topology.sheaves.functors | 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

85d6221d

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

0b7c740e

bump to nightly-2023-10-23-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

7d0f9ed6

Diff

@@ -42,7 +42,6 @@ namespace TopCat
 
 namespace Presheaf.SheafConditionPairwiseIntersections
 
-#print TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagram /-
 theorem map_diagram : Pairwise.diagram U ⋙ Opens.map f = Pairwise.diagram ((Opens.map f).obj ∘ U) :=
   by
   apply functor.hext
@@ -50,9 +49,7 @@ theorem map_diagram : Pairwise.diagram U ⋙ Opens.map f = Pairwise.diagram ((Op
   intro i j g; apply Subsingleton.helim
   iterate 2 rw [map_diagram.obj_eq]
 #align Top.presheaf.sheaf_condition_pairwise_intersections.map_diagram TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagram
--/
 
-#print TopCat.Presheaf.SheafConditionPairwiseIntersections.mapCocone /-
 theorem mapCocone :
     HEq ((Opens.map f).mapCocone (Pairwise.cocone U)) (Pairwise.cocone ((Opens.map f).obj ∘ U)) :=
   by
@@ -61,9 +58,7 @@ theorem mapCocone :
   apply Subsingleton.helim; rw [map_diagram, opens.map_supr]
   apply proof_irrel_heq
 #align Top.presheaf.sheaf_condition_pairwise_intersections.map_cocone TopCat.Presheaf.SheafConditionPairwiseIntersections.mapCocone
--/
 
-#print TopCat.Presheaf.SheafConditionPairwiseIntersections.pushforward_sheaf_of_sheaf /-
 theorem pushforward_sheaf_of_sheaf {F : Presheaf C X} (h : F.IsSheafPairwiseIntersections) :
     (f _* F).IsSheafPairwiseIntersections := fun ι U =>
   by
@@ -72,7 +67,6 @@ theorem pushforward_sheaf_of_sheaf {F : Presheaf C X} (h : F.IsSheafPairwiseInte
   change HEq (F.map_cone ((opens.map f).mapCocone _).op) _
   congr; iterate 2 rw [map_diagram]; apply map_cocone
 #align Top.presheaf.sheaf_condition_pairwise_intersections.pushforward_sheaf_of_sheaf TopCat.Presheaf.SheafConditionPairwiseIntersections.pushforward_sheaf_of_sheaf
--/
 
 end Presheaf.SheafConditionPairwiseIntersections

0b7c740e

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Junyan Xu. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Junyan Xu
 -/
-import Mathbin.Topology.Sheaves.SheafCondition.PairwiseIntersections
+import Topology.Sheaves.SheafCondition.PairwiseIntersections
 
 #align_import topology.sheaves.functors from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"

0b7c740e

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Junyan Xu. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Junyan Xu
-
-! This file was ported from Lean 3 source module topology.sheaves.functors
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Sheaves.SheafCondition.PairwiseIntersections
 
+#align_import topology.sheaves.functors from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # functors between categories of sheaves

0b7c740e

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -45,6 +45,7 @@ namespace TopCat
 
 namespace Presheaf.SheafConditionPairwiseIntersections
 
+#print TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagram /-
 theorem map_diagram : Pairwise.diagram U ⋙ Opens.map f = Pairwise.diagram ((Opens.map f).obj ∘ U) :=
   by
   apply functor.hext
@@ -52,7 +53,9 @@ theorem map_diagram : Pairwise.diagram U ⋙ Opens.map f = Pairwise.diagram ((Op
   intro i j g; apply Subsingleton.helim
   iterate 2 rw [map_diagram.obj_eq]
 #align Top.presheaf.sheaf_condition_pairwise_intersections.map_diagram TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagram
+-/
 
+#print TopCat.Presheaf.SheafConditionPairwiseIntersections.mapCocone /-
 theorem mapCocone :
     HEq ((Opens.map f).mapCocone (Pairwise.cocone U)) (Pairwise.cocone ((Opens.map f).obj ∘ U)) :=
   by
@@ -61,6 +64,7 @@ theorem mapCocone :
   apply Subsingleton.helim; rw [map_diagram, opens.map_supr]
   apply proof_irrel_heq
 #align Top.presheaf.sheaf_condition_pairwise_intersections.map_cocone TopCat.Presheaf.SheafConditionPairwiseIntersections.mapCocone
+-/
 
