HasPushforwards C where
instance hasPushforwards [Π (I : C), MonoidalClosed (Over I)] : HasPushforwards C where
 exponentiable f := ExponentiableMorphism.ofOverExponentiable (Over.mk f)

end CartesianClosedOver
Expand All@@ -242,7 +242,7 @@ is exponentiable and all the slices are cartesian closed. -/
class LocallyCartesianClosed [HasFiniteWidePullbacks C] extends
 HasPushforwards C where
 /-- every slice category `Over I` is cartesian closed. This is filled in by default. -/
 cartesianClosedOver : Π (I : C), CartesianClosed (Over I) := HasPushforwards.cartesianClosedOver
 cartesianClosedOver : Π (I : C), MonoidalClosed (Over I) := HasPushforwards.cartesianClosedOver

namespace LocallyCartesianClosed

Expand All@@ -256,7 +256,7 @@ attribute [scoped instance] hasFiniteLimits_of_hasTerminal_and_pullbacks
instance mkOfHasPushforwards [HasPushforwards C] : LocallyCartesianClosed C where

/-- A category with cartesian closed slices is locally cartesian closed. -/
instance mkOfCartesianClosedOver [Π (I : C), CartesianClosed (Over I)] :
instance mkOfCartesianClosedOver [Π (I : C), MonoidalClosed (Over I)] :
 LocallyCartesianClosed C where

variable [LocallyCartesianClosed C]
Expand All@@ -282,15 +282,16 @@ abbrev ev' {I : C} (X : Over I) (Y : Over X.left) : Reindex X (Pi X Y) ⟶ Y :=
 adj X.hom |>.counit.app Y

/-- A locally cartesian closed category with a terminal object is cartesian closed. -/
def cartesianClosed [HasTerminal C] :
CartesianClosed C := cartesianClosedOfEquiv <| equivOverTerminal C
def monoidalClosed [HasTerminal C] :
MonoidalClosed C := cartesianClosedOfEquiv <| equivOverTerminal C

/-- The slices of a locally cartesian closed category are locally cartesian closed. -/
def overLocallyCartesianClosed (I : C) : LocallyCartesianClosed (Over I) := by
 apply (config := { allowSynthFailures:= true}) mkOfCartesianClosedOver
 intro X
 exact cartesianClosedOfEquiv (C := Over (X.left)) X.iteratedSliceEquiv.symm

open CartesianClosed in
/-- The exponential `X^^A` in the slice category `Over I` is isomorphic to the pushforward of the
pullback of `X` along `A`. -/
def expIso {I : C} (A X : Over I) : Pi A (Reindex A X) ≅ A ⟹ X := Iso.refl _
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/BeckChevalley.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour, Emily Riehl
-/
import Poly.ForMathlib.CategoryTheory.LocallyCartesianClosed.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

/-!
# Beck-Chevalley natural transformations and natural isomorphisms
Expand Down

6 changes: 3 additions & 3 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Presheaf.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -22,10 +22,10 @@ abbrev Psh (C : Type u) [Category.{v} C] : Type (max u (v + 1)) := Cᵒᵖ ⥤ T

variable {C : Type*} [SmallCategory C] [HasTerminal C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

instance cartesianClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
CartesianClosed (Over P) :=
instance monoidalClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
MonoidalClosed (Over P) :=
 cartesianClosedOfEquiv (overEquivPresheafCostructuredArrow P).symm

instance locallyCartesianClosed : LocallyCartesianClosed (Psh C) := by
Expand Down

