category_theory.sites.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

2efd2423

(last sync)

chore(category_theory): simps should not add hom lemmas (#18742)

@[simps] should not be used to simplify the hom field of a category instance.

Very little needs to be changed when removing it.

However the problem in https://github.com/leanprover-community/mathlib4/pull/3244 with a proof by simp failing seems to be implicated by this problem. If we remove the @[simps] generated lemma for Hom there, the original proof works (although is extremely slow).

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff

@@ -373,7 +373,7 @@ instance : has_add (P ⟶ Q) :=
 instance : add_comm_group (P ⟶ Q) :=
 function.injective.add_comm_group (λ (f : Sheaf.hom P Q), f.1)
   (λ _ _ h, Sheaf.hom.ext _ _ h) rfl (λ _ _, rfl) (λ _, rfl) (λ _ _, rfl)
-  (λ _ _, by { dsimp at *, ext, simpa [*] }) (λ _ _, by { dsimp at *, ext, simpa [*] })
+  (λ _ _, by { ext, simpa [*] }) (λ _ _, by { ext, simpa [*] })
 
 instance : preadditive (Sheaf J A) :=
 { hom_group := λ P Q, infer_instance,

a67ec23d

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

2efd2423

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -330,9 +330,9 @@ def sheafToPresheaf : Sheaf J A ⥤ Cᵒᵖ ⥤ A
 #align category_theory.Sheaf_to_presheaf CategoryTheory.sheafToPresheaf
 -/
 
-instance : Full (sheafToPresheaf J A) where preimage X Y f := ⟨f⟩
+instance : CategoryTheory.Functor.Full (sheafToPresheaf J A) where preimage X Y f := ⟨f⟩
 
-instance : Faithful (sheafToPresheaf J A) where
+instance : CategoryTheory.Functor.Faithful (sheafToPresheaf J A) where
 
 #print CategoryTheory.Sheaf.Hom.mono_of_presheaf_mono /-
 /-- This is stated as a lemma to prevent class search from forming a loop since a sheaf morphism is
@@ -716,7 +716,7 @@ for the category of topological spaces, topological rings, etc since reflecting
 hold.
 -/
 theorem isSheaf_iff_isSheaf_forget (s : A ⥤ Type max v₁ u₁) [HasLimits A] [PreservesLimits s]
-    [ReflectsIsomorphisms s] : IsSheaf J P ↔ IsSheaf J (P ⋙ s) :=
+    [CategoryTheory.Functor.ReflectsIsomorphisms s] : IsSheaf J P ↔ IsSheaf J (P ⋙ s) :=
   by
   rw [is_sheaf_iff_is_sheaf', is_sheaf_iff_is_sheaf']
   apply forall_congr' fun U => _

2efd2423

bump to nightly-2024-04-10-08

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

cd0c1af5

Diff

@@ -720,7 +720,7 @@ theorem isSheaf_iff_isSheaf_forget (s : A ⥤ Type max v₁ u₁) [HasLimits A]
   by
   rw [is_sheaf_iff_is_sheaf', is_sheaf_iff_is_sheaf']
   apply forall_congr' fun U => _
-  apply ball_congr fun R hR => _
+  apply forall₂_congr fun R hR => _
   letI : reflects_limits s := reflects_limits_of_reflects_isomorphisms
   have : is_limit (s.map_cone (fork.of_ι _ (w R P))) ≃ is_limit (fork.of_ι _ (w R (P ⋙ s))) :=
     is_sheaf_for_is_sheaf_for' P s U R

2efd2423

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -7,7 +7,7 @@ import CategoryTheory.Limits.Preserves.Shapes.Equalizers
 import CategoryTheory.Limits.Preserves.Shapes.Products
 import CategoryTheory.Limits.Yoneda
 import CategoryTheory.Preadditive.FunctorCategory
-import CategoryTheory.Sites.SheafOfTypes
+import CategoryTheory.Sites.IsSheafFor
 
 #align_import category_theory.sites.sheaf from "leanprover-community/mathlib"@"2efd2423f8d25fa57cf7a179f5d8652ab4d0df44"

2efd2423

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -143,7 +143,7 @@ theorem isLimit_iff_isSheafFor :
   rw [((cone.is_limit_equiv_is_terminal _).trans (is_terminal_equiv_unique _ _)).nonempty_congr]
   rw [Classical.nonempty_pi]; constructor
   · intro hu E x hx; specialize hu hx.cone
-    erw [(hom_equiv_amalgamation hx).uniqueCongr.nonempty_congr] at hu 
+    erw [(hom_equiv_amalgamation hx).uniqueCongr.nonempty_congr] at hu
     exact (unique_subtype_iff_exists_unique _).1 hu
   · rintro h ⟨E, π⟩; let eqv := cones_equiv_sieve_compatible_family P S (op E)
     rw [← eqv.left_inv π]; erw [(hom_equiv_amalgamation (eqv π).2).uniqueCongr.nonempty_congr]
@@ -161,7 +161,7 @@ theorem subsingleton_iff_isSeparatedFor :
   by
   constructor
   · intro hs E x t₁ t₂ h₁ h₂; have hx := is_compatible_of_exists_amalgamation x ⟨t₁, h₁⟩
-    rw [compatible_iff_sieve_compatible] at hx ; specialize hs hx.cone; cases hs
+    rw [compatible_iff_sieve_compatible] at hx; specialize hs hx.cone; cases hs
     have := (hom_equiv_amalgamation hx).symm.Injective
     exact Subtype.ext_iff.1 (@this ⟨t₁, h₁⟩ ⟨t₂, h₂⟩ (hs _ _))
   · rintro h ⟨E, π⟩; let eqv := cones_equiv_sieve_compatible_family P S (op E); constructor
@@ -684,8 +684,8 @@ theorem isSheaf_iff_isSheaf' : IsSheaf J P ↔ IsSheaf' J P :=
     apply coyoneda_jointly_reflects_limits
     intro X
     have q : presieve.is_sheaf_for (P ⋙ coyoneda.obj X) _ := h X.unop _ hR
-    rw [← presieve.is_sheaf_for_iff_generate] at q 
-    rw [equalizer.presieve.sheaf_condition] at q 
+    rw [← presieve.is_sheaf_for_iff_generate] at q
+    rw [equalizer.presieve.sheaf_condition] at q
     replace q := Classical.choice q
     apply (is_sheaf_for_is_sheaf_for' _ _ _ _).symm q
   · intro h U X S hS

