topology.sheaves.sheaf | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

33c67ae6

bump to nightly-2024-04-14-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

f736ea6b

Diff

@@ -159,7 +159,7 @@ namespace Sheaf
 -/
 def forget : TopCat.Sheaf C X ⥤ TopCat.Presheaf C X :=
   sheafToPresheaf _ _
-deriving Full, Faithful
+deriving CategoryTheory.Functor.Full, CategoryTheory.Functor.Faithful
 #align Top.sheaf.forget TopCat.Sheaf.forget
 -/

33c67ae6

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Topology.Sheaves.Presheaf
-import Mathbin.CategoryTheory.Sites.Sheaf
-import Mathbin.CategoryTheory.Sites.Spaces
+import Topology.Sheaves.Presheaf
+import CategoryTheory.Sites.Sheaf
+import CategoryTheory.Sites.Spaces
 
 #align_import topology.sheaves.sheaf from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"

33c67ae6

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module topology.sheaves.sheaf
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Sheaves.Presheaf
 import Mathbin.CategoryTheory.Sites.Sheaf
 import Mathbin.CategoryTheory.Sites.Spaces
 
+#align_import topology.sheaves.sheaf from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
+
 /-!
 # Sheaves

33c67ae6

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -109,15 +109,19 @@ theorem isSheaf_unit (F : Presheaf (CategoryTheory.Discrete Unit) X) : F.IsSheaf
 #align Top.presheaf.is_sheaf_unit TopCat.Presheaf.isSheaf_unit
 -/
 
+#print TopCat.Presheaf.isSheaf_iso_iff /-
 theorem isSheaf_iso_iff {F G : Presheaf C X} (α : F ≅ G) : F.IsSheaf ↔ G.IsSheaf :=
   Presheaf.isSheaf_of_iso_iff α
 #align Top.presheaf.is_sheaf_iso_iff TopCat.Presheaf.isSheaf_iso_iff
+-/
 
+#print TopCat.Presheaf.isSheaf_of_iso /-
 /-- Transfer the sheaf condition across an isomorphism of presheaves.
 -/
 theorem isSheaf_of_iso {F G : Presheaf C X} (α : F ≅ G) (h : F.IsSheaf) : G.IsSheaf :=
   (isSheaf_iso_iff α).1 h
 #align Top.presheaf.is_sheaf_of_iso TopCat.Presheaf.isSheaf_of_iso
+-/
 
 end Presheaf
 
@@ -153,22 +157,28 @@ instance sheafInhabited : Inhabited (Sheaf (CategoryTheory.Discrete PUnit) X) :=
 
 namespace Sheaf
 
+#print TopCat.Sheaf.forget /-
 /-- The forgetful functor from sheaves to presheaves.
 -/
 def forget : TopCat.Sheaf C X ⥤ TopCat.Presheaf C X :=
   sheafToPresheaf _ _
 deriving Full, Faithful
 #align Top.sheaf.forget TopCat.Sheaf.forget
+-/
 
+#print TopCat.Sheaf.id_app /-
 -- Note: These can be proved by simp.
 theorem id_app (F : Sheaf C X) (t) : (𝟙 F : F ⟶ F).1.app t = 𝟙 _ :=
   rfl
 #align Top.sheaf.id_app TopCat.Sheaf.id_app
+-/
 
+#print TopCat.Sheaf.comp_app /-
 theorem comp_app {F G H : Sheaf C X} (f : F ⟶ G) (g : G ⟶ H) (t) :
     (f ≫ g).1.app t = f.1.app t ≫ g.1.app t :=
   rfl
 #align Top.sheaf.comp_app TopCat.Sheaf.comp_app
+-/
 
 end Sheaf

33c67ae6

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -128,7 +128,8 @@ variable (C X)
 satisfying the sheaf condition.
 -/
 def Sheaf : Type max u v w :=
-  Sheaf (Opens.grothendieckTopology X) C deriving Category
+  Sheaf (Opens.grothendieckTopology X) C
+deriving Category
 #align Top.sheaf TopCat.Sheaf
 -/
 
@@ -155,7 +156,8 @@ namespace Sheaf
 /-- The forgetful functor from sheaves to presheaves.
 -/
 def forget : TopCat.Sheaf C X ⥤ TopCat.Presheaf C X :=
-  sheafToPresheaf _ _ deriving Full, Faithful
+  sheafToPresheaf _ _
+deriving Full, Faithful
 #align Top.sheaf.forget TopCat.Sheaf.forget
 
 -- Note: These can be proved by simp.