2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/NatTrans.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -6,7 +6,7 @@ Authors: Sina Hazratpour

import Mathlib.CategoryTheory.NatTrans
import Mathlib.CategoryTheory.Functor.TwoSquare
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

open CategoryTheory Limits IsPullback

Expand Down

4 changes: 3 additions & 1 deletion
Poly/ForMathlib/CategoryTheory/PartialProduct.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Mathlib.CategoryTheory.Comma.Over.Pullback
import Poly.ForMathlib.CategoryTheory.Comma.Over.Pullback
import Mathlib.CategoryTheory.Monoidal.Closed.Cartesian
Expand DownExpand Up@@ -100,6 +100,8 @@ structure Fan.Hom (c c' : Fan s X) where

attribute [reassoc (attr := simp)] Fan.Hom.w_left Fan.Hom.w_right

-- TODO: this is taking ages to check since 4.28.0-rc1.
set_option maxHeartbeats 0 in
@[simps]
instance : Category (Fan s X) where
 Hom := Fan.Hom
Expand Down

2 changes: 1 addition & 1 deletion
Poly/Type/Univariate.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -189,7 +189,7 @@ def Obj.iget [DecidableEq P.B] {X} [Inhabited X] (x : P X) (i : P.Total) : X :=
@[simp]
theorem iget_map [DecidableEq P.B] [Inhabited X] [Inhabited Y] (x : P X)
 (f : X → Y) (i : P.Total) (h : i.1 = x.1) : (P.map f x).iget i = f (x.iget i) := by
 simp only [Obj.iget, fst_map, *, dif_pos, eq_self_iff_true]
 simp only [Obj.iget, fst_map, *, dif_pos]
 cases x
 rfl

Expand Down

20 changes: 10 additions & 10 deletions
lake-manifest.json

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Original file line numberDiff line numberDiff line change
Expand Up@@ -15,7 +15,7 @@
 "type": "git",
 "subDir": null,
 "scope": "",
 "rev": "dd5e5d97469dec395f29661366030566355ad9be",
 "rev": "b8dad038b1b3a05b77d6884b15b8db03ec01dca1",
 "name": "mathlib",
 "manifestFile": "lake-manifest.json",
 "inputRev": null,
Expand All@@ -25,7 +25,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "b3dd6c3ebc0a71685e86bea9223be39ea4c299fb",
 "rev": "7311586e1a56af887b1081d05e80c11b6c41d212",
 "name": "plausible",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -45,7 +45,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "cff9dd30f2c161b9efd7c657cafed1f967645890",
 "rev": "b5908dbac486279f1133cb937648c63c30b455af",
 "name": "importGraph",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -55,17 +55,17 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "ef8377f31b5535430b6753a974d685b0019d0681",
 "rev": "6d65c6e0a25b8a52c13c3adeb63ecde3bfbb6294",
 "name": "proofwidgets",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v0.0.84",
 "inputRev": "v0.0.86",
 "inherited": true,
 "configFile": "lakefile.lean"},
 {"url": "https://github.com/leanprover-community/aesop",
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "fa78cf032194308a950a264ed87b422a2a7c1c6c",
 "rev": "f08e838d4f9aea519f3cde06260cfb686fd4bab0",
 "name": "aesop",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -75,7 +75,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "8920dcbb96a4e8bf641fc399ac9c0888e4a6be72",
 "rev": "23324752757bf28124a518ec284044c8db79fee5",
 "name": "Qq",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -85,7 +85,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "dff865b7ee7011518d59abfc101c368293173150",
 "rev": "100083c18750b6a9b7553c65f6b052c0a2f6bcb4",
 "name": "batteries",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -95,10 +95,10 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover",
 "rev": "726b98c53e2da249c1de768fbbbb5e67bc9cef60",
 "rev": "28e0856d4424863a85b18f38868c5420c55f9bae",
 "name": "Cli",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v4.27.0-rc1",
 "inputRev": "v4.28.0-rc1",
 "inherited": true,
 "configFile": "lakefile.toml"}],
 "name": "Poly",
Expand Down

2 changes: 1 addition & 1 deletion
lean-toolchain

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Original file line numberDiff line numberDiff line change
@@ -1 +1 @@
leanprover/lean4:v4.27.0-rc1
leanprover/lean4:v4.28.0-rc1

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode");
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();