2efd2423

bump to nightly-2023-12-20-06

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

058cd493

Diff

@@ -421,8 +421,8 @@ open Preadditive
 
 variable [Preadditive A] {P Q : Sheaf J A}
 
-#print CategoryTheory.sheafHomHasZsmul /-
-instance sheafHomHasZsmul : SMul ℤ (P ⟶ Q)
+#print CategoryTheory.sheafHomHasZSMul /-
+instance sheafHomHasZSMul : SMul ℤ (P ⟶ Q)
     where smul n f :=
     Sheaf.Hom.mk
       { app := fun U => n • f.1.app U
@@ -436,15 +436,15 @@ instance sheafHomHasZsmul : SMul ℤ (P ⟶ Q)
           ·
             simpa only [sub_smul, one_zsmul, comp_sub, nat_trans.naturality, sub_comp,
               sub_left_inj] using ih }
-#align category_theory.Sheaf_hom_has_zsmul CategoryTheory.sheafHomHasZsmul
+#align category_theory.Sheaf_hom_has_zsmul CategoryTheory.sheafHomHasZSMul
 -/
 
 instance : Sub (P ⟶ Q) where sub f g := Sheaf.Hom.mk <| f.1 - g.1
 
 instance : Neg (P ⟶ Q) where neg f := Sheaf.Hom.mk <| -f.1
 
-#print CategoryTheory.sheafHomHasNsmul /-
-instance sheafHomHasNsmul : SMul ℕ (P ⟶ Q)
+#print CategoryTheory.sheafHomHasNSMul /-
+instance sheafHomHasNSMul : SMul ℕ (P ⟶ Q)
     where smul n f :=
     Sheaf.Hom.mk
       { app := fun U => n • f.1.app U
@@ -454,7 +454,7 @@ instance sheafHomHasNsmul : SMul ℕ (P ⟶ Q)
           ·
             simp only [Nat.succ_eq_add_one, add_smul, ih, one_nsmul, comp_add, nat_trans.naturality,
               add_comp] }
-#align category_theory.Sheaf_hom_has_nsmul CategoryTheory.sheafHomHasNsmul
+#align category_theory.Sheaf_hom_has_nsmul CategoryTheory.sheafHomHasNSMul
 -/
 
 instance : Zero (P ⟶ Q) where zero := Sheaf.Hom.mk 0

2efd2423

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2020 Kevin Buzzard, Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Bhavik Mehta
 -/
-import Mathbin.CategoryTheory.Limits.Preserves.Shapes.Equalizers
-import Mathbin.CategoryTheory.Limits.Preserves.Shapes.Products
-import Mathbin.CategoryTheory.Limits.Yoneda
-import Mathbin.CategoryTheory.Preadditive.FunctorCategory
-import Mathbin.CategoryTheory.Sites.SheafOfTypes
+import CategoryTheory.Limits.Preserves.Shapes.Equalizers
+import CategoryTheory.Limits.Preserves.Shapes.Products
+import CategoryTheory.Limits.Yoneda
+import CategoryTheory.Preadditive.FunctorCategory
+import CategoryTheory.Sites.SheafOfTypes
 
 #align_import category_theory.sites.sheaf from "leanprover-community/mathlib"@"2efd2423f8d25fa57cf7a179f5d8652ab4d0df44"

2efd2423

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Kevin Buzzard, Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.sites.sheaf
-! leanprover-community/mathlib commit 2efd2423f8d25fa57cf7a179f5d8652ab4d0df44
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Limits.Preserves.Shapes.Equalizers
 import Mathbin.CategoryTheory.Limits.Preserves.Shapes.Products
@@ -14,6 +9,8 @@ import Mathbin.CategoryTheory.Limits.Yoneda
 import Mathbin.CategoryTheory.Preadditive.FunctorCategory
 import Mathbin.CategoryTheory.Sites.SheafOfTypes
 
+#align_import category_theory.sites.sheaf from "leanprover-community/mathlib"@"2efd2423f8d25fa57cf7a179f5d8652ab4d0df44"
+
 /-!
 # Sheaves taking values in a category

2efd2423

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -80,6 +80,7 @@ open Presieve Presieve.FamilyOfElements Limits
 
 variable (P : Cᵒᵖ ⥤ A) {X : C} (S : Sieve X) (R : Presieve X) (E : Aᵒᵖ)
 
+#print CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily /-
 /-- Given a sieve `S` on `X : C`, a presheaf `P : Cᵒᵖ ⥤ A`, and an object `E` of `A`,
     the cones over the natural diagram `S.arrows.diagram.op ⋙ P` associated to `S` and `P`
     with cone point `E` are in 1-1 correspondence with sieve_compatible family of elements
@@ -105,9 +106,11 @@ def conesEquivSieveCompatibleFamily :
     rw [op_eq_iff_eq_unop]; ext; symm; apply costructured_arrow.eq_mk
   right_inv x := by ext; rfl
 #align category_theory.presheaf.cones_equiv_sieve_compatible_family CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily
+-/
 
 variable {P S E} {x : FamilyOfElements (P ⋙ coyoneda.obj E) S} (hx : x.SieveCompatible)
 
+#print CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone /-
 /-- The cone corresponding to a sieve_compatible family of elements, dot notation enabled. -/
 @[simp]
 def CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone : Cone (S.arrows.diagram.op ⋙ P)
@@ -115,7 +118,9 @@ def CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone : Cone (S.arro
   pt := E.unop
   π := (conesEquivSieveCompatibleFamily P S E).invFun ⟨x, hx⟩
 #align category_theory.presieve.family_of_elements.sieve_compatible.cone CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone
+-/
 
+#print CategoryTheory.Presheaf.homEquivAmalgamation /-
 /-- Cone morphisms from the cone corresponding to a sieve_compatible family to the natural
     cone associated to a sieve `S` and a presheaf `P` are in 1-1 correspondence with amalgamations
     of the family. -/
@@ -126,9 +131,11 @@ def homEquivAmalgamation : (hx.Cone ⟶ P.mapCone S.arrows.Cocone.op) ≃ { t //
   left_inv l := by ext; rfl
   right_inv t := by ext; rfl
 #align category_theory.presheaf.hom_equiv_amalgamation CategoryTheory.Presheaf.homEquivAmalgamation
+-/
 
 variable (P S)
 
+#print CategoryTheory.Presheaf.isLimit_iff_isSheafFor /-
 /-- Given sieve `S` and presheaf `P : Cᵒᵖ ⥤ A`, their natural associated cone is a limit cone
     iff `Hom (E, P -)` is a sheaf of types for the sieve `S` and all `E : A`. -/
 theorem isLimit_iff_isSheafFor :
@@ -145,7 +152,9 @@ theorem isLimit_iff_isSheafFor :
     rw [← eqv.left_inv π]; erw [(hom_equiv_amalgamation (eqv π).2).uniqueCongr.nonempty_congr]
     rw [unique_subtype_iff_exists_unique]; exact h _ _ (eqv π).2
 #align category_theory.presheaf.is_limit_iff_is_sheaf_for CategoryTheory.Presheaf.isLimit_iff_isSheafFor
+-/
 