33c67ae6

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -109,22 +109,10 @@ theorem isSheaf_unit (F : Presheaf (CategoryTheory.Discrete Unit) X) : F.IsSheaf
 #align Top.presheaf.is_sheaf_unit TopCat.Presheaf.isSheaf_unit
 -/
 
-/- warning: Top.presheaf.is_sheaf_iso_iff -> TopCat.Presheaf.isSheaf_iso_iff is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {F : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {G : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) F G) -> (Iff (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X F) (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X G))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {F : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {G : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) F G) -> (Iff (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X F) (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X G))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.is_sheaf_iso_iff TopCat.Presheaf.isSheaf_iso_iffₓ'. -/
 theorem isSheaf_iso_iff {F G : Presheaf C X} (α : F ≅ G) : F.IsSheaf ↔ G.IsSheaf :=
   Presheaf.isSheaf_of_iso_iff α
 #align Top.presheaf.is_sheaf_iso_iff TopCat.Presheaf.isSheaf_iso_iff
 
-/- warning: Top.presheaf.is_sheaf_of_iso -> TopCat.Presheaf.isSheaf_of_iso is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {F : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {G : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) F G) -> (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X F) -> (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X G)
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {F : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {G : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) F G) -> (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X F) -> (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X G)
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.is_sheaf_of_iso TopCat.Presheaf.isSheaf_of_isoₓ'. -/
 /-- Transfer the sheaf condition across an isomorphism of presheaves.
 -/
 theorem isSheaf_of_iso {F G : Presheaf C X} (α : F ≅ G) (h : F.IsSheaf) : G.IsSheaf :=
@@ -164,29 +152,17 @@ instance sheafInhabited : Inhabited (Sheaf (CategoryTheory.Discrete PUnit) X) :=
 
 namespace Sheaf
 
-/- warning: Top.sheaf.forget -> TopCat.Sheaf.forget is a dubious translation:
-lean 3 declaration is
-  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] (X : TopCat.{u1}), CategoryTheory.Functor.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Sheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X)
-but is expected to have type
-  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] (X : TopCat.{u1}), CategoryTheory.Functor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (TopCat.SheafCat.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X)
-Case conversion may be inaccurate. Consider using '#align Top.sheaf.forget TopCat.Sheaf.forgetₓ'. -/
 /-- The forgetful functor from sheaves to presheaves.
 -/
 def forget : TopCat.Sheaf C X ⥤ TopCat.Presheaf C X :=
   sheafToPresheaf _ _ deriving Full, Faithful
 #align Top.sheaf.forget TopCat.Sheaf.forget
 
-/- warning: Top.sheaf.id_app -> TopCat.Sheaf.id_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.sheaf.id_app TopCat.Sheaf.id_appₓ'. -/
 -- Note: These can be proved by simp.
 theorem id_app (F : Sheaf C X) (t) : (𝟙 F : F ⟶ F).1.app t = 𝟙 _ :=
   rfl
 #align Top.sheaf.id_app TopCat.Sheaf.id_app
 
-/- warning: Top.sheaf.comp_app -> TopCat.Sheaf.comp_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.sheaf.comp_app TopCat.Sheaf.comp_appₓ'. -/
 theorem comp_app {F G H : Sheaf C X} (f : F ⟶ G) (g : G ⟶ H) (t) :
     (f ≫ g).1.app t = f.1.app t ≫ g.1.app t :=
   rfl

33c67ae6

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -177,10 +177,7 @@ def forget : TopCat.Sheaf C X ⥤ TopCat.Presheaf C X :=
 #align Top.sheaf.forget TopCat.Sheaf.forget
 