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Jul 10, 2026
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feat: bump to Lean v4.28.0-rc1
#36
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4 changes: 0 additions & 4 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Basic.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -35,10 +35,6 @@ lemma homMk_comp'_assoc {X Y Z W : T} (f : X ⟶ Y) (g : Y ⟶ Z) (h : Z ⟶ W)
lemma homMk_id {X B : T} (f : X ⟶ B) (h : 𝟙 X ≫ f = f) : homMk (𝟙 X) h = 𝟙 (mk f) :=
 rfl

@[simp]
theorem mkIdTerminal_from_left {B : T} (U : Over B) : (mkIdTerminal.from U).left = U.hom := by
 simp [mkIdTerminal, CostructuredArrow.mkIdTerminal, Limits.IsTerminal.from, Functor.preimage]

/-- `Over.Sigma Y U` is a shorthand for `(Over.map Y.hom).obj U`.
This is a category-theoretic analogue of `Sigma` for types. -/
abbrev Sigma {X : T} (Y : Over X) (U : Over (Y.left)) : Over X :=
Expand Down

12 changes: 3 additions & 9 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Pullback.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -9,7 +9,7 @@ import Mathlib.CategoryTheory.Limits.Constructions.Over.Basic
import Mathlib.CategoryTheory.Monad.Products
import Poly.ForMathlib.CategoryTheory.Comma.Over.Basic
import Poly.ForMathlib.CategoryTheory.NatTrans
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Poly.ForMathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

noncomputable section

Expand All@@ -19,7 +19,7 @@ namespace CategoryTheory

open Category Limits Comonad MonoidalCategory CartesianMonoidalCategory

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

variable {C : Type u₁} [Category.{v₁} C]

Expand DownExpand Up@@ -211,7 +211,7 @@ lemma star_map [HasBinaryProducts C] {X : C} {Y Z : C} (f : Y ⟶ Z) :
instance [HasBinaryProducts C] (X : C) : (forget X).IsLeftAdjoint :=
 ⟨_, ⟨forgetAdjStar X⟩⟩

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

lemma whiskerLeftProdMapId [HasFiniteLimits C] {X : C} {A A' : C} {g : A ⟶ A'} :
 X ◁ g = prod.map (𝟙 X) g := by
Expand DownExpand Up@@ -298,12 +298,6 @@ def starIsoToOverTerminal [HasTerminal C] [HasBinaryProducts C] :

variable {C}

/-- A natural isomorphism between the functors `star X` and `star Y ⋙ pullback f`
for any morphism `f : X ⟶ Y`. -/
def starPullbackIsoStar [HasBinaryProducts C] [HasPullbacks C] {X Y : C} (f : X ⟶ Y) :
 star Y ⋙ pullback f ≅ star X :=
 conjugateIsoEquiv ((mapPullbackAdj f).comp (forgetAdjStar Y)) (forgetAdjStar X) (mapForget f)

/-- The functor `Over.pullback f : Over Y ⥤ Over X` is naturally isomorphic to
`Over.star : Over Y ⥤ Over (Over.mk f)` post-composed with the
iterated slice equivlanece `Over (Over.mk f) ⥤ Over X`. -/
Expand Down

33 changes: 17 additions & 16 deletions
Poly/ForMathlib/CategoryTheory/Comma/Over/Sections.lean

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Original file line numberDiff line numberDiff line change
Expand Up@@ -28,7 +28,7 @@ variable {C : Type u₁} [Category.{v₁} C]

attribute [local instance] hasBinaryProducts_of_hasTerminal_and_pullbacks
attribute [local instance] hasFiniteProducts_of_has_binary_and_terminal
attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

section

Expand DownExpand Up@@ -69,11 +69,11 @@ end

variable [HasTerminal C] [HasPullbacks C]

variable (I : C) [Exponentiable I]
variable (I : C) [Closed I]

