category_theory.sites.compatible_sheafification
⟷
Mathlib.CategoryTheory.Sites.CompatibleSheafification
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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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -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]
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -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"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -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"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -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.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f
@@ -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.
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
These notions on functors are now Functor.Full
, Functor.Faithful
, Functor.EssSurj
, Functor.IsEquivalence
, Functor.ReflectsIsomorphisms
. Deprecated aliases are introduced for the previous names.
@@ -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 :
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)
@@ -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
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -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]
refine
s (#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 refine
s, but maybe the current change is beneficial.
@@ -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]
@@ -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"
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.
@@ -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"
@@ -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"
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.
@@ -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
@@ -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
The unported dependencies are