 /- warning: Top.sheaf.id_app -> TopCat.Sheaf.id_app is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.sheaf.id_app TopCat.Sheaf.id_appₓ'. -/
 -- Note: These can be proved by simp.
 theorem id_app (F : Sheaf C X) (t) : (𝟙 F : F ⟶ F).1.app t = 𝟙 _ :=
@@ -188,10 +185,7 @@ theorem id_app (F : Sheaf C X) (t) : (𝟙 F : F ⟶ F).1.app t = 𝟙 _ :=
 #align Top.sheaf.id_app TopCat.Sheaf.id_app
 
 /- warning: Top.sheaf.comp_app -> TopCat.Sheaf.comp_app is a dubious translation:
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TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 F H (CategoryTheory.CategoryStruct.comp.{max u2 u1, max (max u3 u2) u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max (max u3 u2) u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (TopCat.SheafCat.{u1, u2, u3} C _inst_1 X)) F G H f g)) t) (CategoryTheory.CategoryStruct.comp.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} 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TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) 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(TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 G)) t) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) 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TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 F) (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 G) (CategoryTheory.Sheaf.Hom.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 F G f) t) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 G) (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 H) (CategoryTheory.Sheaf.Hom.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 G H g) t))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.sheaf.comp_app TopCat.Sheaf.comp_appₓ'. -/
 theorem comp_app {F G H : Sheaf C X} (f : F ⟶ G) (g : G ⟶ H) (t) :
     (f ≫ g).1.app t = f.1.app t ≫ g.1.app t :=

33c67ae6

bump to nightly-2023-05-21-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

7b1466d5

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module topology.sheaves.sheaf
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Sites.Spaces
 /-!
 # Sheaves
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define sheaves on a topological space, with values in an arbitrary category.
 
 A presheaf on a topological space `X` is a sheaf presicely when it is a sheaf under the

70fd9563

bump to nightly-2023-05-18-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

d8748bc4

Diff

@@ -53,6 +53,7 @@ variable {X : TopCat.{w}} (F : Presheaf C X) {ι : Type v} (U : ι → Opens X)
 
 namespace Presheaf
 
+#print TopCat.Presheaf.IsSheaf /-
 /-- The sheaf condition has several different equivalent formulations.
 The official definition chosen here is in terms of grothendieck topologies so that the results on
 sites could be applied here easily, and this condition does not require additional constraints on
@@ -95,17 +96,32 @@ preserve limits. This applies to most "algebraic" categories, e.g. groups, abeli
 def IsSheaf (F : Presheaf.{w, v, u} C X) : Prop :=
   Presheaf.IsSheaf (Opens.grothendieckTopology X) F
 #align Top.presheaf.is_sheaf TopCat.Presheaf.IsSheaf
+-/
 
+#print TopCat.Presheaf.isSheaf_unit /-
 /-- The presheaf valued in `unit` over any topological space is a sheaf.
 -/
 theorem isSheaf_unit (F : Presheaf (CategoryTheory.Discrete Unit) X) : F.IsSheaf :=
   fun x U S hS x hx => ⟨eqToHom (Subsingleton.elim _ _), by tidy, by tidy⟩
 #align Top.presheaf.is_sheaf_unit TopCat.Presheaf.isSheaf_unit
+-/
 
+/- warning: Top.presheaf.is_sheaf_iso_iff -> TopCat.Presheaf.isSheaf_iso_iff is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {F : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {G : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) F G) -> (Iff (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X F) (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X G))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {F : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {G : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) F G) -> (Iff (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X F) (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X G))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.is_sheaf_iso_iff TopCat.Presheaf.isSheaf_iso_iffₓ'. -/
 theorem isSheaf_iso_iff {F G : Presheaf C X} (α : F ≅ G) : F.IsSheaf ↔ G.IsSheaf :=
   Presheaf.isSheaf_of_iso_iff α
 #align Top.presheaf.is_sheaf_iso_iff TopCat.Presheaf.isSheaf_iso_iff
 