/-- The first leg of a cospan constructing a pullback diagram in `C` used to define `sections` . -/
def curryId : ⊤_ C ⟶ (I ⟹ I) :=
CartesianClosed.curry (fst I (⊤_ C))
MonoidalClosed.curry (fst I (⊤_ C))

variable {I}

Expand All@@ -90,14 +90,14 @@ pullback diagram:
 ⊤_ C ----> I ⟹ I
```-/
abbrev sectionsObj (X : Over I) : C :=
 Limits.pullback (curryId I) ((exp I).map X.hom)
 Limits.pullback (curryId I) ((ihom I).map X.hom)

/-- The functoriality of `sectionsObj`. -/
def sectionsMap {X X' : Over I} (u : X ⟶ X') :
 sectionsObj X ⟶ sectionsObj X' := by
 fapply pullback.map
 · exact 𝟙 _
 · exact (exp I).map u.left
 · exact (ihom I).map u.left
 · exact 𝟙 _
 · simp only [comp_id, id_comp]
 · simp only [comp_id, ← Functor.map_comp, w]
Expand DownExpand Up@@ -130,29 +130,30 @@ variable {I}
in `C`. See `sectionsCurry`. -/
def sectionsCurryAux {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (I ⟹ X.left) :=
CartesianClosed.curry (u.left)
MonoidalClosed.curry (u.left)

/-- The currying operation `Hom ((star I).obj A) X → Hom A (I ⟹ X.left)`. -/
def sectionsCurry {X : Over I} {A : C} (u : (star I).obj A ⟶ X) :
 A ⟶ (sections I).obj X := by
 apply pullback.lift (terminal.from A)
 (CartesianClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left)) (uncurry_injective _)
 rw [uncurry_natural_left]
 simp [curryId, uncurry_natural_right, uncurry_curry]
 (MonoidalClosed.curry ((prodIsoTensorObj _ _).inv ≫ u.left))
 (MonoidalClosed.uncurry_injective _)
 rw [MonoidalClosed.uncurry_natural_left]
 simp [curryId, MonoidalClosed.uncurry_natural_right, MonoidalClosed.uncurry_curry]

/-- The uncurrying operation `Hom A (section X) → Hom ((star I).obj A) X`. -/
def sectionsUncurry {X : Over I} {A : C} (v : A ⟶ (sections I).obj X) :
 (star I).obj A ⟶ X := by
 let v₂ : A ⟶ (I ⟹ X.left) := v ≫ pullback.snd ..
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (exp I).map X.hom := by
 have w : terminal.from A ≫ (curryId I) = v₂ ≫ (ihom I).map X.hom := by
 rw [IsTerminal.hom_ext terminalIsTerminal (terminal.from A ) (v ≫ (pullback.fst ..))]
 simp [v₂, pullback.condition]
 dsimp [curryId] at w
 have w' := homEquiv_naturality_right_square (F := MonoidalCategory.tensorLeft I)
 (adj := exp.adjunction I) _ _ _ _ w
 simp [CartesianClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ CartesianClosed.uncurry v₂) ?_
 · dsimp [CartesianClosed.uncurry] at *
 (adj := ihom.adjunction I) _ _ _ _ w
 simp [MonoidalClosed.curry] at w'
 refine Over.homMk ((prodIsoTensorObj I A).hom ≫ MonoidalClosed.uncurry v₂) ?_
 · dsimp [MonoidalClosed.uncurry] at *
 rw [Category.assoc, ← w']
 simp [star_obj_hom]

Expand DownExpand Up@@ -188,13 +189,13 @@ def coreHomEquiv : CoreHomEquiv (star I) (sections I) where
 simp only [star_map]
 rw [← Over.homMk_comp] -- note: in a newer version of mathlib this is `Over.homMk_eta`
 congr 1
 simp [CartesianClosed.uncurry_natural_left]
 simp [MonoidalClosed.uncurry_natural_left]
 homEquiv_naturality_right := by
 intro A X' X u g
 dsimp [sectionsCurry, sectionsUncurry, curryId]
 apply pullback.hom_ext (IsTerminal.hom_ext terminalIsTerminal _ _)
 simp [sectionsMap, curryId]
 rw [← CartesianClosed.curry_natural_right, Category.assoc]
 rw [← MonoidalClosed.curry_natural_right, Category.assoc]

variable (I)

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2 changes: 1 addition & 1 deletion
...Theory/Limits/Shapes/Pullback/CommSq.lean → ...its/Shapes/Pullback/IsPullback/Basic.lean

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Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Poly.ForMathlib.CategoryTheory.CommSq