 #print TopCat.Presheaf.SheafConditionPairwiseIntersections.pushforward_sheaf_of_sheaf /-
 theorem pushforward_sheaf_of_sheaf {F : Presheaf C X} (h : F.IsSheafPairwiseIntersections) :
@@ -88,6 +92,7 @@ theorem pushforward_sheaf_of_sheaf {F : X.Presheaf C} (h : F.IsSheaf) : (f _* F)
 #align Top.sheaf.pushforward_sheaf_of_sheaf TopCat.Sheaf.pushforward_sheaf_of_sheaf
 -/
 
+#print TopCat.Sheaf.pushforward /-
 /-- The pushforward functor.
 -/
 def pushforward (f : X ⟶ Y) : X.Sheaf C ⥤ Y.Sheaf C
@@ -95,6 +100,7 @@ def pushforward (f : X ⟶ Y) : X.Sheaf C ⥤ Y.Sheaf C
   obj ℱ := ⟨f _* ℱ.1, pushforward_sheaf_of_sheaf f ℱ.2⟩
   map _ _ g := ⟨pushforwardMap f g.1⟩
 #align Top.sheaf.pushforward TopCat.Sheaf.pushforward
+-/
 
 end Sheaf

0b7c740e

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -69,7 +69,7 @@ theorem pushforward_sheaf_of_sheaf {F : Presheaf C X} (h : F.IsSheafPairwiseInte
   convert h ((opens.map f).obj ∘ U) using 2
   rw [← map_diagram]; rfl
   change HEq (F.map_cone ((opens.map f).mapCocone _).op) _
-  congr ; iterate 2 rw [map_diagram]; apply map_cocone
+  congr; iterate 2 rw [map_diagram]; apply map_cocone
 #align Top.presheaf.sheaf_condition_pairwise_intersections.pushforward_sheaf_of_sheaf TopCat.Presheaf.SheafConditionPairwiseIntersections.pushforward_sheaf_of_sheaf
 -/
 
@@ -83,7 +83,7 @@ open Presheaf
 /-- The pushforward of a sheaf (by a continuous map) is a sheaf.
 -/
 theorem pushforward_sheaf_of_sheaf {F : X.Presheaf C} (h : F.IsSheaf) : (f _* F).IsSheaf := by
-  rw [is_sheaf_iff_is_sheaf_pairwise_intersections] at h⊢ <;>
+  rw [is_sheaf_iff_is_sheaf_pairwise_intersections] at h ⊢ <;>
     exact sheaf_condition_pairwise_intersections.pushforward_sheaf_of_sheaf f h
 #align Top.sheaf.pushforward_sheaf_of_sheaf TopCat.Sheaf.pushforward_sheaf_of_sheaf
 -/

0b7c740e

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -45,9 +45,6 @@ namespace TopCat
 
 namespace Presheaf.SheafConditionPairwiseIntersections
 
-/- warning: Top.presheaf.sheaf_condition_pairwise_intersections.map_diagram -> TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagram is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.sheaf_condition_pairwise_intersections.map_diagram TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagramₓ'. -/
 theorem map_diagram : Pairwise.diagram U ⋙ Opens.map f = Pairwise.diagram ((Opens.map f).obj ∘ U) :=
   by
   apply functor.hext
@@ -56,9 +53,6 @@ theorem map_diagram : Pairwise.diagram U ⋙ Opens.map f = Pairwise.diagram ((Op
   iterate 2 rw [map_diagram.obj_eq]
 #align Top.presheaf.sheaf_condition_pairwise_intersections.map_diagram TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagram
 
-/- warning: Top.presheaf.sheaf_condition_pairwise_intersections.map_cocone -> TopCat.Presheaf.SheafConditionPairwiseIntersections.mapCocone is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.sheaf_condition_pairwise_intersections.map_cocone TopCat.Presheaf.SheafConditionPairwiseIntersections.mapCoconeₓ'. -/
 theorem mapCocone :
     HEq ((Opens.map f).mapCocone (Pairwise.cocone U)) (Pairwise.cocone ((Opens.map f).obj ∘ U)) :=
   by
@@ -94,12 +88,6 @@ theorem pushforward_sheaf_of_sheaf {F : X.Presheaf C} (h : F.IsSheaf) : (f _* F)
 #align Top.sheaf.pushforward_sheaf_of_sheaf TopCat.Sheaf.pushforward_sheaf_of_sheaf
 -/
 
-/- warning: Top.sheaf.pushforward -> TopCat.Sheaf.pushforward is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) -> (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.Sheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Sheaf.category.{u2, u1, u3} C _inst_1 Y))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) -> (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.Sheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.SheafCat.{u1, u2, u3} C _inst_1 Y))
-Case conversion may be inaccurate. Consider using '#align Top.sheaf.pushforward TopCat.Sheaf.pushforwardₓ'. -/
 /-- The pushforward functor.
 -/
 def pushforward (f : X ⟶ Y) : X.Sheaf C ⥤ Y.Sheaf C

0b7c740e

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Junyan Xu
 
 ! This file was ported from Lean 3 source module topology.sheaves.functors
-! leanprover-community/mathlib commit 85d6221d32c37e68f05b2e42cde6cee658dae5e9
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Topology.Sheaves.SheafCondition.PairwiseIntersections
 /-!
 # functors between categories of sheaves
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Show that the pushforward of a sheaf is a sheaf, and define
 the pushforward functor from the category of C-valued sheaves
 on X to that of sheaves on Y, given a continuous map between
@@ -42,6 +45,9 @@ namespace TopCat
 
 namespace Presheaf.SheafConditionPairwiseIntersections
 
+/- warning: Top.presheaf.sheaf_condition_pairwise_intersections.map_diagram -> TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagram is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.sheaf_condition_pairwise_intersections.map_diagram TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagramₓ'. -/
 theorem map_diagram : Pairwise.diagram U ⋙ Opens.map f = Pairwise.diagram ((Opens.map f).obj ∘ U) :=
   by
   apply functor.hext
@@ -50,6 +56,9 @@ theorem map_diagram : Pairwise.diagram U ⋙ Opens.map f = Pairwise.diagram ((Op
   iterate 2 rw [map_diagram.obj_eq]
 #align Top.presheaf.sheaf_condition_pairwise_intersections.map_diagram TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagram
 
+/- warning: Top.presheaf.sheaf_condition_pairwise_intersections.map_cocone -> TopCat.Presheaf.SheafConditionPairwiseIntersections.mapCocone is a dubious translation:
+<too large>
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.sheaf_condition_pairwise_intersections.map_cocone TopCat.Presheaf.SheafConditionPairwiseIntersections.mapCoconeₓ'. -/
 theorem mapCocone :
     HEq ((Opens.map f).mapCocone (Pairwise.cocone U)) (Pairwise.cocone ((Opens.map f).obj ∘ U)) :=
   by
@@ -59,6 +68,7 @@ theorem mapCocone :
   apply proof_irrel_heq
 #align Top.presheaf.sheaf_condition_pairwise_intersections.map_cocone TopCat.Presheaf.SheafConditionPairwiseIntersections.mapCocone
 
+#print TopCat.Presheaf.SheafConditionPairwiseIntersections.pushforward_sheaf_of_sheaf /-
 theorem pushforward_sheaf_of_sheaf {F : Presheaf C X} (h : F.IsSheafPairwiseIntersections) :
     (f _* F).IsSheafPairwiseIntersections := fun ι U =>
   by
@@ -67,6 +77,7 @@ theorem pushforward_sheaf_of_sheaf {F : Presheaf C X} (h : F.IsSheafPairwiseInte
   change HEq (F.map_cone ((opens.map f).mapCocone _).op) _
   congr ; iterate 2 rw [map_diagram]; apply map_cocone
 #align Top.presheaf.sheaf_condition_pairwise_intersections.pushforward_sheaf_of_sheaf TopCat.Presheaf.SheafConditionPairwiseIntersections.pushforward_sheaf_of_sheaf
+-/
 
 end Presheaf.SheafConditionPairwiseIntersections
 
@@ -74,13 +85,21 @@ namespace Sheaf
 
 open Presheaf
 
+#print TopCat.Sheaf.pushforward_sheaf_of_sheaf /-
 /-- The pushforward of a sheaf (by a continuous map) is a sheaf.
 -/
 theorem pushforward_sheaf_of_sheaf {F : X.Presheaf C} (h : F.IsSheaf) : (f _* F).IsSheaf := by
   rw [is_sheaf_iff_is_sheaf_pairwise_intersections] at h⊢ <;>
     exact sheaf_condition_pairwise_intersections.pushforward_sheaf_of_sheaf f h
 #align Top.sheaf.pushforward_sheaf_of_sheaf TopCat.Sheaf.pushforward_sheaf_of_sheaf
+-/
 
+/- warning: Top.sheaf.pushforward -> TopCat.Sheaf.pushforward is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} TopCat.largeCategory.{u1})) X Y) -> (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.Sheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.Sheaf.category.{u2, u1, u3} C _inst_1 Y))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} {Y : TopCat.{u1}}, (Quiver.Hom.{succ u1, succ u1} TopCat.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} TopCat.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} TopCat.{u1} instTopCatLargeCategory.{u1})) X Y) -> (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.Sheaf.{u1, u2, u3} C _inst_1 Y) (TopCat.SheafCat.{u1, u2, u3} C _inst_1 Y))
+Case conversion may be inaccurate. Consider using '#align Top.sheaf.pushforward TopCat.Sheaf.pushforwardₓ'. -/
 /-- The pushforward functor.
 -/
 def pushforward (f : X ⟶ Y) : X.Sheaf C ⥤ Y.Sheaf C

85d6221d

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

85d6221d

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

@@ -82,7 +82,7 @@ variable {C}
 variable (A : Type*) [Category.{w} A] [ConcreteCategory.{w} A] [HasColimits A] [HasLimits A]
 variable [PreservesLimits (CategoryTheory.forget A)]
 variable [PreservesFilteredColimits (CategoryTheory.forget A)]
-variable [ReflectsIsomorphisms (CategoryTheory.forget A)]
+variable [(CategoryTheory.forget A).ReflectsIsomorphisms]
 
 /--
 The pullback functor.

85d6221d

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

@@ -37,9 +37,7 @@ open CategoryTheory.Limits
 open TopologicalSpace
 
 variable {C : Type u} [Category.{v} C]
-
 variable {X Y : TopCat.{w}} (f : X ⟶ Y)
-
 variable ⦃ι : Type w⦄ {U : ι → Opens Y}
 
 namespace TopCat

85d6221d

refactor(CategoryTheory/Sites): continuous functors (#8408)

This PR introduces the typeclass Functor.IsContinuous which says that the precomposition with a functor preserves the sheaf condition for Grothendieck topologies. It slightly refactors the previous main theorem about CoverPreserving and CompatiblePreserving functors: it now states that such functors are continuous. The pushforward functor for a continuous functor is defined under the Functor.IsContinuous assumption rather than the combination of both CoverPreserving and CompatiblePreserving. The property CoverLifting is renamed IsCocontinuous and it is made a class. The property IsCoverDense is also made a class.

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

83613d27

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Junyan Xu, Andrew Yang
 -/
 import Mathlib.Topology.Sheaves.SheafCondition.Sites
-import Mathlib.CategoryTheory.Sites.Pushforward
+import Mathlib.CategoryTheory.Sites.Pullback
 
 #align_import topology.sheaves.functors from "leanprover-community/mathlib"@"85d6221d32c37e68f05b2e42cde6cee658dae5e9"
 
@@ -51,8 +51,7 @@ open Presheaf
 /-- The pushforward of a sheaf (by a continuous map) is a sheaf.
 -/
 theorem pushforward_sheaf_of_sheaf {F : X.Presheaf C} (h : F.IsSheaf) : (f _* F).IsSheaf :=
-  pullback_isSheaf_of_coverPreserving (compatiblePreserving_opens_map f)
-    (coverPreserving_opens_map f) ⟨F, h⟩
+  (Opens.map f).op_comp_isSheaf _ _ ⟨_, h⟩
 set_option linter.uppercaseLean3 false in
 #align Top.sheaf.pushforward_sheaf_of_sheaf TopCat.Sheaf.pushforward_sheaf_of_sheaf
 
@@ -61,7 +60,7 @@ variable (C)
 /-- The pushforward functor.
 -/
 def pushforward (f : X ⟶ Y) : X.Sheaf C ⥤ Y.Sheaf C :=
-  Sites.pullback _ (compatiblePreserving_opens_map f) (coverPreserving_opens_map f)
+  (Opens.map f).sheafPushforwardContinuous _ _ _
 set_option linter.uppercaseLean3 false in
 #align Top.sheaf.pushforward TopCat.Sheaf.pushforward
 
@@ -88,10 +87,10 @@ variable [PreservesFilteredColimits (CategoryTheory.forget A)]
 variable [ReflectsIsomorphisms (CategoryTheory.forget A)]
 
 /--
-The pushforward functor.
+The pullback functor.
 -/
 def pullback (f : X ⟶ Y) : Y.Sheaf A ⥤ X.Sheaf A :=
-Sites.pushforward A _ _ (Opens.map f)
+  (Opens.map f).sheafPullback _ _ _
 
 lemma pullback_eq (f : X ⟶ Y) :
     pullback A f = forget A Y ⋙ Presheaf.pullback A f ⋙ presheafToSheaf _ _ := rfl
@@ -106,7 +105,7 @@ def pullbackIso (f : X ⟶ Y) :
 /-- The adjunction between pullback and pushforward for sheaves on topological spaces. -/
 def pullbackPushforwardAdjunction (f : X ⟶ Y) :
     pullback A f ⊣ pushforward A f :=
-Sites.pullbackPushforwardAdjunction _ _ _ _ _
+  (Opens.map f).sheafAdjunctionContinuous _ _ _
 
 instance : IsLeftAdjoint (pullback A f) := ⟨_, pullbackPushforwardAdjunction A f⟩
 instance : IsRightAdjoint (pushforward A f) := ⟨_, pullbackPushforwardAdjunction A f⟩

85d6221d

chore: tidy various files (#8175)

11572f18

Diff

@@ -51,8 +51,8 @@ open Presheaf
 /-- The pushforward of a sheaf (by a continuous map) is a sheaf.
 -/
 theorem pushforward_sheaf_of_sheaf {F : X.Presheaf C} (h : F.IsSheaf) : (f _* F).IsSheaf :=
-pullback_isSheaf_of_coverPreserving (compatiblePreserving_opens_map f)
-  (coverPreserving_opens_map f) ⟨F, h⟩
+  pullback_isSheaf_of_coverPreserving (compatiblePreserving_opens_map f)
+    (coverPreserving_opens_map f) ⟨F, h⟩
 set_option linter.uppercaseLean3 false in
 #align Top.sheaf.pushforward_sheaf_of_sheaf TopCat.Sheaf.pushforward_sheaf_of_sheaf
 
@@ -61,7 +61,7 @@ variable (C)
 /-- The pushforward functor.
 -/
 def pushforward (f : X ⟶ Y) : X.Sheaf C ⥤ Y.Sheaf C :=
-Sites.pullback _ (compatiblePreserving_opens_map f) (coverPreserving_opens_map f)
+  Sites.pullback _ (compatiblePreserving_opens_map f) (coverPreserving_opens_map f)
 set_option linter.uppercaseLean3 false in
 #align Top.sheaf.pushforward TopCat.Sheaf.pushforward
 
@@ -77,10 +77,10 @@ def pushforwardForgetIso (f : X ⟶ Y) :
 variable {C}
 
 @[simp] lemma pushforward_obj_val (f : X ⟶ Y) (F : X.Sheaf C) :
-  ((pushforward C f).obj F).1 = f _* F.1 := rfl
+    ((pushforward C f).obj F).1 = f _* F.1 := rfl
 
 @[simp] lemma pushforward_map (f : X ⟶ Y) {F F' : X.Sheaf C} (α : F ⟶ F') :
-  ((pushforward C f).map α).1 = (Presheaf.pushforward C f).map α.1 := rfl
+    ((pushforward C f).map α).1 = (Presheaf.pushforward C f).map α.1 := rfl
 
 variable (A : Type*) [Category.{w} A] [ConcreteCategory.{w} A] [HasColimits A] [HasLimits A]
 variable [PreservesLimits (CategoryTheory.forget A)]

85d6221d

feat(Topology/Sheaves/Functors): Specialize pullback-pushforward adjunction to sheaves over topological spaces. (#7722)

Port of https://github.com/leanprover-community/mathlib/pull/17561

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

33e0d3e6

Diff

@@ -1,9 +1,10 @@
 /-
 Copyright (c) 2021 Junyan Xu. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Junyan Xu
+Authors: Junyan Xu, Andrew Yang
 -/
-import Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections
+import Mathlib.Topology.Sheaves.SheafCondition.Sites
+import Mathlib.CategoryTheory.Sites.Pushforward
 
 #align_import topology.sheaves.functors from "leanprover-community/mathlib"@"85d6221d32c37e68f05b2e42cde6cee658dae5e9"
 
@@ -15,7 +16,13 @@ the pushforward functor from the category of C-valued sheaves
 on X to that of sheaves on Y, given a continuous map between
 topological spaces X and Y.
 
-TODO: pullback for presheaves and sheaves
+## Main definitions
+- `TopCat.Sheaf.pushforward`:
+    The pushforward functor between sheaf categories over topological spaces.
+- `TopCat.Sheaf.pullback`: The pullback functor between sheaf categories over topological spaces.
+- `TopCat.Sheaf.pullbackPushforwardAdjunction`:
+  The adjunction between pullback and pushforward for sheaves on topological spaces.
+
 -/
 
 
@@ -37,62 +44,74 @@ variable ⦃ι : Type w⦄ {U : ι → Opens Y}
 
 namespace TopCat
 
-namespace Presheaf.SheafConditionPairwiseIntersections
-
-theorem map_diagram :
-    Pairwise.diagram U ⋙ Opens.map f = Pairwise.diagram ((Opens.map f).obj ∘ U) := by
-  have obj_eq : ∀ (j : Pairwise ι), (Pairwise.diagram U ⋙ Opens.map f).obj j =
-    (Pairwise.diagram ((Opens.map f).toPrefunctor.obj ∘ U)).obj j
-  · rintro ⟨i⟩ <;> rfl
-  refine Functor.hext obj_eq ?_
-  intro i j g; apply Subsingleton.helim
-  rw [obj_eq, obj_eq]
-set_option linter.uppercaseLean3 false in
-#align Top.presheaf.sheaf_condition_pairwise_intersections.map_diagram TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagram
-
-theorem mapCocone :
-    HEq ((Opens.map f).mapCocone (Pairwise.cocone U))
-      (Pairwise.cocone ((Opens.map f).obj ∘ U)) := by
-  unfold Functor.mapCocone Cocones.functoriality; dsimp; congr
-  iterate 2 rw [map_diagram]; rw [Opens.map_iSup]
-  apply Subsingleton.helim; rw [map_diagram, Opens.map_iSup]
-  apply proof_irrel_heq
-set_option linter.uppercaseLean3 false in
-#align Top.presheaf.sheaf_condition_pairwise_intersections.map_cocone TopCat.Presheaf.SheafConditionPairwiseIntersections.mapCocone
-
-theorem pushforward_sheaf_of_sheaf {F : Presheaf C X} (h : F.IsSheafPairwiseIntersections) :
-    (f _* F).IsSheafPairwiseIntersections := fun ι U => by
-  convert h ((Opens.map f).obj ∘ U) using 2
-  rw [← map_diagram]; rfl
-  change HEq (Functor.mapCone F ((Opens.map f).mapCocone (Pairwise.cocone U)).op) _
-  congr
-  iterate 2 rw [map_diagram]
-  apply mapCocone
-set_option linter.uppercaseLean3 false in
-#align Top.presheaf.sheaf_condition_pairwise_intersections.pushforward_sheaf_of_sheaf TopCat.Presheaf.SheafConditionPairwiseIntersections.pushforward_sheaf_of_sheaf
-
-end Presheaf.SheafConditionPairwiseIntersections
-
 namespace Sheaf
 
 open Presheaf
 
 /-- The pushforward of a sheaf (by a continuous map) is a sheaf.
 -/
-theorem pushforward_sheaf_of_sheaf {F : X.Presheaf C} (h : F.IsSheaf) : (f _* F).IsSheaf := by
-  rw [isSheaf_iff_isSheafPairwiseIntersections] at h ⊢
-  exact SheafConditionPairwiseIntersections.pushforward_sheaf_of_sheaf f h
+theorem pushforward_sheaf_of_sheaf {F : X.Presheaf C} (h : F.IsSheaf) : (f _* F).IsSheaf :=
+pullback_isSheaf_of_coverPreserving (compatiblePreserving_opens_map f)
+  (coverPreserving_opens_map f) ⟨F, h⟩
 set_option linter.uppercaseLean3 false in
 #align Top.sheaf.pushforward_sheaf_of_sheaf TopCat.Sheaf.pushforward_sheaf_of_sheaf
 
+variable (C)
+
 /-- The pushforward functor.
 -/
-def pushforward (f : X ⟶ Y) : X.Sheaf C ⥤ Y.Sheaf C where
-  obj ℱ := ⟨f _* ℱ.1, pushforward_sheaf_of_sheaf f ℱ.2⟩
-  map {_ _} g := ⟨pushforwardMap f g.1⟩
+def pushforward (f : X ⟶ Y) : X.Sheaf C ⥤ Y.Sheaf C :=
+Sites.pullback _ (compatiblePreserving_opens_map f) (coverPreserving_opens_map f)
 set_option linter.uppercaseLean3 false in
 #align Top.sheaf.pushforward TopCat.Sheaf.pushforward
 
+lemma pushforward_forget (f : X ⟶ Y) :
+    pushforward C f ⋙ forget C Y = forget C X ⋙ Presheaf.pushforward C f := rfl
+
+/--
+Pushforward of sheaves is isomorphic (actually definitionally equal) to pushforward of presheaves.
+-/
+def pushforwardForgetIso (f : X ⟶ Y) :
+    pushforward C f ⋙ forget C Y ≅ forget C X ⋙ Presheaf.pushforward C f := Iso.refl _
+
+variable {C}
+
+@[simp] lemma pushforward_obj_val (f : X ⟶ Y) (F : X.Sheaf C) :
+  ((pushforward C f).obj F).1 = f _* F.1 := rfl
+
+@[simp] lemma pushforward_map (f : X ⟶ Y) {F F' : X.Sheaf C} (α : F ⟶ F') :
+  ((pushforward C f).map α).1 = (Presheaf.pushforward C f).map α.1 := rfl
+
+variable (A : Type*) [Category.{w} A] [ConcreteCategory.{w} A] [HasColimits A] [HasLimits A]
+variable [PreservesLimits (CategoryTheory.forget A)]
+variable [PreservesFilteredColimits (CategoryTheory.forget A)]
+variable [ReflectsIsomorphisms (CategoryTheory.forget A)]
+
+/--
+The pushforward functor.
+-/
+def pullback (f : X ⟶ Y) : Y.Sheaf A ⥤ X.Sheaf A :=
+Sites.pushforward A _ _ (Opens.map f)
+
+lemma pullback_eq (f : X ⟶ Y) :
+    pullback A f = forget A Y ⋙ Presheaf.pullback A f ⋙ presheafToSheaf _ _ := rfl
+
+/--
+The pullback of a sheaf is isomorphic (actually definitionally equal) to the sheafification
+of the pullback as a presheaf.
+-/
+def pullbackIso (f : X ⟶ Y) :
+    pullback A f ≅ forget A Y ⋙ Presheaf.pullback A f ⋙ presheafToSheaf _ _ := Iso.refl _
+
+/-- The adjunction between pullback and pushforward for sheaves on topological spaces. -/
+def pullbackPushforwardAdjunction (f : X ⟶ Y) :
+    pullback A f ⊣ pushforward A f :=
+Sites.pullbackPushforwardAdjunction _ _ _ _ _
+
+instance : IsLeftAdjoint (pullback A f) := ⟨_, pullbackPushforwardAdjunction A f⟩
+instance : IsRightAdjoint (pushforward A f) := ⟨_, pullbackPushforwardAdjunction A f⟩
+
+
 end Sheaf
 
 end TopCat

85d6221d

style: remove trailing whitespace and modify the linter to detect it (#6519)

ecc61a3b

Diff

@@ -51,7 +51,7 @@ set_option linter.uppercaseLean3 false in
 #align Top.presheaf.sheaf_condition_pairwise_intersections.map_diagram TopCat.Presheaf.SheafConditionPairwiseIntersections.map_diagram
 
 theorem mapCocone :
-    HEq ((Opens.map f).mapCocone (Pairwise.cocone U)) 
+    HEq ((Opens.map f).mapCocone (Pairwise.cocone U))
       (Pairwise.cocone ((Opens.map f).obj ∘ U)) := by
   unfold Functor.mapCocone Cocones.functoriality; dsimp; congr
   iterate 2 rw [map_diagram]; rw [Opens.map_iSup]

85d6221d

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Junyan Xu. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Junyan Xu
-
-! This file was ported from Lean 3 source module topology.sheaves.functors
-! leanprover-community/mathlib commit 85d6221d32c37e68f05b2e42cde6cee658dae5e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections
 
+#align_import topology.sheaves.functors from "leanprover-community/mathlib"@"85d6221d32c37e68f05b2e42cde6cee658dae5e9"
+
 /-!
 # functors between categories of sheaves

85d6221d

chore: remove occurrences of semicolon after space (#5713)

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

c795bd35

Diff

@@ -83,7 +83,7 @@ open Presheaf
 /-- The pushforward of a sheaf (by a continuous map) is a sheaf.
 -/
 theorem pushforward_sheaf_of_sheaf {F : X.Presheaf C} (h : F.IsSheaf) : (f _* F).IsSheaf := by
-  rw [isSheaf_iff_isSheafPairwiseIntersections] at h ⊢ ;
+  rw [isSheaf_iff_isSheafPairwiseIntersections] at h ⊢
   exact SheafConditionPairwiseIntersections.pushforward_sheaf_of_sheaf f h
 set_option linter.uppercaseLean3 false in
 #align Top.sheaf.pushforward_sheaf_of_sheaf TopCat.Sheaf.pushforward_sheaf_of_sheaf

85d6221d

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -46,7 +46,7 @@ theorem map_diagram :
     Pairwise.diagram U ⋙ Opens.map f = Pairwise.diagram ((Opens.map f).obj ∘ U) := by
   have obj_eq : ∀ (j : Pairwise ι), (Pairwise.diagram U ⋙ Opens.map f).obj j =
     (Pairwise.diagram ((Opens.map f).toPrefunctor.obj ∘ U)).obj j
-  . rintro ⟨i⟩ <;> rfl
+  · rintro ⟨i⟩ <;> rfl
   refine Functor.hext obj_eq ?_
   intro i j g; apply Subsingleton.helim
   rw [obj_eq, obj_eq]

85d6221d

feat: port Topology.Sheaves.Functors (#4392)

60dc12af

`topology.sheaves.functors` ⟷ `Mathlib.Topology.Sheaves.Functors`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 765

topology.sheaves.functors ⟷ Mathlib.Topology.Sheaves.Functors

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 765

`topology.sheaves.functors` ⟷ `Mathlib.Topology.Sheaves.Functors`