+/- warning: Top.presheaf.is_sheaf_of_iso -> TopCat.Presheaf.isSheaf_of_iso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {F : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {G : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (CategoryTheory.Iso.{max u1 u2, max u3 u2 u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X) F G) -> (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X F) -> (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X G)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {F : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X} {G : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X}, (CategoryTheory.Iso.{max u2 u1, max (max u3 u2) u1} (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X) F G) -> (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X F) -> (TopCat.Presheaf.IsSheaf.{u1, u2, u3} C _inst_1 X G)
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.is_sheaf_of_iso TopCat.Presheaf.isSheaf_of_isoₓ'. -/
 /-- Transfer the sheaf condition across an isomorphism of presheaves.
 -/
 theorem isSheaf_of_iso {F G : Presheaf C X} (α : F ≅ G) (h : F.IsSheaf) : G.IsSheaf :=
@@ -116,40 +132,64 @@ end Presheaf
 
 variable (C X)
 
+#print TopCat.Sheaf /-
 /-- A `sheaf C X` is a presheaf of objects from `C` over a (bundled) topological space `X`,
 satisfying the sheaf condition.
 -/
 def Sheaf : Type max u v w :=
   Sheaf (Opens.grothendieckTopology X) C deriving Category
 #align Top.sheaf TopCat.Sheaf
+-/
 
 variable {C X}
 
+#print TopCat.Sheaf.presheaf /-
 /-- The underlying presheaf of a sheaf -/
 abbrev Sheaf.presheaf (F : X.Sheaf C) : TopCat.Presheaf C X :=
   F.1
 #align Top.sheaf.presheaf TopCat.Sheaf.presheaf
+-/
 
 variable (C X)
 
+#print TopCat.sheafInhabited /-
 -- Let's construct a trivial example, to keep the inhabited linter happy.
 instance sheafInhabited : Inhabited (Sheaf (CategoryTheory.Discrete PUnit) X) :=
   ⟨⟨Functor.star _, Presheaf.isSheaf_unit _⟩⟩
 #align Top.sheaf_inhabited TopCat.sheafInhabited
+-/
 
 namespace Sheaf
 
+/- warning: Top.sheaf.forget -> TopCat.Sheaf.forget is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] (X : TopCat.{u1}), CategoryTheory.Functor.{max u1 u2, max u1 u2, max u3 u2 u1, max u3 u2 u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Sheaf.category.{u2, u1, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.category.{u2, u1, u3} C _inst_1 X)
+but is expected to have type
+  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] (X : TopCat.{u1}), CategoryTheory.Functor.{max u2 u1, max u2 u1, max (max u3 u2) u1, max (max u3 u2) u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (TopCat.SheafCat.{u1, u2, u3} C _inst_1 X) (TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) (TopCat.instCategoryPresheaf.{u1, u2, u3} C _inst_1 X)
+Case conversion may be inaccurate. Consider using '#align Top.sheaf.forget TopCat.Sheaf.forgetₓ'. -/
 /-- The forgetful functor from sheaves to presheaves.
 -/
 def forget : TopCat.Sheaf C X ⥤ TopCat.Presheaf C X :=
   sheafToPresheaf _ _ deriving Full, Faithful
 #align Top.sheaf.forget TopCat.Sheaf.forget
 
+/- warning: Top.sheaf.id_app -> TopCat.Sheaf.id_app is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] (X : TopCat.{u1}) (F : TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (t : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} TopCat.{u1} Type.{u1} TopCat.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (coeSort.{succ (succ u1), succ (succ u1)} 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align Top.sheaf.id_app TopCat.Sheaf.id_appₓ'. -/
 -- Note: These can be proved by simp.
 theorem id_app (F : Sheaf C X) (t) : (𝟙 F : F ⟶ F).1.app t = 𝟙 _ :=
   rfl
 #align Top.sheaf.id_app TopCat.Sheaf.id_app
 