namespace CategoryTheory.Functor
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21 changes: 11 additions & 10 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Basic.lean

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Expand Up@@ -67,7 +67,7 @@ open CategoryTheory Category MonoidalCategory CartesianMonoidalCategory Limits F

variable {C : Type u} [Category.{v} C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

/-- A morphism `f : I ⟶ J` is exponentiable if the pullback functor `Over J ⥤ Over I`
has a right adjoint. -/
Expand DownExpand Up@@ -179,7 +179,7 @@ instance isMultiplicative : (ExponentiableMorphism (C:= C)).IsMultiplicative whe
/-- A morphism with a pushforward is an exponentiable object in the slice category. -/
def exponentiableOverMk [HasFiniteWidePullbacks C] {X I : C} (f : X ⟶ I)
 [ExponentiableMorphism f] :
Exponentiable (Over.mk f) where
Closed (Over.mk f) where
 rightAdj := pullback f ⋙ pushforward f
 adj := by
 apply ofNatIsoLeft _ _
Expand All@@ -192,7 +192,7 @@ morphism `X.hom`.
Here the pushforward functor along a morphism `f : I ⟶ J` is defined using the section functor
`Over (Over.mk f) ⥤ Over J`.
-/
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Exponentiable X] :
def ofOverExponentiable [HasFiniteWidePullbacks C] {I : C} (X : Over I) [Closed X] :
 ExponentiableMorphism X.hom :=
 ⟨X.iteratedSliceEquiv.inverse ⋙ sections X, ⟨by
 refine ofNatIsoLeft (Adjunction.comp ?_ ?_) (starIteratedSliceForwardIsoPullback X.hom)
Expand All@@ -217,7 +217,7 @@ variable {C} [HasFiniteWidePullbacks C] [HasPushforwards C]
/-- In a category where pushforwards exists along all morphisms, every slice category `Over I` is
cartesian closed. -/
instance cartesianClosedOver (I : C) :
CartesianClosed (Over I) where
MonoidalClosed (Over I) where
 closed X := @exponentiableOverMk _ _ _ _ _ _ X.hom (HasPushforwards.exponentiable X.hom)

end HasPushforwards
Expand All@@ -226,13 +226,13 @@ namespace CartesianClosedOver

open Over Reindex IsIso CartesianClosed HasPushforwards ExponentiableMorphism

variable {C} [HasFiniteWidePullbacks C] {I J : C} [CartesianClosed (Over J)]
variable {C} [HasFiniteWidePullbacks C] {I J : C} [MonoidalClosed (Over J)]

instance (f : I ⟶ J) : ExponentiableMorphism f :=
 ExponentiableMorphism.ofOverExponentiable (Over.mk f)

/-- A category with cartesian closed slices has pushforwards along all morphisms. -/
instance hasPushforwards [Π (I : C), CartesianClosed (Over I)] : HasPushforwards C where
instance hasPushforwards [Π (I : C), MonoidalClosed (Over I)] : HasPushforwards C where
 exponentiable f := ExponentiableMorphism.ofOverExponentiable (Over.mk f)

end CartesianClosedOver
Expand All@@ -242,7 +242,7 @@ is exponentiable and all the slices are cartesian closed. -/
class LocallyCartesianClosed [HasFiniteWidePullbacks C] extends
 HasPushforwards C where
 /-- every slice category `Over I` is cartesian closed. This is filled in by default. -/
 cartesianClosedOver : Π (I : C), CartesianClosed (Over I) := HasPushforwards.cartesianClosedOver
 cartesianClosedOver : Π (I : C), MonoidalClosed (Over I) := HasPushforwards.cartesianClosedOver

namespace LocallyCartesianClosed

Expand All@@ -256,7 +256,7 @@ attribute [scoped instance] hasFiniteLimits_of_hasTerminal_and_pullbacks
instance mkOfHasPushforwards [HasPushforwards C] : LocallyCartesianClosed C where

/-- A category with cartesian closed slices is locally cartesian closed. -/
