category_theory.sites.canonicalMathlib.CategoryTheory.Sites.Canonical

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
@@ -3,7 +3,7 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 -/
-import CategoryTheory.Sites.SheafOfTypes
+import CategoryTheory.Sites.IsSheafFor
 
 #align_import category_theory.sites.canonical from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
 
Diff
@@ -93,12 +93,12 @@ theorem isSheafFor_bind (P : Cᵒᵖ ⥤ Type v) (U : Sieve X) (B : ∀ ⦃Y⦄
       simpa using this
     trans s (m ≫ l ≫ h ≫ f) this
     · have := ht (U.downward_closed hf h) _ ((B _).downward_closed hl m)
-      rw [op_comp, functor_to_types.map_comp_apply] at this 
+      rw [op_comp, functor_to_types.map_comp_apply] at this
       rw [this]
       change s _ _ = s _ _
       simp
     · have : s _ _ = _ := (ht hf _ hm).symm
-      simp only [assoc] at this 
+      simp only [assoc] at this
       rw [this]
       simp
   refine' ⟨hU.amalgamate t hT, _, _⟩
@@ -181,7 +181,7 @@ def finestTopologySingle (P : Cᵒᵖ ⥤ Type v) : GrothendieckTopology C
       apply (hS _ _).IsSeparatedFor
     · intro Y f hf
       have := hR hf _ (𝟙 _)
-      rw [pullback_id, pullback_comp] at this 
+      rw [pullback_id, pullback_comp] at this
       apply this
 #align category_theory.sheaf.finest_topology_single CategoryTheory.Sheaf.finestTopologySingle
 -/
Diff
@@ -3,7 +3,7 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 -/
-import Mathbin.CategoryTheory.Sites.SheafOfTypes
+import CategoryTheory.Sites.SheafOfTypes
 
 #align_import category_theory.sites.canonical from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
 
Diff
@@ -2,14 +2,11 @@
 Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.sites.canonical
-! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Sites.SheafOfTypes
 
+#align_import category_theory.sites.canonical from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+
 /-!
 # The canonical topology on a category
 
Diff
@@ -146,7 +146,7 @@ theorem isSheafFor_trans (P : Cᵒᵖ ⥤ Type v) (R S : Sieve X) (hR : Presieve
   · intro Y f hf
     have : sieve.pullback f (bind R fun T (k : T ⟶ X) (hf : R k) => pullback k S) = R.pullback f :=
       by
-      ext (Z g)
+      ext Z g
       constructor
       · rintro ⟨W, k, l, hl, _, comm⟩
         rw [pullback_apply, ← comm]
Diff
@@ -233,10 +233,12 @@ def canonicalTopology (C : Type u) [Category.{v} C] : GrothendieckTopology C :=
 #align category_theory.sheaf.canonical_topology CategoryTheory.Sheaf.canonicalTopology
 -/
 
+#print CategoryTheory.Sheaf.isSheaf_yoneda_obj /-
 /-- `yoneda.obj X` is a sheaf for the canonical topology. -/
 theorem isSheaf_yoneda_obj (X : C) : Presieve.IsSheaf (canonicalTopology C) (yoneda.obj X) :=
   fun Y S hS => sheaf_for_finestTopology _ (Set.mem_range_self _) _ hS
 #align category_theory.sheaf.is_sheaf_yoneda_obj CategoryTheory.Sheaf.isSheaf_yoneda_obj
+-/
 
 #print CategoryTheory.Sheaf.isSheaf_of_representable /-
 /-- A representable functor is a sheaf for the canonical topology. -/
@@ -257,11 +259,13 @@ def Subcanonical (J : GrothendieckTopology C) : Prop :=
 
 namespace Subcanonical
 
+#print CategoryTheory.Sheaf.Subcanonical.of_yoneda_isSheaf /-
 /-- If every functor `yoneda.obj X` is a `J`-sheaf, then `J` is subcanonical. -/
 theorem of_yoneda_isSheaf (J : GrothendieckTopology C)
     (h : ∀ X, Presieve.IsSheaf J (yoneda.obj X)) : Subcanonical J :=
   le_finestTopology _ _ (by rintro P ⟨X, rfl⟩; apply h)
 #align category_theory.sheaf.subcanonical.of_yoneda_is_sheaf CategoryTheory.Sheaf.Subcanonical.of_yoneda_isSheaf
+-/
 