+/- warning: Top.sheaf.comp_app -> TopCat.Sheaf.comp_app is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C] (X : TopCat.{u1}) {F : TopCat.Sheaf.{u1, u2, u3} C _inst_1 X} {G : TopCat.Sheaf.{u1, u2, u3} C _inst_1 X} {H : TopCat.Sheaf.{u1, u2, u3} C _inst_1 X} (f : Quiver.Hom.{succ (max u1 u2), max u3 u2 u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u3 u2 u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u3 u2 u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Sheaf.category.{u2, u1, u3} C _inst_1 X))) F G) (g : Quiver.Hom.{succ (max u1 u2), max u3 u2 u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max u3 u2 u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max u3 u2 u1} (TopCat.Sheaf.{u1, u2, u3} C _inst_1 X) (TopCat.Sheaf.category.{u2, u1, u3} C _inst_1 X))) G H) (t : Opposite.{succ u1} (TopologicalSpace.Opens.{u1} 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(TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 F)) t) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} 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(CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 H)) t)) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} 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(CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 H) (CategoryTheory.Sheaf.Hom.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} 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TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} 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(TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 G)) t) (Prefunctor.obj.{succ u1, succ u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 H)) t) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 F) (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 G) (CategoryTheory.Sheaf.Hom.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 F G f) t) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 G) (CategoryTheory.Sheaf.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 H) (CategoryTheory.Sheaf.Hom.val.{u1, u2, u1, u3} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) C _inst_1 G H g) t))
+Case conversion may be inaccurate. Consider using '#align Top.sheaf.comp_app TopCat.Sheaf.comp_appₓ'. -/
 theorem comp_app {F G H : Sheaf C X} (f : F ⟶ G) (g : G ⟶ H) (t) :
     (f ≫ g).1.app t = f.1.app t ≫ g.1.app t :=
   rfl

70fd9563

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

chore(CategoryTheory): make Functor.Full a Prop (#12449)

Before this PR, Functor.Full contained the data of the preimage of maps by a full functor F. This PR makes Functor.Full a proposition. This is to prevent any diamond to appear.

The lemma Functor.image_preimage is also renamed Functor.map_preimage.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

ce289a0e

Diff

@@ -146,8 +146,8 @@ set_option linter.uppercaseLean3 false in
 #align Top.sheaf.forget TopCat.Sheaf.forget
 
 -- Porting note: `deriving Full` failed
-instance forgetFull : (forget C X).Full where
-  preimage := Sheaf.Hom.mk
+instance forget_full : (forget C X).Full where
+  map_surjective f := ⟨Sheaf.Hom.mk f, rfl⟩
 
 -- Porting note: `deriving Faithful` failed
 instance forgetFaithful : (forget C X).Faithful where

70fd9563

chore(CategoryTheory): move Full, Faithful, EssSurj, IsEquivalence and ReflectsIsomorphisms to the Functor namespace (#11985)

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

65b7affc

Diff

@@ -146,11 +146,11 @@ set_option linter.uppercaseLean3 false in
 #align Top.sheaf.forget TopCat.Sheaf.forget
 
 -- Porting note: `deriving Full` failed
-instance forgetFull : Full (forget C X) where
+instance forgetFull : (forget C X).Full where
   preimage := Sheaf.Hom.mk
 
 -- Porting note: `deriving Faithful` failed
-instance forgetFaithful : Faithful (forget C X) where
+instance forgetFaithful : (forget C X).Faithful where
   map_injective := Sheaf.Hom.ext _ _
 
 -- Note: These can be proved by simp.

70fd9563

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -37,7 +37,6 @@ open CategoryTheory CategoryTheory.Limits TopologicalSpace Opposite TopologicalS
 namespace TopCat
 
 variable {C : Type u} [Category.{v} C]
-
 variable {X : TopCat.{w}} (F : Presheaf C X) {ι : Type v} (U : ι → Opens X)
 
 namespace Presheaf

70fd9563

style: reduce spacing variation in "porting note" comments (#10886)

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

86b84c52

Diff

@@ -117,7 +117,7 @@ nonrec def Sheaf : Type max u v w :=
 set_option linter.uppercaseLean3 false in
 #align Top.sheaf TopCat.Sheaf
 
--- Porting Note : `deriving Cat` failed
+-- Porting note: `deriving Cat` failed
 instance SheafCat : Category (Sheaf C X) :=
   show Category (CategoryTheory.Sheaf (Opens.grothendieckTopology X) C) from inferInstance
 
@@ -146,11 +146,11 @@ def forget : TopCat.Sheaf C X ⥤ TopCat.Presheaf C X :=
 set_option linter.uppercaseLean3 false in
 #align Top.sheaf.forget TopCat.Sheaf.forget
 