instance mkOfCartesianClosedOver [Π (I : C), CartesianClosed (Over I)] :
instance mkOfCartesianClosedOver [Π (I : C), MonoidalClosed (Over I)] :
 LocallyCartesianClosed C where

variable [LocallyCartesianClosed C]
Expand All@@ -282,15 +282,16 @@ abbrev ev' {I : C} (X : Over I) (Y : Over X.left) : Reindex X (Pi X Y) ⟶ Y :=
 adj X.hom |>.counit.app Y

/-- A locally cartesian closed category with a terminal object is cartesian closed. -/
def cartesianClosed [HasTerminal C] :
CartesianClosed C := cartesianClosedOfEquiv <| equivOverTerminal C
def monoidalClosed [HasTerminal C] :
MonoidalClosed C := cartesianClosedOfEquiv <| equivOverTerminal C

/-- The slices of a locally cartesian closed category are locally cartesian closed. -/
def overLocallyCartesianClosed (I : C) : LocallyCartesianClosed (Over I) := by
 apply (config := { allowSynthFailures:= true}) mkOfCartesianClosedOver
 intro X
 exact cartesianClosedOfEquiv (C := Over (X.left)) X.iteratedSliceEquiv.symm

open CartesianClosed in
/-- The exponential `X^^A` in the slice category `Over I` is isomorphic to the pushforward of the
pullback of `X` along `A`. -/
def expIso {I : C} (A X : Over I) : Pi A (Reindex A X) ≅ A ⟹ X := Iso.refl _
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2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/BeckChevalley.lean

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Expand Up@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour, Emily Riehl
-/
import Poly.ForMathlib.CategoryTheory.LocallyCartesianClosed.Basic
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

/-!
# Beck-Chevalley natural transformations and natural isomorphisms
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6 changes: 3 additions & 3 deletions
Poly/ForMathlib/CategoryTheory/LocallyCartesianClosed/Presheaf.lean

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Expand Up@@ -22,10 +22,10 @@ abbrev Psh (C : Type u) [Category.{v} C] : Type (max u (v + 1)) := Cᵒᵖ ⥤ T

variable {C : Type*} [SmallCategory C] [HasTerminal C]

attribute [local instance] CartesianMonoidalCategory.ofFiniteProducts
attribute [local instance] CartesianMonoidalCategory.ofHasFiniteProducts

instance cartesianClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
CartesianClosed (Over P) :=
instance monoidalClosedOver {C : Type u} [Category.{max u v} C] (P : Psh C) :
MonoidalClosed (Over P) :=
 cartesianClosedOfEquiv (overEquivPresheafCostructuredArrow P).symm

instance locallyCartesianClosed : LocallyCartesianClosed (Psh C) := by
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2 changes: 1 addition & 1 deletion
Poly/ForMathlib/CategoryTheory/NatTrans.lean

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Expand Up@@ -6,7 +6,7 @@ Authors: Sina Hazratpour

import Mathlib.CategoryTheory.NatTrans
import Mathlib.CategoryTheory.Functor.TwoSquare
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

open CategoryTheory Limits IsPullback

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4 changes: 3 additions & 1 deletion
Poly/ForMathlib/CategoryTheory/PartialProduct.lean

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Expand Up@@ -3,7 +3,7 @@ Copyright (c) 2025 Sina Hazratpour. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sina Hazratpour
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.CommSq
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic
import Mathlib.CategoryTheory.Comma.Over.Pullback
import Poly.ForMathlib.CategoryTheory.Comma.Over.Pullback
import Mathlib.CategoryTheory.Monoidal.Closed.Cartesian
Expand DownExpand Up@@ -100,6 +100,8 @@ structure Fan.Hom (c c' : Fan s X) where

attribute [reassoc (attr := simp)] Fan.Hom.w_left Fan.Hom.w_right

-- TODO: this is taking ages to check since 4.28.0-rc1.
set_option maxHeartbeats 0 in
@[simps]
instance : Category (Fan s X) where
 Hom := Fan.Hom
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2 changes: 1 addition & 1 deletion
Poly/Type/Univariate.lean

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Expand Up@@ -189,7 +189,7 @@ def Obj.iget [DecidableEq P.B] {X} [Inhabited X] (x : P X) (i : P.Total) : X :=
@[simp]
theorem iget_map [DecidableEq P.B] [Inhabited X] [Inhabited Y] (x : P X)
 (f : X → Y) (i : P.Total) (h : i.1 = x.1) : (P.map f x).iget i = f (x.iget i) := by
 simp only [Obj.iget, fst_map, *, dif_pos, eq_self_iff_true]
 simp only [Obj.iget, fst_map, *, dif_pos]
 cases x
 rfl

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20 changes: 10 additions & 10 deletions
lake-manifest.json

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Expand Up@@ -15,7 +15,7 @@
 "type": "git",
 "subDir": null,
 "scope": "",
 "rev": "dd5e5d97469dec395f29661366030566355ad9be",
 "rev": "b8dad038b1b3a05b77d6884b15b8db03ec01dca1",
 "name": "mathlib",
 "manifestFile": "lake-manifest.json",
 "inputRev": null,
Expand All@@ -25,7 +25,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "b3dd6c3ebc0a71685e86bea9223be39ea4c299fb",
 "rev": "7311586e1a56af887b1081d05e80c11b6c41d212",
 "name": "plausible",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -45,7 +45,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "cff9dd30f2c161b9efd7c657cafed1f967645890",
 "rev": "b5908dbac486279f1133cb937648c63c30b455af",
 "name": "importGraph",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -55,17 +55,17 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "ef8377f31b5535430b6753a974d685b0019d0681",
 "rev": "6d65c6e0a25b8a52c13c3adeb63ecde3bfbb6294",
 "name": "proofwidgets",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v0.0.84",
 "inputRev": "v0.0.86",
 "inherited": true,
 "configFile": "lakefile.lean"},
 {"url": "https://github.com/leanprover-community/aesop",
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "fa78cf032194308a950a264ed87b422a2a7c1c6c",
 "rev": "f08e838d4f9aea519f3cde06260cfb686fd4bab0",
 "name": "aesop",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -75,7 +75,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "8920dcbb96a4e8bf641fc399ac9c0888e4a6be72",
 "rev": "23324752757bf28124a518ec284044c8db79fee5",
 "name": "Qq",
 "manifestFile": "lake-manifest.json",
 "inputRev": "master",
Expand All@@ -85,7 +85,7 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover-community",
 "rev": "dff865b7ee7011518d59abfc101c368293173150",
 "rev": "100083c18750b6a9b7553c65f6b052c0a2f6bcb4",
 "name": "batteries",
 "manifestFile": "lake-manifest.json",
 "inputRev": "main",
Expand All@@ -95,10 +95,10 @@
 "type": "git",
 "subDir": null,
 "scope": "leanprover",
 "rev": "726b98c53e2da249c1de768fbbbb5e67bc9cef60",
 "rev": "28e0856d4424863a85b18f38868c5420c55f9bae",
 "name": "Cli",
 "manifestFile": "lake-manifest.json",
 "inputRev": "v4.27.0-rc1",
 "inputRev": "v4.28.0-rc1",
 "inherited": true,
 "configFile": "lakefile.toml"}],
 "name": "Poly",
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2 changes: 1 addition & 1 deletion
lean-toolchain

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@@ -1 +1 @@
leanprover/lean4:v4.27.0-rc1
leanprover/lean4:v4.28.0-rc1