 #print CategoryTheory.Sheaf.Subcanonical.isSheaf_of_representable /-
 /-- If `J` is subcanonical, then any representable is a `J`-sheaf. -/
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 
 ! This file was ported from Lean 3 source module category_theory.sites.canonical
-! leanprover-community/mathlib commit 9e7c80f638149bfb3504ba8ff48dfdbfc949fb1a
+! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.CategoryTheory.Sites.SheafOfTypes
 /-!
 # The canonical topology on a category
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define the finest (largest) Grothendieck topology for which a given presheaf `P` is a sheaf.
 This is well defined since if `P` is a sheaf for a topology `J`, then it is a sheaf for any
 coarser (smaller) topology. Nonetheless we define the topology explicitly by specifying its sieves:
Diff
@@ -53,6 +53,7 @@ variable {X Y : C} {S : Sieve X} {R : Presieve X}
 
 variable (J J₂ : GrothendieckTopology C)
 
+#print CategoryTheory.Sheaf.isSheafFor_bind /-
 /--
 To show `P` is a sheaf for the binding of `U` with `B`, it suffices to show that `P` is a sheaf for
 `U`, that `P` is a sheaf for each sieve in `B`, and that it is separated for any pullback of any
@@ -112,7 +113,9 @@ theorem isSheafFor_bind (P : Cᵒᵖ ⥤ Type v) (U : Sieve X) (B : ∀ ⦃Y⦄
     rw [← functor_to_types.map_comp_apply, ← op_comp, hy _ (presieve.bind_comp _ _ hg),
       hU.valid_glue _ _ hf, ht hf _ hg]
 #align category_theory.sheaf.is_sheaf_for_bind CategoryTheory.Sheaf.isSheafFor_bind
+-/
 
+#print CategoryTheory.Sheaf.isSheafFor_trans /-
 /-- Given two sieves `R` and `S`, to show that `P` is a sheaf for `S`, we can show:
 * `P` is a sheaf for `R`
 * `P` is a sheaf for the pullback of `S` along any arrow in `R`
@@ -151,7 +154,9 @@ theorem isSheafFor_trans (P : Cᵒᵖ ⥤ Type v) (R S : Sieve X) (hR : Presieve
     rw [this]
     apply hR' hf
 #align category_theory.sheaf.is_sheaf_for_trans CategoryTheory.Sheaf.isSheafFor_trans
+-/
 
+#print CategoryTheory.Sheaf.finestTopologySingle /-
 /-- Construct the finest (largest) Grothendieck topology for which the given presheaf is a sheaf.
 
 This is a special case of https://stacks.math.columbia.edu/tag/00Z9, but following a different
@@ -179,7 +184,9 @@ def finestTopologySingle (P : Cᵒᵖ ⥤ Type v) : GrothendieckTopology C
       rw [pullback_id, pullback_comp] at this 
       apply this
 #align category_theory.sheaf.finest_topology_single CategoryTheory.Sheaf.finestTopologySingle
+-/
 
+#print CategoryTheory.Sheaf.finestTopology /-
 /--
 Construct the finest (largest) Grothendieck topology for which all the given presheaves are sheaves.
 
@@ -188,13 +195,17 @@ This is equal to the construction of <https://stacks.math.columbia.edu/tag/00Z9>
 def finestTopology (Ps : Set (Cᵒᵖ ⥤ Type v)) : GrothendieckTopology C :=
   sInf (finestTopologySingle '' Ps)
 #align category_theory.sheaf.finest_topology CategoryTheory.Sheaf.finestTopology
+-/
 
+#print CategoryTheory.Sheaf.sheaf_for_finestTopology /-
 /-- Check that if `P ∈ Ps`, then `P` is indeed a sheaf for the finest topology on `Ps`. -/
 theorem sheaf_for_finestTopology (Ps : Set (Cᵒᵖ ⥤ Type v)) (h : P ∈ Ps) :
     Presieve.IsSheaf (finestTopology Ps) P := fun X S hS => by
   simpa using hS _ ⟨⟨_, _, ⟨_, h, rfl⟩, rfl⟩, rfl⟩ _ (𝟙 _)
 #align category_theory.sheaf.sheaf_for_finest_topology CategoryTheory.Sheaf.sheaf_for_finestTopology
+-/
 
+#print CategoryTheory.Sheaf.le_finestTopology /-
 /--
 Check that if each `P ∈ Ps` is a sheaf for `J`, then `J` is a subtopology of `finest_topology Ps`.
 -/
@@ -206,7 +217,9 @@ theorem le_finestTopology (Ps : Set (Cᵒᵖ ⥤ Type v)) (J : GrothendieckTopol
   -- this can't be combined with the previous because the `subst` is applied at the end
   exact hJ P hP (S.pullback f) (J.pullback_stable f hS)
 #align category_theory.sheaf.le_finest_topology CategoryTheory.Sheaf.le_finestTopology
+-/
 
+#print CategoryTheory.Sheaf.canonicalTopology /-
 /-- The `canonical_topology` on a category is the finest (largest) topology for which every
 representable presheaf is a sheaf.
 
@@ -215,24 +228,29 @@ See <https://stacks.math.columbia.edu/tag/00ZA>
 def canonicalTopology (C : Type u) [Category.{v} C] : GrothendieckTopology C :=
   finestTopology (Set.range yoneda.obj)
 #align category_theory.sheaf.canonical_topology CategoryTheory.Sheaf.canonicalTopology
+-/
 
 /-- `yoneda.obj X` is a sheaf for the canonical topology. -/
 theorem isSheaf_yoneda_obj (X : C) : Presieve.IsSheaf (canonicalTopology C) (yoneda.obj X) :=
   fun Y S hS => sheaf_for_finestTopology _ (Set.mem_range_self _) _ hS
 #align category_theory.sheaf.is_sheaf_yoneda_obj CategoryTheory.Sheaf.isSheaf_yoneda_obj
 
+#print CategoryTheory.Sheaf.isSheaf_of_representable /-
 /-- A representable functor is a sheaf for the canonical topology. -/
 theorem isSheaf_of_representable (P : Cᵒᵖ ⥤ Type v) [P.Representable] :
     Presieve.IsSheaf (canonicalTopology C) P :=
   Presieve.isSheaf_iso (canonicalTopology C) P.reprW (isSheaf_yoneda_obj _)
 #align category_theory.sheaf.is_sheaf_of_representable CategoryTheory.Sheaf.isSheaf_of_representable
+-/
 
+#print CategoryTheory.Sheaf.Subcanonical /-
 /-- A subcanonical topology is a topology which is smaller than the canonical topology.
 Equivalently, a topology is subcanonical iff every representable is a sheaf.
 -/
 def Subcanonical (J : GrothendieckTopology C) : Prop :=
   J ≤ canonicalTopology C
 #align category_theory.sheaf.subcanonical CategoryTheory.Sheaf.Subcanonical
+-/
 
 namespace Subcanonical
 
@@ -242,11 +260,13 @@ theorem of_yoneda_isSheaf (J : GrothendieckTopology C)
   le_finestTopology _ _ (by rintro P ⟨X, rfl⟩; apply h)
 #align category_theory.sheaf.subcanonical.of_yoneda_is_sheaf CategoryTheory.Sheaf.Subcanonical.of_yoneda_isSheaf
 
+#print CategoryTheory.Sheaf.Subcanonical.isSheaf_of_representable /-
 /-- If `J` is subcanonical, then any representable is a `J`-sheaf. -/
 theorem isSheaf_of_representable {J : GrothendieckTopology C} (hJ : Subcanonical J)
     (P : Cᵒᵖ ⥤ Type v) [P.Representable] : Presieve.IsSheaf J P :=
   Presieve.isSheaf_of_le _ hJ (isSheaf_of_representable P)
 #align category_theory.sheaf.subcanonical.is_sheaf_of_representable CategoryTheory.Sheaf.Subcanonical.isSheaf_of_representable
+-/
 
 end Subcanonical
 
Diff
@@ -92,12 +92,12 @@ theorem isSheafFor_bind (P : Cᵒᵖ ⥤ Type v) (U : Sieve X) (B : ∀ ⦃Y⦄
       simpa using this
     trans s (m ≫ l ≫ h ≫ f) this
     · have := ht (U.downward_closed hf h) _ ((B _).downward_closed hl m)
-      rw [op_comp, functor_to_types.map_comp_apply] at this
+      rw [op_comp, functor_to_types.map_comp_apply] at this 
       rw [this]
       change s _ _ = s _ _
       simp
     · have : s _ _ = _ := (ht hf _ hm).symm
-      simp only [assoc] at this
+      simp only [assoc] at this 
       rw [this]
       simp
   refine' ⟨hU.amalgamate t hT, _, _⟩
@@ -176,7 +176,7 @@ def finestTopologySingle (P : Cᵒᵖ ⥤ Type v) : GrothendieckTopology C
       apply (hS _ _).IsSeparatedFor
     · intro Y f hf
       have := hR hf _ (𝟙 _)
-      rw [pullback_id, pullback_comp] at this
+      rw [pullback_id, pullback_comp] at this 
       apply this
 #align category_theory.sheaf.finest_topology_single CategoryTheory.Sheaf.finestTopologySingle
 
Diff
@@ -239,10 +239,7 @@ namespace Subcanonical
 /-- If every functor `yoneda.obj X` is a `J`-sheaf, then `J` is subcanonical. -/
 theorem of_yoneda_isSheaf (J : GrothendieckTopology C)
     (h : ∀ X, Presieve.IsSheaf J (yoneda.obj X)) : Subcanonical J :=
-  le_finestTopology _ _
-    (by
-      rintro P ⟨X, rfl⟩
-      apply h)
+  le_finestTopology _ _ (by rintro P ⟨X, rfl⟩; apply h)
 #align category_theory.sheaf.subcanonical.of_yoneda_is_sheaf CategoryTheory.Sheaf.Subcanonical.of_yoneda_isSheaf
 
 /-- If `J` is subcanonical, then any representable is a `J`-sheaf. -/
Diff
@@ -186,7 +186,7 @@ Construct the finest (largest) Grothendieck topology for which all the given pre
 This is equal to the construction of <https://stacks.math.columbia.edu/tag/00Z9>.
 -/
 def finestTopology (Ps : Set (Cᵒᵖ ⥤ Type v)) : GrothendieckTopology C :=
-  infₛ (finestTopologySingle '' Ps)
+  sInf (finestTopologySingle '' Ps)
 #align category_theory.sheaf.finest_topology CategoryTheory.Sheaf.finestTopology
 
 /-- Check that if `P ∈ Ps`, then `P` is indeed a sheaf for the finest topology on `Ps`. -/

Changes in mathlib4

mathlib3
mathlib4
chore: adapt to multiple goal linter 1 (#12338)

A PR accompanying #12339.

Zulip discussion

Diff
@@ -131,8 +131,8 @@ theorem isSheafFor_trans (P : Cᵒᵖ ⥤ Type v) (R S : Sieve X)
     rintro Z f ⟨W, f, g, hg, hf : S _, rfl⟩
     apply hf
   apply Presieve.isSheafFor_subsieve_aux P this
-  apply isSheafFor_bind _ _ _ hR hS
-  · intro Y f hf Z g
+  · apply isSheafFor_bind _ _ _ hR hS
+    intro Y f hf Z g
     rw [← pullback_comp]
     apply (hS (R.downward_closed hf _)).isSeparatedFor
   · intro Y f hf
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
@@ -46,9 +46,7 @@ variable {C : Type u} [Category.{v} C]
 namespace Sheaf
 
 variable {P : Cᵒᵖ ⥤ Type v}
-
 variable {X Y : C} {S : Sieve X} {R : Presieve X}
-
 variable (J J₂ : GrothendieckTopology C)
 
 /--
chore: scope open Classical (#11199)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

Diff
@@ -38,7 +38,8 @@ universe v u
 
 namespace CategoryTheory
 
-open CategoryTheory Category Limits Sieve Classical
+open scoped Classical
+open CategoryTheory Category Limits Sieve
 
 variable {C : Type u} [Category.{v} C]
 
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
@@ -84,7 +84,7 @@ theorem isSheafFor_bind (P : Cᵒᵖ ⥤ Type v) (U : Sieve X) (B : ∀ ⦃Y⦄
     apply (hB' hf (l ≫ h)).ext
     intro M m hm
     have : bind U B (m ≫ l ≫ h ≫ f) := by
-      -- porting note: had to make explicit the parameter `((m ≫ l ≫ h) ≫ f)` and
+      -- Porting note: had to make explicit the parameter `((m ≫ l ≫ h) ≫ f)` and
       -- using `by exact`
       have : bind U B ((m ≫ l ≫ h) ≫ f) := by exact Presieve.bind_comp f hf hm
       simpa using this
@@ -93,11 +93,11 @@ theorem isSheafFor_bind (P : Cᵒᵖ ⥤ Type v) (U : Sieve X) (B : ∀ ⦃Y⦄
       rw [op_comp, FunctorToTypes.map_comp_apply] at this
       rw [this]
       change s _ _ = s _ _
-      -- porting note: the proof was `by simp`
+      -- Porting note: the proof was `by simp`
       congr 1
       simp only [assoc]
     · have h : s _ _ = _ := (ht hf _ hm).symm
-      -- porting note: this was done by `simp only [assoc] at`
+      -- Porting note: this was done by `simp only [assoc] at`
       conv_lhs at h => congr; rw [assoc, assoc]
       rw [h]
       simp only [op_comp, assoc, FunctorToTypes.map_comp_apply]
chore: remove unused simps (#6632)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

Diff
@@ -134,7 +134,6 @@ theorem isSheafFor_trans (P : Cᵒᵖ ⥤ Type v) (R S : Sieve X)
   apply Presieve.isSheafFor_subsieve_aux P this
   apply isSheafFor_bind _ _ _ hR hS
   · intro Y f hf Z g
-    dsimp
     rw [← pullback_comp]
     apply (hS (R.downward_closed hf _)).isSeparatedFor
   · intro Y f hf
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
@@ -2,14 +2,11 @@
 Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.sites.canonical
-! leanprover-community/mathlib commit 9e7c80f638149bfb3504ba8ff48dfdbfc949fb1a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Sites.SheafOfTypes
 
+#align_import category_theory.sites.canonical from "leanprover-community/mathlib"@"9e7c80f638149bfb3504ba8ff48dfdbfc949fb1a"
+
 /-!
 # The canonical topology on a category
 
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.

Diff
@@ -101,7 +101,7 @@ theorem isSheafFor_bind (P : Cᵒᵖ ⥤ Type v) (U : Sieve X) (B : ∀ ⦃Y⦄
       simp only [assoc]
     · have h : s _ _ = _ := (ht hf _ hm).symm
       -- porting note: this was done by `simp only [assoc] at`
-      conv_lhs at h => congr ; rw [assoc, assoc]
+      conv_lhs at h => congr; rw [assoc, assoc]
       rw [h]
       simp only [op_comp, assoc, FunctorToTypes.map_comp_apply]
   refine' ⟨hU.amalgamate t hT, _, _⟩
chore: bump Std4 (#5219)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

Diff
@@ -143,8 +143,7 @@ theorem isSheafFor_trans (P : Cᵒᵖ ⥤ Type v) (R S : Sieve X)
   · intro Y f hf
     have : Sieve.pullback f (bind R fun T (k : T ⟶ X) (_ : R k) => pullback k S) =
         R.pullback f := by
-      ext Z
-      intro g
+      ext Z g
       constructor
       · rintro ⟨W, k, l, hl, _, comm⟩
         rw [pullback_apply, ← comm]
feat: port CategoryTheory.Sites.Canonical (#3936)

Dependencies 2 + 259

260 files ported (99.2%)
112736 lines ported (99.9%)
Show graph

The unported dependencies are