+#print CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor /-
 /-- Given sieve `S` and presheaf `P : Cᵒᵖ ⥤ A`, their natural associated cone admits at most one
     morphism from every cone in the same category (i.e. over the same diagram),
     iff `Hom (E, P -)`is separated for the sieve `S` and all `E : A`. -/
@@ -162,7 +171,9 @@ theorem subsingleton_iff_isSeparatedFor :
     rw [← eqv.left_inv π]; intro f₁ f₂; let eqv' := hom_equiv_amalgamation (eqv π).2
     apply eqv'.injective; ext; apply h _ (eqv π).1 <;> exact (eqv' _).2
 #align category_theory.presheaf.subsingleton_iff_is_separated_for CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor
+-/
 
+#print CategoryTheory.Presheaf.isSheaf_iff_isLimit /-
 /-- A presheaf `P` is a sheaf for the Grothendieck topology `J` iff for every covering sieve
     `S` of `J`, the natural cone associated to `P` and `S` is a limit cone. -/
 theorem isSheaf_iff_isLimit :
@@ -171,7 +182,9 @@ theorem isSheaf_iff_isLimit :
   ⟨fun h X S hS => (isLimit_iff_isSheafFor P S).2 fun E => h E.unop S hS, fun h E X S hS =>
     (isLimit_iff_isSheafFor P S).1 (h S hS) (op E)⟩
 #align category_theory.presheaf.is_sheaf_iff_is_limit CategoryTheory.Presheaf.isSheaf_iff_isLimit
+-/
 
+#print CategoryTheory.Presheaf.isSeparated_iff_subsingleton /-
 /-- A presheaf `P` is separated for the Grothendieck topology `J` iff for every covering sieve
     `S` of `J`, the natural cone associated to `P` and `S` admits at most one morphism from every
     cone in the same category. -/
@@ -181,7 +194,9 @@ theorem isSeparated_iff_subsingleton :
   ⟨fun h X S hS => (subsingleton_iff_isSeparatedFor P S).2 fun E => h E.unop S hS, fun h E X S hS =>
     (subsingleton_iff_isSeparatedFor P S).1 (h S hS) (op E)⟩
 #align category_theory.presheaf.is_separated_iff_subsingleton CategoryTheory.Presheaf.isSeparated_iff_subsingleton
+-/
 
+#print CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve /-
 /-- Given presieve `R` and presheaf `P : Cᵒᵖ ⥤ A`, the natural cone associated to `P` and
     the sieve `sieve.generate R` generated by `R` is a limit cone iff `Hom (E, P -)` is a
     sheaf of types for the presieve `R` and all `E : A`. -/
@@ -190,7 +205,9 @@ theorem isLimit_iff_isSheafFor_presieve :
       ∀ E : Aᵒᵖ, IsSheafFor (P ⋙ coyoneda.obj E) R :=
   (isLimit_iff_isSheafFor P _).trans (forall_congr' fun _ => (isSheafFor_iff_generate _).symm)
 #align category_theory.presheaf.is_limit_iff_is_sheaf_for_presieve CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve
+-/
 
+#print CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology /-
 /-- A presheaf `P` is a sheaf for the Grothendieck topology generated by a pretopology `K`
     iff for every covering presieve `R` of `K`, the natural cone associated to `P` and
     `sieve.generate R` is a limit cone. -/
@@ -203,11 +220,13 @@ theorem isSheaf_iff_isLimit_pretopology [HasPullbacks C] (K : Pretopology C) :
     ⟨fun h X R hR => (is_limit_iff_is_sheaf_for_presieve P R).2 fun E => h E.unop R hR,
       fun h E X R hR => (is_limit_iff_is_sheaf_for_presieve P R).1 (h R hR) (op E)⟩
 #align category_theory.presheaf.is_sheaf_iff_is_limit_pretopology CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology
+-/
 
 end LimitSheafCondition
 
 variable {J}
 
+#print CategoryTheory.Presheaf.IsSheaf.amalgamate /-
 /-- This is a wrapper around `presieve.is_sheaf_for.amalgamate` to be used below.
   If `P`s a sheaf, `S` is a cover of `X`, and `x` is a collection of morphisms from `E`
   to `P` evaluated at terms in the cover which are compatible, then we can amalgamate
@@ -218,7 +237,9 @@ def IsSheaf.amalgamate {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X :
   (hP _ _ S.condition).amalgamate (fun Y f hf => x ⟨Y, f, hf⟩) fun Y₁ Y₂ Z g₁ g₂ f₁ f₂ h₁ h₂ w =>
     hx ⟨Y₁, Y₂, Z, g₁, g₂, f₁, f₂, h₁, h₂, w⟩
 #align category_theory.presheaf.is_sheaf.amalgamate CategoryTheory.Presheaf.IsSheaf.amalgamate
+-/
 
+#print CategoryTheory.Presheaf.IsSheaf.amalgamate_map /-
 @[simp, reassoc]
 theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
     (hP : Presheaf.IsSheaf J P) (S : J.cover X) (x : ∀ I : S.arrow, E ⟶ P.obj (op I.y))
@@ -230,12 +251,15 @@ theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{max v₁ u₁} A] {E :
     @presieve.is_sheaf_for.valid_glue _ _ _ _ _ _ (hP _ _ S.condition) (fun Y f hf => x ⟨Y, f, hf⟩)
       (fun Y₁ Y₂ Z g₁ g₂ f₁ f₂ h₁ h₂ w => hx ⟨Y₁, Y₂, Z, g₁, g₂, f₁, f₂, h₁, h₂, w⟩) f hf
 #align category_theory.presheaf.is_sheaf.amalgamate_map CategoryTheory.Presheaf.IsSheaf.amalgamate_map
+-/
 
+#print CategoryTheory.Presheaf.IsSheaf.hom_ext /-
 theorem IsSheaf.hom_ext {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
     (hP : Presheaf.IsSheaf J P) (S : J.cover X) (e₁ e₂ : E ⟶ P.obj (op X))
     (h : ∀ I : S.arrow, e₁ ≫ P.map I.f.op = e₂ ≫ P.map I.f.op) : e₁ = e₂ :=
   (hP _ _ S.condition).IsSeparatedFor.ext fun Y f hf => h ⟨Y, f, hf⟩
 #align category_theory.presheaf.is_sheaf.hom_ext CategoryTheory.Presheaf.IsSheaf.hom_ext
+-/
 
 #print CategoryTheory.Presheaf.isSheaf_of_iso_iff /-
 theorem isSheaf_of_iso_iff {P P' : Cᵒᵖ ⥤ A} (e : P ≅ P') : IsSheaf J P ↔ IsSheaf J P' :=
@@ -247,10 +271,12 @@ theorem isSheaf_of_iso_iff {P P' : Cᵒᵖ ⥤ A} (e : P ≅ P') : IsSheaf J P 
 
 variable (J)
 
+#print CategoryTheory.Presheaf.isSheaf_of_isTerminal /-
 theorem isSheaf_of_isTerminal {X : A} (hX : IsTerminal X) :
     Presheaf.IsSheaf J ((CategoryTheory.Functor.const _).obj X) := fun _ _ _ _ _ _ =>
   ⟨hX.from _, fun _ _ _ => hX.hom_ext _ _, fun _ _ => hX.hom_ext _ _⟩
 #align category_theory.presheaf.is_sheaf_of_is_terminal CategoryTheory.Presheaf.isSheaf_of_isTerminal
+-/
 
 end Presheaf
 
@@ -358,6 +384,7 @@ theorem isSheaf_iff_isSheaf_of_type (P : Cᵒᵖ ⥤ Type w) :
 #align category_theory.is_sheaf_iff_is_sheaf_of_type CategoryTheory.isSheaf_iff_isSheaf_of_type
 -/
 
+#print CategoryTheory.sheafEquivSheafOfTypes /-
 /-- The category of sheaves taking values in Type is the same as the category of set-valued sheaves.
 -/
 @[simps]
@@ -372,12 +399,14 @@ def sheafEquivSheafOfTypes : Sheaf J (Type w) ≌ SheafOfTypes J
   unitIso := NatIso.ofComponents (fun X => ⟨⟨𝟙 _⟩, ⟨𝟙 _⟩, by tidy, by tidy⟩) (by tidy)
   counitIso := NatIso.ofComponents (fun X => ⟨⟨𝟙 _⟩, ⟨𝟙 _⟩, by tidy, by tidy⟩) (by tidy)
 #align category_theory.Sheaf_equiv_SheafOfTypes CategoryTheory.sheafEquivSheafOfTypes
+-/
 
 instance : Inhabited (Sheaf (⊥ : GrothendieckTopology C) (Type w)) :=
   ⟨(sheafEquivSheafOfTypes _).inverse.obj default⟩
 
 variable {J} {A}
 
+#print CategoryTheory.Sheaf.isTerminalOfBotCover /-
 /-- If the empty sieve is a cover of `X`, then `F(X)` is terminal. -/
 def Sheaf.isTerminalOfBotCover (F : Sheaf J A) (X : C) (H : ⊥ ∈ J X) :
     IsTerminal (F.1.obj (op X)) :=
@@ -387,6 +416,7 @@ def Sheaf.isTerminalOfBotCover (F : Sheaf J A) (X : C) (H : ⊥ ∈ J X) :
   choose t h using F.2 Y _ H (by tidy) (by tidy)
   exact ⟨⟨t⟩, fun a => h.2 a (by tidy)⟩
 #align category_theory.Sheaf.is_terminal_of_bot_cover CategoryTheory.Sheaf.isTerminalOfBotCover
+-/
 
 section Preadditive
 
@@ -434,10 +464,12 @@ instance : Zero (P ⟶ Q) where zero := Sheaf.Hom.mk 0
 
 instance : Add (P ⟶ Q) where add f g := Sheaf.Hom.mk <| f.1 + g.1
 
+#print CategoryTheory.Sheaf.Hom.add_app /-
 @[simp]
 theorem Sheaf.Hom.add_app (f g : P ⟶ Q) (U) : (f + g).1.app U = f.1.app U + g.1.app U :=
   rfl
 #align category_theory.Sheaf.hom.add_app CategoryTheory.Sheaf.Hom.add_app
+-/
 
 instance : AddCommGroup (P ⟶ Q) :=
   Function.Injective.addCommGroup (fun f : Sheaf.Hom P Q => f.1) (fun _ _ h => Sheaf.Hom.ext _ _ h)
@@ -521,6 +553,7 @@ theorem isSheaf_iff_multifork :
 #align category_theory.presheaf.is_sheaf_iff_multifork CategoryTheory.Presheaf.isSheaf_iff_multifork
 -/
 
+#print CategoryTheory.Presheaf.isSheaf_iff_multiequalizer /-
 theorem isSheaf_iff_multiequalizer [∀ (X : C) (S : J.cover X), HasMultiequalizer (S.index P)] :
     IsSheaf J P ↔ ∀ (X : C) (S : J.cover X), IsIso (S.toMultiequalizer P) :=
   by
@@ -539,6 +572,7 @@ theorem isSheaf_iff_multiequalizer [∀ (X : C) (S : J.cover X), HasMultiequaliz
       change _ = limit.lift _ _ ≫ _
       simp
 #align category_theory.presheaf.is_sheaf_iff_multiequalizer CategoryTheory.Presheaf.isSheaf_iff_multiequalizer
+-/
 
 end MultiequalizerConditions
 
@@ -556,6 +590,7 @@ def firstObj : A :=
 #align category_theory.presheaf.first_obj CategoryTheory.Presheaf.firstObj
 -/
 
+#print CategoryTheory.Presheaf.forkMap /-
 /--
 The left morphism of the fork diagram given in Equation (3) of [MM92], as well as the fork diagram
 of <https://stacks.math.columbia.edu/tag/00VM>.
@@ -563,6 +598,7 @@ of <https://stacks.math.columbia.edu/tag/00VM>.
 def forkMap : P.obj (op U) ⟶ firstObj R P :=
   Pi.lift fun f => P.map f.2.1.op
 #align category_theory.presheaf.fork_map CategoryTheory.Presheaf.forkMap
+-/
 
 variable [HasPullbacks C]
 
@@ -590,6 +626,7 @@ def secondMap : firstObj R P ⟶ secondObj R P :=
 #align category_theory.presheaf.second_map CategoryTheory.Presheaf.secondMap
 -/
 
+#print CategoryTheory.Presheaf.w /-
 theorem w : forkMap R P ≫ firstMap R P = forkMap R P ≫ secondMap R P :=
   by
   apply limit.hom_ext
@@ -599,6 +636,7 @@ theorem w : forkMap R P ≫ firstMap R P = forkMap R P ≫ secondMap R P :=
   rw [← P.map_comp, ← op_comp, pullback.condition]
   simp
 #align category_theory.presheaf.w CategoryTheory.Presheaf.w
+-/
 
 #print CategoryTheory.Presheaf.IsSheaf' /-
 /-- An alternative definition of the sheaf condition in terms of equalizers. This is shown to be

2efd2423

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -92,14 +92,14 @@ def conesEquivSieveCompatibleFamily :
   toFun π :=
     ⟨fun Y f h => π.app (op ⟨Over.mk f, h⟩), fun _ =>
       by
-      intros ; apply (id_comp _).symm.trans; dsimp
+      intros; apply (id_comp _).symm.trans; dsimp
       convert π.naturality (Quiver.Hom.op (over.hom_mk _ _)) <;> dsimp <;> rfl⟩
   invFun x :=
     { app := fun f => x.1 f.unop.1.Hom f.unop.2
       naturality' := fun f f' g =>
         by
         refine' Eq.trans _ (x.2 f.unop.1.Hom g.unop.left f.unop.2)
-        erw [id_comp]; congr ; rw [over.w g.unop] }
+        erw [id_comp]; congr; rw [over.w g.unop] }
   left_inv π := by
     ext; dsimp; congr
     rw [op_eq_iff_eq_unop]; ext; symm; apply costructured_arrow.eq_mk
@@ -139,7 +139,7 @@ theorem isLimit_iff_isSheafFor :
   rw [((cone.is_limit_equiv_is_terminal _).trans (is_terminal_equiv_unique _ _)).nonempty_congr]
   rw [Classical.nonempty_pi]; constructor
   · intro hu E x hx; specialize hu hx.cone
-    erw [(hom_equiv_amalgamation hx).uniqueCongr.nonempty_congr] at hu
+    erw [(hom_equiv_amalgamation hx).uniqueCongr.nonempty_congr] at hu 
     exact (unique_subtype_iff_exists_unique _).1 hu
   · rintro h ⟨E, π⟩; let eqv := cones_equiv_sieve_compatible_family P S (op E)
     rw [← eqv.left_inv π]; erw [(hom_equiv_amalgamation (eqv π).2).uniqueCongr.nonempty_congr]
@@ -155,7 +155,7 @@ theorem subsingleton_iff_isSeparatedFor :
   by
   constructor
   · intro hs E x t₁ t₂ h₁ h₂; have hx := is_compatible_of_exists_amalgamation x ⟨t₁, h₁⟩
-    rw [compatible_iff_sieve_compatible] at hx; specialize hs hx.cone; cases hs
+    rw [compatible_iff_sieve_compatible] at hx ; specialize hs hx.cone; cases hs
     have := (hom_equiv_amalgamation hx).symm.Injective
     exact Subtype.ext_iff.1 (@this ⟨t₁, h₁⟩ ⟨t₂, h₂⟩ (hs _ _))
   · rintro h ⟨E, π⟩; let eqv := cones_equiv_sieve_compatible_family P S (op E); constructor
@@ -441,7 +441,7 @@ theorem Sheaf.Hom.add_app (f g : P ⟶ Q) (U) : (f + g).1.app U = f.1.app U + g.
 
 instance : AddCommGroup (P ⟶ Q) :=
   Function.Injective.addCommGroup (fun f : Sheaf.Hom P Q => f.1) (fun _ _ h => Sheaf.Hom.ext _ _ h)
-    rfl (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl) (fun _ _ => by ext; simpa [*] ) fun _ _ =>
+    rfl (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl) (fun _ _ => by ext; simpa [*]) fun _ _ =>
     by ext; simpa [*]
 
 instance : Preadditive (Sheaf J A)
@@ -552,7 +552,7 @@ The middle object of the fork diagram given in Equation (3) of [MM92], as well a
 of <https://stacks.math.columbia.edu/tag/00VM>.
 -/
 def firstObj : A :=
-  ∏ fun f : ΣV, { f : V ⟶ U // R f } => P.obj (op f.1)
+  ∏ fun f : Σ V, { f : V ⟶ U // R f } => P.obj (op f.1)
 #align category_theory.presheaf.first_obj CategoryTheory.Presheaf.firstObj
 -/
 
@@ -571,7 +571,7 @@ variable [HasPullbacks C]
 contains the data used to check a family of elements for a presieve is compatible.
 -/
 def secondObj : A :=
-  ∏ fun fg : (ΣV, { f : V ⟶ U // R f }) × ΣW, { g : W ⟶ U // R g } =>
+  ∏ fun fg : (Σ V, { f : V ⟶ U // R f }) × Σ W, { g : W ⟶ U // R g } =>
     P.obj (op (pullback fg.1.2.1 fg.2.2.1))
 #align category_theory.presheaf.second_obj CategoryTheory.Presheaf.secondObj
 -/
@@ -649,8 +649,8 @@ theorem isSheaf_iff_isSheaf' : IsSheaf J P ↔ IsSheaf' J P :=
     apply coyoneda_jointly_reflects_limits
     intro X
     have q : presieve.is_sheaf_for (P ⋙ coyoneda.obj X) _ := h X.unop _ hR
-    rw [← presieve.is_sheaf_for_iff_generate] at q
-    rw [equalizer.presieve.sheaf_condition] at q
+    rw [← presieve.is_sheaf_for_iff_generate] at q 
+    rw [equalizer.presieve.sheaf_condition] at q 
     replace q := Classical.choice q
     apply (is_sheaf_for_is_sheaf_for' _ _ _ _).symm q
   · intro h U X S hS

2efd2423

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -80,9 +80,6 @@ open Presieve Presieve.FamilyOfElements Limits
 
 variable (P : Cᵒᵖ ⥤ A) {X : C} (S : Sieve X) (R : Presieve X) (E : Aᵒᵖ)
 
-/- warning: category_theory.presheaf.cones_equiv_sieve_compatible_family -> CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.cones_equiv_sieve_compatible_family CategoryTheory.Presheaf.conesEquivSieveCompatibleFamilyₓ'. -/
 /-- Given a sieve `S` on `X : C`, a presheaf `P : Cᵒᵖ ⥤ A`, and an object `E` of `A`,
     the cones over the natural diagram `S.arrows.diagram.op ⋙ P` associated to `S` and `P`
     with cone point `E` are in 1-1 correspondence with sieve_compatible family of elements
@@ -111,9 +108,6 @@ def conesEquivSieveCompatibleFamily :
 
 variable {P S E} {x : FamilyOfElements (P ⋙ coyoneda.obj E) S} (hx : x.SieveCompatible)
 
-/- warning: category_theory.presieve.family_of_elements.sieve_compatible.cone -> CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presieve.family_of_elements.sieve_compatible.cone CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.coneₓ'. -/
 /-- The cone corresponding to a sieve_compatible family of elements, dot notation enabled. -/
 @[simp]
 def CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone : Cone (S.arrows.diagram.op ⋙ P)
@@ -122,9 +116,6 @@ def CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone : Cone (S.arro
   π := (conesEquivSieveCompatibleFamily P S E).invFun ⟨x, hx⟩
 #align category_theory.presieve.family_of_elements.sieve_compatible.cone CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone
 
-/- warning: category_theory.presheaf.hom_equiv_amalgamation -> CategoryTheory.Presheaf.homEquivAmalgamation is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.hom_equiv_amalgamation CategoryTheory.Presheaf.homEquivAmalgamationₓ'. -/
 /-- Cone morphisms from the cone corresponding to a sieve_compatible family to the natural
     cone associated to a sieve `S` and a presheaf `P` are in 1-1 correspondence with amalgamations
     of the family. -/
@@ -138,9 +129,6 @@ def homEquivAmalgamation : (hx.Cone ⟶ P.mapCone S.arrows.Cocone.op) ≃ { t //
 
 variable (P S)
 
-/- warning: category_theory.presheaf.is_limit_iff_is_sheaf_for -> CategoryTheory.Presheaf.isLimit_iff_isSheafFor is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_limit_iff_is_sheaf_for CategoryTheory.Presheaf.isLimit_iff_isSheafForₓ'. -/
 /-- Given sieve `S` and presheaf `P : Cᵒᵖ ⥤ A`, their natural associated cone is a limit cone
     iff `Hom (E, P -)` is a sheaf of types for the sieve `S` and all `E : A`. -/
 theorem isLimit_iff_isSheafFor :
@@ -158,9 +146,6 @@ theorem isLimit_iff_isSheafFor :
     rw [unique_subtype_iff_exists_unique]; exact h _ _ (eqv π).2
 #align category_theory.presheaf.is_limit_iff_is_sheaf_for CategoryTheory.Presheaf.isLimit_iff_isSheafFor
 
-/- warning: category_theory.presheaf.subsingleton_iff_is_separated_for -> CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.subsingleton_iff_is_separated_for CategoryTheory.Presheaf.subsingleton_iff_isSeparatedForₓ'. -/
 /-- Given sieve `S` and presheaf `P : Cᵒᵖ ⥤ A`, their natural associated cone admits at most one
     morphism from every cone in the same category (i.e. over the same diagram),
     iff `Hom (E, P -)`is separated for the sieve `S` and all `E : A`. -/
@@ -178,9 +163,6 @@ theorem subsingleton_iff_isSeparatedFor :
     apply eqv'.injective; ext; apply h _ (eqv π).1 <;> exact (eqv' _).2
 #align category_theory.presheaf.subsingleton_iff_is_separated_for CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor
 
-/- warning: category_theory.presheaf.is_sheaf_iff_is_limit -> CategoryTheory.Presheaf.isSheaf_iff_isLimit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf_iff_is_limit CategoryTheory.Presheaf.isSheaf_iff_isLimitₓ'. -/
 /-- A presheaf `P` is a sheaf for the Grothendieck topology `J` iff for every covering sieve
     `S` of `J`, the natural cone associated to `P` and `S` is a limit cone. -/
 theorem isSheaf_iff_isLimit :
@@ -190,9 +172,6 @@ theorem isSheaf_iff_isLimit :
     (isLimit_iff_isSheafFor P S).1 (h S hS) (op E)⟩
 #align category_theory.presheaf.is_sheaf_iff_is_limit CategoryTheory.Presheaf.isSheaf_iff_isLimit
 
-/- warning: category_theory.presheaf.is_separated_iff_subsingleton -> CategoryTheory.Presheaf.isSeparated_iff_subsingleton is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_separated_iff_subsingleton CategoryTheory.Presheaf.isSeparated_iff_subsingletonₓ'. -/
 /-- A presheaf `P` is separated for the Grothendieck topology `J` iff for every covering sieve
     `S` of `J`, the natural cone associated to `P` and `S` admits at most one morphism from every
     cone in the same category. -/
@@ -203,9 +182,6 @@ theorem isSeparated_iff_subsingleton :
     (subsingleton_iff_isSeparatedFor P S).1 (h S hS) (op E)⟩
 #align category_theory.presheaf.is_separated_iff_subsingleton CategoryTheory.Presheaf.isSeparated_iff_subsingleton
 
-/- warning: category_theory.presheaf.is_limit_iff_is_sheaf_for_presieve -> CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_limit_iff_is_sheaf_for_presieve CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieveₓ'. -/
 /-- Given presieve `R` and presheaf `P : Cᵒᵖ ⥤ A`, the natural cone associated to `P` and
     the sieve `sieve.generate R` generated by `R` is a limit cone iff `Hom (E, P -)` is a
     sheaf of types for the presieve `R` and all `E : A`. -/
@@ -215,9 +191,6 @@ theorem isLimit_iff_isSheafFor_presieve :
   (isLimit_iff_isSheafFor P _).trans (forall_congr' fun _ => (isSheafFor_iff_generate _).symm)
 #align category_theory.presheaf.is_limit_iff_is_sheaf_for_presieve CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve
 
-/- warning: category_theory.presheaf.is_sheaf_iff_is_limit_pretopology -> CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf_iff_is_limit_pretopology CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopologyₓ'. -/
 /-- A presheaf `P` is a sheaf for the Grothendieck topology generated by a pretopology `K`
     iff for every covering presieve `R` of `K`, the natural cone associated to `P` and
     `sieve.generate R` is a limit cone. -/
@@ -235,9 +208,6 @@ end LimitSheafCondition
 
 variable {J}
 
-/- warning: category_theory.presheaf.is_sheaf.amalgamate -> CategoryTheory.Presheaf.IsSheaf.amalgamate is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf.amalgamate CategoryTheory.Presheaf.IsSheaf.amalgamateₓ'. -/
 /-- This is a wrapper around `presieve.is_sheaf_for.amalgamate` to be used below.
   If `P`s a sheaf, `S` is a cover of `X`, and `x` is a collection of morphisms from `E`
   to `P` evaluated at terms in the cover which are compatible, then we can amalgamate
@@ -249,9 +219,6 @@ def IsSheaf.amalgamate {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X :
     hx ⟨Y₁, Y₂, Z, g₁, g₂, f₁, f₂, h₁, h₂, w⟩
 #align category_theory.presheaf.is_sheaf.amalgamate CategoryTheory.Presheaf.IsSheaf.amalgamate
 
-/- warning: category_theory.presheaf.is_sheaf.amalgamate_map -> CategoryTheory.Presheaf.IsSheaf.amalgamate_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf.amalgamate_map CategoryTheory.Presheaf.IsSheaf.amalgamate_mapₓ'. -/
 @[simp, reassoc]
 theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
     (hP : Presheaf.IsSheaf J P) (S : J.cover X) (x : ∀ I : S.arrow, E ⟶ P.obj (op I.y))
@@ -264,9 +231,6 @@ theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{max v₁ u₁} A] {E :
       (fun Y₁ Y₂ Z g₁ g₂ f₁ f₂ h₁ h₂ w => hx ⟨Y₁, Y₂, Z, g₁, g₂, f₁, f₂, h₁, h₂, w⟩) f hf
 #align category_theory.presheaf.is_sheaf.amalgamate_map CategoryTheory.Presheaf.IsSheaf.amalgamate_map
 
-/- warning: category_theory.presheaf.is_sheaf.hom_ext -> CategoryTheory.Presheaf.IsSheaf.hom_ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf.hom_ext CategoryTheory.Presheaf.IsSheaf.hom_extₓ'. -/
 theorem IsSheaf.hom_ext {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
     (hP : Presheaf.IsSheaf J P) (S : J.cover X) (e₁ e₂ : E ⟶ P.obj (op X))
     (h : ∀ I : S.arrow, e₁ ≫ P.map I.f.op = e₂ ≫ P.map I.f.op) : e₁ = e₂ :=
@@ -283,12 +247,6 @@ theorem isSheaf_of_iso_iff {P P' : Cᵒᵖ ⥤ A} (e : P ≅ P') : IsSheaf J P 
 
 variable (J)
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf_of_is_terminal CategoryTheory.Presheaf.isSheaf_of_isTerminalₓ'. -/
 theorem isSheaf_of_isTerminal {X : A} (hX : IsTerminal X) :
     Presheaf.IsSheaf J ((CategoryTheory.Functor.const _).obj X) := fun _ _ _ _ _ _ =>
   ⟨hX.from _, fun _ _ _ => hX.hom_ext _ _, fun _ _ => hX.hom_ext _ _⟩
@@ -400,12 +358,6 @@ theorem isSheaf_iff_isSheaf_of_type (P : Cᵒᵖ ⥤ Type w) :
 #align category_theory.is_sheaf_iff_is_sheaf_of_type CategoryTheory.isSheaf_iff_isSheaf_of_type
 -/
 
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 /-- The category of sheaves taking values in Type is the same as the category of set-valued sheaves.
 -/
 @[simps]
@@ -426,12 +378,6 @@ instance : Inhabited (Sheaf (⊥ : GrothendieckTopology C) (Type w)) :=
 
 variable {J} {A}
 
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 /-- If the empty sieve is a cover of `X`, then `F(X)` is terminal. -/
 def Sheaf.isTerminalOfBotCover (F : Sheaf J A) (X : C) (H : ⊥ ∈ J X) :
     IsTerminal (F.1.obj (op X)) :=
@@ -488,9 +434,6 @@ instance : Zero (P ⟶ Q) where zero := Sheaf.Hom.mk 0
 
 instance : Add (P ⟶ Q) where add f g := Sheaf.Hom.mk <| f.1 + g.1
 
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 @[simp]
 theorem Sheaf.Hom.add_app (f g : P ⟶ Q) (U) : (f + g).1.app U = f.1.app U + g.1.app U :=
   rfl
@@ -578,12 +521,6 @@ theorem isSheaf_iff_multifork :
 #align category_theory.presheaf.is_sheaf_iff_multifork CategoryTheory.Presheaf.isSheaf_iff_multifork
 -/
 
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 theorem isSheaf_iff_multiequalizer [∀ (X : C) (S : J.cover X), HasMultiequalizer (S.index P)] :
     IsSheaf J P ↔ ∀ (X : C) (S : J.cover X), IsIso (S.toMultiequalizer P) :=
   by
@@ -619,12 +556,6 @@ def firstObj : A :=
 #align category_theory.presheaf.first_obj CategoryTheory.Presheaf.firstObj
 -/
 
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 /--
 The left morphism of the fork diagram given in Equation (3) of [MM92], as well as the fork diagram
 of <https://stacks.math.columbia.edu/tag/00VM>.
@@ -659,12 +590,6 @@ def secondMap : firstObj R P ⟶ secondObj R P :=
 #align category_theory.presheaf.second_map CategoryTheory.Presheaf.secondMap
 -/
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.w CategoryTheory.Presheaf.wₓ'. -/
 theorem w : forkMap R P ≫ firstMap R P = forkMap R P ≫ secondMap R P :=
   by
   apply limit.hom_ext

2efd2423

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -95,29 +95,18 @@ def conesEquivSieveCompatibleFamily :
   toFun π :=
     ⟨fun Y f h => π.app (op ⟨Over.mk f, h⟩), fun _ =>
       by
-      intros
-      apply (id_comp _).symm.trans
-      dsimp
+      intros ; apply (id_comp _).symm.trans; dsimp
       convert π.naturality (Quiver.Hom.op (over.hom_mk _ _)) <;> dsimp <;> rfl⟩
   invFun x :=
     { app := fun f => x.1 f.unop.1.Hom f.unop.2
       naturality' := fun f f' g =>
         by
         refine' Eq.trans _ (x.2 f.unop.1.Hom g.unop.left f.unop.2)
-        erw [id_comp]
-        congr
-        rw [over.w g.unop] }
+        erw [id_comp]; congr ; rw [over.w g.unop] }
   left_inv π := by
-    ext
-    dsimp
-    congr
-    rw [op_eq_iff_eq_unop]
-    ext
-    symm
-    apply costructured_arrow.eq_mk
-  right_inv x := by
-    ext
-    rfl
+    ext; dsimp; congr
+    rw [op_eq_iff_eq_unop]; ext; symm; apply costructured_arrow.eq_mk
+  right_inv x := by ext; rfl
 #align category_theory.presheaf.cones_equiv_sieve_compatible_family CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily
 
 variable {P S E} {x : FamilyOfElements (P ⋙ coyoneda.obj E) S} (hx : x.SieveCompatible)
@@ -143,12 +132,8 @@ def homEquivAmalgamation : (hx.Cone ⟶ P.mapCone S.arrows.Cocone.op) ≃ { t //
     where
   toFun l := ⟨l.Hom, fun Y f hf => l.w (op ⟨Over.mk f, hf⟩)⟩
   invFun t := ⟨t.1, fun f => t.2 f.unop.1.Hom f.unop.2⟩
-  left_inv l := by
-    ext
-    rfl
-  right_inv t := by
-    ext
-    rfl
+  left_inv l := by ext; rfl
+  right_inv t := by ext; rfl
 #align category_theory.presheaf.hom_equiv_amalgamation CategoryTheory.Presheaf.homEquivAmalgamation
 
 variable (P S)
@@ -165,16 +150,12 @@ theorem isLimit_iff_isSheafFor :
   dsimp [is_sheaf_for]; simp_rw [compatible_iff_sieve_compatible]
   rw [((cone.is_limit_equiv_is_terminal _).trans (is_terminal_equiv_unique _ _)).nonempty_congr]
   rw [Classical.nonempty_pi]; constructor
-  · intro hu E x hx
-    specialize hu hx.cone
+  · intro hu E x hx; specialize hu hx.cone
     erw [(hom_equiv_amalgamation hx).uniqueCongr.nonempty_congr] at hu
     exact (unique_subtype_iff_exists_unique _).1 hu
-  · rintro h ⟨E, π⟩
-    let eqv := cones_equiv_sieve_compatible_family P S (op E)
-    rw [← eqv.left_inv π]
-    erw [(hom_equiv_amalgamation (eqv π).2).uniqueCongr.nonempty_congr]
-    rw [unique_subtype_iff_exists_unique]
-    exact h _ _ (eqv π).2
+  · rintro h ⟨E, π⟩; let eqv := cones_equiv_sieve_compatible_family P S (op E)
+    rw [← eqv.left_inv π]; erw [(hom_equiv_amalgamation (eqv π).2).uniqueCongr.nonempty_congr]
+    rw [unique_subtype_iff_exists_unique]; exact h _ _ (eqv π).2
 #align category_theory.presheaf.is_limit_iff_is_sheaf_for CategoryTheory.Presheaf.isLimit_iff_isSheafFor
 
 /- warning: category_theory.presheaf.subsingleton_iff_is_separated_for -> CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor is a dubious translation:
@@ -188,22 +169,13 @@ theorem subsingleton_iff_isSeparatedFor :
       ∀ E : Aᵒᵖ, IsSeparatedFor (P ⋙ coyoneda.obj E) S :=
   by
   constructor
-  · intro hs E x t₁ t₂ h₁ h₂
-    have hx := is_compatible_of_exists_amalgamation x ⟨t₁, h₁⟩
-    rw [compatible_iff_sieve_compatible] at hx
-    specialize hs hx.cone
-    cases hs
+  · intro hs E x t₁ t₂ h₁ h₂; have hx := is_compatible_of_exists_amalgamation x ⟨t₁, h₁⟩
+    rw [compatible_iff_sieve_compatible] at hx; specialize hs hx.cone; cases hs
     have := (hom_equiv_amalgamation hx).symm.Injective
     exact Subtype.ext_iff.1 (@this ⟨t₁, h₁⟩ ⟨t₂, h₂⟩ (hs _ _))
-  · rintro h ⟨E, π⟩
-    let eqv := cones_equiv_sieve_compatible_family P S (op E)
-    constructor
-    rw [← eqv.left_inv π]
-    intro f₁ f₂
-    let eqv' := hom_equiv_amalgamation (eqv π).2
-    apply eqv'.injective
-    ext
-    apply h _ (eqv π).1 <;> exact (eqv' _).2
+  · rintro h ⟨E, π⟩; let eqv := cones_equiv_sieve_compatible_family P S (op E); constructor
+    rw [← eqv.left_inv π]; intro f₁ f₂; let eqv' := hom_equiv_amalgamation (eqv π).2
+    apply eqv'.injective; ext; apply h _ (eqv π).1 <;> exact (eqv' _).2
 #align category_theory.presheaf.subsingleton_iff_is_separated_for CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor
 
 /- warning: category_theory.presheaf.is_sheaf_iff_is_limit -> CategoryTheory.Presheaf.isSheaf_iff_isLimit is a dubious translation:
@@ -253,9 +225,7 @@ theorem isSheaf_iff_isLimit_pretopology [HasPullbacks C] (K : Pretopology C) :
     IsSheaf (K.toGrothendieck C) P ↔
       ∀ ⦃X : C⦄ (R : Presieve X),
         R ∈ K X → Nonempty (IsLimit (P.mapCone (generate R).arrows.Cocone.op)) :=
-  by
-  dsimp [is_sheaf]
-  simp_rw [is_sheaf_pretopology]
+  by dsimp [is_sheaf]; simp_rw [is_sheaf_pretopology];
   exact
     ⟨fun h X R hR => (is_limit_iff_is_sheaf_for_presieve P R).2 fun E => h E.unop R hR,
       fun h E X R hR => (is_limit_iff_is_sheaf_for_presieve P R).1 (h R hR) (op E)⟩
@@ -528,23 +498,14 @@ theorem Sheaf.Hom.add_app (f g : P ⟶ Q) (U) : (f + g).1.app U = f.1.app U + g.
 
 instance : AddCommGroup (P ⟶ Q) :=
   Function.Injective.addCommGroup (fun f : Sheaf.Hom P Q => f.1) (fun _ _ h => Sheaf.Hom.ext _ _ h)
-    rfl (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl)
-    (fun _ _ => by
-      ext
-      simpa [*] )
-    fun _ _ => by
-    ext
-    simpa [*]
+    rfl (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl) (fun _ _ => by ext; simpa [*] ) fun _ _ =>
+    by ext; simpa [*]
 
 instance : Preadditive (Sheaf J A)
     where
   homGroup P Q := inferInstance
-  add_comp P Q R f f' g := by
-    ext
-    simp
-  comp_add P Q R f g g' := by
-    ext
-    simp
+  add_comp P Q R f f' g := by ext; simp
+  comp_add P Q R f g g' := by ext; simp
 
 end Preadditive

2efd2423

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -81,10 +81,7 @@ open Presieve Presieve.FamilyOfElements Limits
 variable (P : Cᵒᵖ ⥤ A) {X : C} (S : Sieve X) (R : Presieve X) (E : Aᵒᵖ)
 
 /- warning: category_theory.presheaf.cones_equiv_sieve_compatible_family -> CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.cones_equiv_sieve_compatible_family CategoryTheory.Presheaf.conesEquivSieveCompatibleFamilyₓ'. -/
 /-- Given a sieve `S` on `X : C`, a presheaf `P : Cᵒᵖ ⥤ A`, and an object `E` of `A`,
     the cones over the natural diagram `S.arrows.diagram.op ⋙ P` associated to `S` and `P`
@@ -126,10 +123,7 @@ def conesEquivSieveCompatibleFamily :
 variable {P S E} {x : FamilyOfElements (P ⋙ coyoneda.obj E) S} (hx : x.SieveCompatible)
 
 /- warning: category_theory.presieve.family_of_elements.sieve_compatible.cone -> CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.presieve.family_of_elements.sieve_compatible.cone CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.coneₓ'. -/
 /-- The cone corresponding to a sieve_compatible family of elements, dot notation enabled. -/
 @[simp]
@@ -140,10 +134,7 @@ def CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone : Cone (S.arro
 #align category_theory.presieve.family_of_elements.sieve_compatible.cone CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.hom_equiv_amalgamation CategoryTheory.Presheaf.homEquivAmalgamationₓ'. -/
 /-- