category_theory.sites.compatible_sheafificationMathlib.CategoryTheory.Sites.CompatibleSheafification

This file has been ported!

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.

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -170,7 +170,8 @@ section
 
 -- We will sheafify `D`-valued presheaves in this section.
 variable [ConcreteCategory.{max v u} D] [PreservesLimits (forget D)]
-  [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)] [ReflectsIsomorphisms (forget D)]
+  [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)]
+  [CategoryTheory.Functor.ReflectsIsomorphisms (forget D)]
 
 #print CategoryTheory.GrothendieckTopology.sheafifyCompIso_inv_eq_sheafifyLift /-
 @[simp]
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
 import CategoryTheory.Sites.CompatiblePlus
-import CategoryTheory.Sites.Sheafification
+import CategoryTheory.Sites.ConcreteSheafification
 
 #align_import category_theory.sites.compatible_sheafification from "leanprover-community/mathlib"@"660b3a2db3522fa0db036e569dc995a615c4c848"
 
Diff
@@ -3,8 +3,8 @@ Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
-import Mathbin.CategoryTheory.Sites.CompatiblePlus
-import Mathbin.CategoryTheory.Sites.Sheafification
+import CategoryTheory.Sites.CompatiblePlus
+import CategoryTheory.Sites.Sheafification
 
 #align_import category_theory.sites.compatible_sheafification from "leanprover-community/mathlib"@"660b3a2db3522fa0db036e569dc995a615c4c848"
 
Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.sites.compatible_sheafification
-! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Sites.CompatiblePlus
 import Mathbin.CategoryTheory.Sites.Sheafification
 
+#align_import category_theory.sites.compatible_sheafification from "leanprover-community/mathlib"@"660b3a2db3522fa0db036e569dc995a615c4c848"
+
 /-!
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
 > Any changes to this file require a corresponding PR to mathlib4.
Diff
@@ -56,6 +56,7 @@ variable [∀ (X : C) (W : J.cover X) (P : Cᵒᵖ ⥤ D), PreservesLimit (W.ind
 
 variable (P : Cᵒᵖ ⥤ D)
 
+#print CategoryTheory.GrothendieckTopology.sheafifyCompIso /-
 /-- The isomorphism between the sheafification of `P` composed with `F` and
 the sheafification of `P ⋙ F`.
 
@@ -66,7 +67,9 @@ of sheafification. -/
 def sheafifyCompIso : J.sheafify P ⋙ F ≅ J.sheafify (P ⋙ F) :=
   J.plusCompIso _ _ ≪≫ (J.plusFunctor _).mapIso (J.plusCompIso _ _)
 #align category_theory.grothendieck_topology.sheafify_comp_iso CategoryTheory.GrothendieckTopology.sheafifyCompIso
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso /-
 /-- The isomorphism between the sheafification of `P` composed with `F` and
 the sheafification of `P ⋙ F`, functorially in `F`. -/
 def sheafificationWhiskerLeftIso (P : Cᵒᵖ ⥤ D)
@@ -79,7 +82,9 @@ def sheafificationWhiskerLeftIso (P : Cᵒᵖ ⥤ D)
   refine' iso_whisker_right _ _
   refine' J.plus_functor_whisker_left_iso _
 #align category_theory.grothendieck_topology.sheafification_whisker_left_iso CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_hom_app /-
 @[simp]
 theorem sheafificationWhiskerLeftIso_hom_app (P : Cᵒᵖ ⥤ D) (F : D ⥤ E)
     [∀ (F : D ⥤ E) (X : C), PreservesColimitsOfShape (J.cover X)ᵒᵖ F]
@@ -90,7 +95,9 @@ theorem sheafificationWhiskerLeftIso_hom_app (P : Cᵒᵖ ⥤ D) (F : D ⥤ E)
   dsimp [sheafification_whisker_left_iso, sheafify_comp_iso]
   rw [category.comp_id]
 #align category_theory.grothendieck_topology.sheafification_whisker_left_iso_hom_app CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_hom_app
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_inv_app /-
 @[simp]
 theorem sheafificationWhiskerLeftIso_inv_app (P : Cᵒᵖ ⥤ D) (F : D ⥤ E)
     [∀ (F : D ⥤ E) (X : C), PreservesColimitsOfShape (J.cover X)ᵒᵖ F]
@@ -101,7 +108,9 @@ theorem sheafificationWhiskerLeftIso_inv_app (P : Cᵒᵖ ⥤ D) (F : D ⥤ E)
   dsimp [sheafification_whisker_left_iso, sheafify_comp_iso]
   erw [category.id_comp]
 #align category_theory.grothendieck_topology.sheafification_whisker_left_iso_inv_app CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso_inv_app
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso /-
 /-- The isomorphism between the sheafification of `P` composed with `F` and
 the sheafification of `P ⋙ F`, functorially in `P`. -/
 def sheafificationWhiskerRightIso :
@@ -114,7 +123,9 @@ def sheafificationWhiskerRightIso :
   refine' (functor.associator _ _ _).symm ≪≫ _
   exact iso_whisker_right (J.plus_functor_whisker_right_iso _) (J.plus_functor E)
 #align category_theory.grothendieck_topology.sheafification_whisker_right_iso CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_hom_app /-
 @[simp]
 theorem sheafificationWhiskerRightIso_hom_app :
     (J.sheafificationWhiskerRightIso F).Hom.app P = (J.sheafifyCompIso F P).Hom :=
@@ -123,7 +134,9 @@ theorem sheafificationWhiskerRightIso_hom_app :
   simp only [category.id_comp, category.comp_id]
   erw [category.id_comp]
 #align category_theory.grothendieck_topology.sheafification_whisker_right_iso_hom_app CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_hom_app
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_inv_app /-
 @[simp]
 theorem sheafificationWhiskerRightIso_inv_app :
     (J.sheafificationWhiskerRightIso F).inv.app P = (J.sheafifyCompIso F P).inv :=
@@ -132,7 +145,9 @@ theorem sheafificationWhiskerRightIso_inv_app :
   simp only [category.id_comp, category.comp_id]
   erw [category.id_comp]
 #align category_theory.grothendieck_topology.sheafification_whisker_right_iso_inv_app CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_inv_app
+-/
 
+#print CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom /-
 @[simp, reassoc]
 theorem whiskerRight_toSheafify_sheafifyCompIso_hom :
     whiskerRight (J.toSheafify _) _ ≫ (J.sheafifyCompIso F P).Hom = J.toSheafify _ :=
@@ -144,12 +159,15 @@ theorem whiskerRight_toSheafify_sheafifyCompIso_hom :
     category.assoc, whisker_right_to_plus_comp_plus_comp_iso_hom]
   rfl
 #align category_theory.grothendieck_topology.whisker_right_to_sheafify_sheafify_comp_iso_hom CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom
+-/
 
+#print CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv /-
 @[simp, reassoc]
 theorem toSheafify_comp_sheafifyCompIso_inv :
     J.toSheafify _ ≫ (J.sheafifyCompIso F P).inv = whiskerRight (J.toSheafify _) _ := by
   rw [iso.comp_inv_eq]; simp
 #align category_theory.grothendieck_topology.to_sheafify_comp_sheafify_comp_iso_inv CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv
+-/
 
 section
 
@@ -157,6 +175,7 @@ section
 variable [ConcreteCategory.{max v u} D] [PreservesLimits (forget D)]
   [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)] [ReflectsIsomorphisms (forget D)]
 
+#print CategoryTheory.GrothendieckTopology.sheafifyCompIso_inv_eq_sheafifyLift /-
 @[simp]
 theorem sheafifyCompIso_inv_eq_sheafifyLift :
     (J.sheafifyCompIso F P).inv =
@@ -166,6 +185,7 @@ theorem sheafifyCompIso_inv_eq_sheafifyLift :
   rw [iso.comp_inv_eq]
   simp
 #align category_theory.grothendieck_topology.sheafify_comp_iso_inv_eq_sheafify_lift CategoryTheory.GrothendieckTopology.sheafifyCompIso_inv_eq_sheafifyLift
+-/
 
 end
 
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 
 ! This file was ported from Lean 3 source module category_theory.sites.compatible_sheafification
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 660b3a2db3522fa0db036e569dc995a615c4c848
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,9 @@ import Mathbin.CategoryTheory.Sites.CompatiblePlus
 import Mathbin.CategoryTheory.Sites.Sheafification
 
 /-!
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 
 In this file, we prove that sheafification is compatible with functors which
 preserve the correct limits and colimits.
Diff
@@ -144,10 +144,8 @@ theorem whiskerRight_toSheafify_sheafifyCompIso_hom :
 
 @[simp, reassoc]
 theorem toSheafify_comp_sheafifyCompIso_inv :
-    J.toSheafify _ ≫ (J.sheafifyCompIso F P).inv = whiskerRight (J.toSheafify _) _ :=
-  by
-  rw [iso.comp_inv_eq]
-  simp
+    J.toSheafify _ ≫ (J.sheafifyCompIso F P).inv = whiskerRight (J.toSheafify _) _ := by
+  rw [iso.comp_inv_eq]; simp
 #align category_theory.grothendieck_topology.to_sheafify_comp_sheafify_comp_iso_inv CategoryTheory.GrothendieckTopology.toSheafify_comp_sheafifyCompIso_inv
 
 section
Diff
@@ -130,7 +130,7 @@ theorem sheafificationWhiskerRightIso_inv_app :
   erw [category.id_comp]
 #align category_theory.grothendieck_topology.sheafification_whisker_right_iso_inv_app CategoryTheory.GrothendieckTopology.sheafificationWhiskerRightIso_inv_app
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem whiskerRight_toSheafify_sheafifyCompIso_hom :
     whiskerRight (J.toSheafify _) _ ≫ (J.sheafifyCompIso F P).Hom = J.toSheafify _ :=
   by
@@ -142,7 +142,7 @@ theorem whiskerRight_toSheafify_sheafifyCompIso_hom :
   rfl
 #align category_theory.grothendieck_topology.whisker_right_to_sheafify_sheafify_comp_iso_hom CategoryTheory.GrothendieckTopology.whiskerRight_toSheafify_sheafifyCompIso_hom
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem toSheafify_comp_sheafifyCompIso_inv :
     J.toSheafify _ ≫ (J.sheafifyCompIso F P).inv = whiskerRight (J.toSheafify _) _ :=
   by

Changes in mathlib4

mathlib3
mathlib4
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.

Diff
@@ -135,7 +135,7 @@ section
 
 -- We will sheafify `D`-valued presheaves in this section.
 variable [ConcreteCategory.{max v u} D] [PreservesLimits (forget D)]
-  [∀ X : C, PreservesColimitsOfShape (J.Cover X)ᵒᵖ (forget D)] [ReflectsIsomorphisms (forget D)]
+  [∀ X : C, PreservesColimitsOfShape (J.Cover X)ᵒᵖ (forget D)] [(forget D).ReflectsIsomorphisms]
 
 @[simp]
 theorem sheafifyCompIso_inv_eq_sheafifyLift :
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)
Diff
@@ -27,28 +27,19 @@ open Opposite
 universe w₁ w₂ v u
 
 variable {C : Type u} [Category.{v} C] (J : GrothendieckTopology C)
-
 variable {D : Type w₁} [Category.{max v u} D]
-
 variable {E : Type w₂} [Category.{max v u} E]
-
 variable (F : D ⥤ E)
 
 -- Porting note: Removed this and made whatever necessary noncomputable
 -- noncomputable section
 
 variable [∀ (α β : Type max v u) (fst snd : β → α), HasLimitsOfShape (WalkingMulticospan fst snd) D]
-
 variable [∀ (α β : Type max v u) (fst snd : β → α), HasLimitsOfShape (WalkingMulticospan fst snd) E]
-
 variable [∀ X : C, HasColimitsOfShape (J.Cover X)ᵒᵖ D]
-
 variable [∀ X : C, HasColimitsOfShape (J.Cover X)ᵒᵖ E]
-
 variable [∀ X : C, PreservesColimitsOfShape (J.Cover X)ᵒᵖ F]
-
 variable [∀ (X : C) (W : J.Cover X) (P : Cᵒᵖ ⥤ D), PreservesLimit (W.index P).multicospan F]
-
 variable (P : Cᵒᵖ ⥤ D)
 
 /-- The isomorphism between the sheafification of `P` composed with `F` and
style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

  • converts "--porting note" into "-- Porting note";
  • converts "porting note" into "Porting note".
Diff
@@ -34,7 +34,7 @@ variable {E : Type w₂} [Category.{max v u} E]
 
 variable (F : D ⥤ E)
 
--- porting note: Removed this and made whatever necessary noncomputable
+-- Porting note: Removed this and made whatever necessary noncomputable
 -- noncomputable section
 
 variable [∀ (α β : Type max v u) (fst snd : β → α), HasLimitsOfShape (WalkingMulticospan fst snd) D]
chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

Diff
@@ -72,7 +72,7 @@ noncomputable def sheafificationWhiskerLeftIso (P : Cᵒᵖ ⥤ D)
     (whiskeringLeft _ _ _).obj P ⋙ J.sheafification E := by
   refine' J.plusFunctorWhiskerLeftIso _ ≪≫ _ ≪≫ Functor.associator _ _ _
   refine' isoWhiskerRight _ _
-  refine' J.plusFunctorWhiskerLeftIso _
+  exact J.plusFunctorWhiskerLeftIso _
 #align category_theory.grothendieck_topology.sheafification_whisker_left_iso CategoryTheory.GrothendieckTopology.sheafificationWhiskerLeftIso
 
 @[simp]
chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
 import Mathlib.CategoryTheory.Sites.CompatiblePlus
-import Mathlib.CategoryTheory.Sites.LeftExact
+import Mathlib.CategoryTheory.Sites.ConcreteSheafification
 
 #align_import category_theory.sites.compatible_sheafification from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
 
refactor(CategoryTheory/Sites): sheafification as an abstract left adjoint (#9012)

We define a typeclass HasSheafify which says that presheaves on a site with values in some category can be sheafified, i.e. that the inclusion functor from sheaves to presheaves has a left exact left adjoint. We redefine presheafToSheaf as an arbitrary choice of such a left adjoint.

Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
 import Mathlib.CategoryTheory.Sites.CompatiblePlus
-import Mathlib.CategoryTheory.Sites.ConcreteSheafification
+import Mathlib.CategoryTheory.Sites.LeftExact
 
 #align_import category_theory.sites.compatible_sheafification from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
 
refactor(CategoryTheory/Sites): rename Sheafification file (#9042)

In preparation for #9012, to make the diff nicer.

Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
 import Mathlib.CategoryTheory.Sites.CompatiblePlus
-import Mathlib.CategoryTheory.Sites.Sheafification
+import Mathlib.CategoryTheory.Sites.ConcreteSheafification
 
 #align_import category_theory.sites.compatible_sheafification from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
 
feat(CategoryTheory): a version of sheafCompose for functors preserving smaller limits (#8235)

Introduces a new typeclass GrothendieckTopology.HasSheafCompose F which says that a sheaf postcomposed with the functor F is still a sheaf. The previous API proved that a functor preserving certain limits has this property, this PR also adds a proof that a functor preserving limits of a smaller size has this property.

Diff
@@ -149,7 +149,8 @@ variable [ConcreteCategory.{max v u} D] [PreservesLimits (forget D)]
 @[simp]
 theorem sheafifyCompIso_inv_eq_sheafifyLift :
     (J.sheafifyCompIso F P).inv =
-      J.sheafifyLift (whiskerRight (J.toSheafify P) F) ((J.sheafify_isSheaf _).comp _) := by
+      J.sheafifyLift (whiskerRight (J.toSheafify P) F)
+        (HasSheafCompose.isSheaf _ ((J.sheafify_isSheaf _))) := by
   apply J.sheafifyLift_unique
   rw [Iso.comp_inv_eq]
   simp
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

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

Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.sites.compatible_sheafification
-! 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.CategoryTheory.Sites.CompatiblePlus
 import Mathlib.CategoryTheory.Sites.Sheafification
 
+#align_import category_theory.sites.compatible_sheafification from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 
 In this file, we prove that sheafification is compatible with functors which
feat: port CategoryTheory.Sites.CompatibleSheafification (#4953)

Co-authored-by: Moritz Firsching <firsching@google.com>

Dependencies 3 + 325

326 files ported (99.1%)
134011 lines ported (99.2%)
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The unported dependencies are