--- Porting note : `deriving Full` failed
+-- Porting note: `deriving Full` failed
 instance forgetFull : Full (forget C X) where
   preimage := Sheaf.Hom.mk
 
--- Porting note : `deriving Faithful` failed
+-- Porting note: `deriving Faithful` failed
 instance forgetFaithful : Faithful (forget C X) where
   map_injective := Sheaf.Hom.ext _ _

70fd9563

chore: fix some cases in names (#7469)

And fix some names in comments where this revealed issues

be0d066c

Diff

@@ -23,7 +23,7 @@ See the docstring of `TopCat.Presheaf.IsSheaf` for an explanation on the design
 of equivalent conditions.
 
 We provide the instance `CategoryTheory.Category (TopCat.Sheaf C X)` as the full subcategory of
-presheaves, and the fully faithful functor `sheaf.forget : TopCat.Sheaf C X ⥤ TopCat.Presheaf C X`.
+presheaves, and the fully faithful functor `Sheaf.forget : TopCat.Sheaf C X ⥤ TopCat.Presheaf C X`.
 
 -/

70fd9563

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module topology.sheaves.sheaf
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Sheaves.Presheaf
 import Mathlib.CategoryTheory.Sites.Sheaf
 import Mathlib.CategoryTheory.Sites.Spaces
 
+#align_import topology.sheaves.sheaf from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 # Sheaves

70fd9563

chore: fix grammar 3/3 (#5003)

Part 3 of #5001

df58f20b

Diff

@@ -19,7 +19,7 @@ We define sheaves on a topological space, with values in an arbitrary category.
 
 A presheaf on a topological space `X` is a sheaf precisely when it is a sheaf under the
 grothendieck topology on `opens X`, which expands out to say: For each open cover `{ Uᵢ }` of
-`U`, and a family of compatible functions `A ⟶ F(Uᵢ)` for an `A : X`, there exists an unique
+`U`, and a family of compatible functions `A ⟶ F(Uᵢ)` for an `A : X`, there exists a unique
 gluing `A ⟶ F(U)` compatible with the restriction.
 
 See the docstring of `TopCat.Presheaf.IsSheaf` for an explanation on the design decisions and a list
@@ -54,7 +54,7 @@ The equivalent formulations of the sheaf condition on `presheaf C X` are as foll
 1. `TopCat.Presheaf.IsSheaf`: (the official definition)
   It is a sheaf with respect to the grothendieck topology on `opens X`, which is to say:
   For each open cover `{ Uᵢ }` of `U`, and a family of compatible functions `A ⟶ F(Uᵢ)` for an
-  `A : X`, there exists an unique gluing `A ⟶ F(U)` compatible with the restriction.
+  `A : X`, there exists a unique gluing `A ⟶ F(U)` compatible with the restriction.
 
 2. `TopCat.Presheaf.IsSheafEqualizerProducts`: (requires `C` to have all products)
   For each open cover `{ Uᵢ }` of `U`, `F(U) ⟶ ∏ F(Uᵢ)` is the equalizer of the two morphisms

70fd9563

chore: tidy various files (#4466)

46aa58dc

Diff

@@ -25,8 +25,8 @@ gluing `A ⟶ F(U)` compatible with the restriction.
 See the docstring of `TopCat.Presheaf.IsSheaf` for an explanation on the design decisions and a list
 of equivalent conditions.
 
-We provide the instance `category (sheaf C X)` as the full subcategory of presheaves,
-and the fully faithful functor `sheaf.forget : sheaf C X ⥤ presheaf C X`.
+We provide the instance `CategoryTheory.Category (TopCat.Sheaf C X)` as the full subcategory of
+presheaves, and the fully faithful functor `sheaf.forget : TopCat.Sheaf C X ⥤ TopCat.Presheaf C X`.
 
 -/
 
@@ -35,15 +35,7 @@ universe w v u
 
 noncomputable section
 
-open CategoryTheory
-
-open CategoryTheory.Limits
-
-open TopologicalSpace
-
-open Opposite
-
-open TopologicalSpace.Opens
+open CategoryTheory CategoryTheory.Limits TopologicalSpace Opposite TopologicalSpace.Opens
 
 namespace TopCat
 
@@ -64,37 +56,36 @@ The equivalent formulations of the sheaf condition on `presheaf C X` are as foll
   For each open cover `{ Uᵢ }` of `U`, and a family of compatible functions `A ⟶ F(Uᵢ)` for an
   `A : X`, there exists an unique gluing `A ⟶ F(U)` compatible with the restriction.
 
-2. `Top.presheaf.is_sheaf_equalizer_products`: (requires `C` to have all products)
+2. `TopCat.Presheaf.IsSheafEqualizerProducts`: (requires `C` to have all products)
   For each open cover `{ Uᵢ }` of `U`, `F(U) ⟶ ∏ F(Uᵢ)` is the equalizer of the two morphisms
   `∏ F(Uᵢ) ⟶ ∏ F(Uᵢ ∩ Uⱼ)`.
-  See `Top.presheaf.is_sheaf_iff_is_sheaf_equalizer_products`.
+  See `TopCat.Presheaf.isSheaf_iff_isSheafEqualizerProducts`.
 
 3. `TopCat.Presheaf.IsSheafOpensLeCover`:
   For each open cover `{ Uᵢ }` of `U`, `F(U)` is the limit of the diagram consisting of arrows
   `F(V₁) ⟶ F(V₂)` for every pair of open sets `V₁ ⊇ V₂` that are contained in some `Uᵢ`.
   See `TopCat.Presheaf.isSheaf_iff_isSheafOpensLeCover`.
 
-4. `Top.presheaf.is_sheaf_pairwise_intersections`:
+4. `TopCat.Presheaf.IsSheafPairwiseIntersections`:
   For each open cover `{ Uᵢ }` of `U`, `F(U)` is the limit of the diagram consisting of arrows
   from `F(Uᵢ)` and `F(Uⱼ)` to `F(Uᵢ ∩ Uⱼ)` for each pair `(i, j)`.
-  See `Top.presheaf.is_sheaf_iff_is_sheaf_pairwise_intersections`.
+  See `TopCat.Presheaf.isSheaf_iff_isSheafPairwiseIntersections`.
 
 The following requires `C` to be concrete and complete, and `forget C` to reflect isomorphisms and
 preserve limits. This applies to most "algebraic" categories, e.g. groups, abelian groups and rings.
 
-5. `Top.presheaf.is_sheaf_unique_gluing`:
+5. `TopCat.Presheaf.IsSheafUniqueGluing`:
   (requires `C` to be concrete and complete; `forget C` to reflect isomorphisms and preserve limits)
   For each open cover `{ Uᵢ }` of `U`, and a compatible family of elements `x : F(Uᵢ)`, there exists
   a unique gluing `x : F(U)` that restricts to the given elements.
-  See `Top.presheaf.is_sheaf_iff_is_sheaf_unique_gluing`.
+  See `TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluing`.
 
 6. The underlying sheaf of types is a sheaf.
-  See `Top.presheaf.is_sheaf_iff_is_sheaf_comp` and
+  See `TopCat.Presheaf.isSheaf_iff_isSheaf_comp` and
   `CategoryTheory.Presheaf.isSheaf_iff_isSheaf_forget`.
 -/
-def IsSheaf (F : Presheaf.{w, v, u} C X) : Prop :=
-  -- Porting Note : needs full name
-  CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology X) F
+nonrec def IsSheaf (F : Presheaf.{w, v, u} C X) : Prop :=
+  Presheaf.IsSheaf (Opens.grothendieckTopology X) F
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.is_sheaf TopCat.Presheaf.IsSheaf
 
@@ -121,12 +112,11 @@ end Presheaf
 
 variable (C X)
 
-/-- A `sheaf C X` is a presheaf of objects from `C` over a (bundled) topological space `X`,
+/-- A `TopCat.Sheaf C X` is a presheaf of objects from `C` over a (bundled) topological space `X`,
 satisfying the sheaf condition.
 -/
-def Sheaf : Type max u v w :=
-  -- Porting note : need full name
-  CategoryTheory.Sheaf (Opens.grothendieckTopology X) C
+nonrec def Sheaf : Type max u v w :=
+  Sheaf (Opens.grothendieckTopology X) C
 set_option linter.uppercaseLean3 false in
 #align Top.sheaf TopCat.Sheaf

70fd9563

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -22,7 +22,7 @@ grothendieck topology on `opens X`, which expands out to say: For each open cove
 `U`, and a family of compatible functions `A ⟶ F(Uᵢ)` for an `A : X`, there exists an unique
 gluing `A ⟶ F(U)` compatible with the restriction.
 
-See the docstring of `Top.presheaf.is_sheaf` for an explanation on the design decisions and a list
+See the docstring of `TopCat.Presheaf.IsSheaf` for an explanation on the design decisions and a list
 of equivalent conditions.
 
 We provide the instance `category (sheaf C X)` as the full subcategory of presheaves,
@@ -59,7 +59,7 @@ sites could be applied here easily, and this condition does not require addition
 the value category.
 The equivalent formulations of the sheaf condition on `presheaf C X` are as follows :
 
-1. `Top.presheaf.is_sheaf`: (the official definition)
+1. `TopCat.Presheaf.IsSheaf`: (the official definition)
   It is a sheaf with respect to the grothendieck topology on `opens X`, which is to say:
   For each open cover `{ Uᵢ }` of `U`, and a family of compatible functions `A ⟶ F(Uᵢ)` for an
   `A : X`, there exists an unique gluing `A ⟶ F(U)` compatible with the restriction.
@@ -69,10 +69,10 @@ The equivalent formulations of the sheaf condition on `presheaf C X` are as foll
   `∏ F(Uᵢ) ⟶ ∏ F(Uᵢ ∩ Uⱼ)`.
   See `Top.presheaf.is_sheaf_iff_is_sheaf_equalizer_products`.
 
-3. `Top.presheaf.is_sheaf_opens_le_cover`:
+3. `TopCat.Presheaf.IsSheafOpensLeCover`:
   For each open cover `{ Uᵢ }` of `U`, `F(U)` is the limit of the diagram consisting of arrows
   `F(V₁) ⟶ F(V₂)` for every pair of open sets `V₁ ⊇ V₂` that are contained in some `Uᵢ`.
-  See `Top.presheaf.is_sheaf_iff_is_sheaf_opens_le_cover`.
+  See `TopCat.Presheaf.isSheaf_iff_isSheafOpensLeCover`.
 
 4. `Top.presheaf.is_sheaf_pairwise_intersections`:
   For each open cover `{ Uᵢ }` of `U`, `F(U)` is the limit of the diagram consisting of arrows
@@ -90,7 +90,7 @@ preserve limits. This applies to most "algebraic" categories, e.g. groups, abeli
 
 6. The underlying sheaf of types is a sheaf.
   See `Top.presheaf.is_sheaf_iff_is_sheaf_comp` and
-  `category_theory.presheaf.is_sheaf_iff_is_sheaf_forget`.
+  `CategoryTheory.Presheaf.isSheaf_iff_isSheaf_forget`.
 -/
 def IsSheaf (F : Presheaf.{w, v, u} C X) : Prop :=
   -- Porting Note : needs full name
@@ -98,7 +98,7 @@ def IsSheaf (F : Presheaf.{w, v, u} C X) : Prop :=
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.is_sheaf TopCat.Presheaf.IsSheaf
 
-/-- The presheaf valued in `unit` over any topological space is a sheaf.
+/-- The presheaf valued in `Unit` over any topological space is a sheaf.
 -/
 theorem isSheaf_unit (F : Presheaf (CategoryTheory.Discrete Unit) X) : F.IsSheaf :=
   fun x U S _ x _ => ⟨eqToHom (Subsingleton.elim _ _), by aesop_cat, fun _ => by aesop_cat⟩

70fd9563

feat: port Topology.Sheaves.Sheaf (#4088)

d8005bc5

`topology.sheaves.sheaf` ⟷ `Mathlib.Topology.Sheaves.Sheaf`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 433

topology.sheaves.sheaf ⟷ Mathlib.Topology.Sheaves.Sheaf

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 433

`topology.sheaves.sheaf` ⟷ `Mathlib.Topology.Sheaves.Sheaf`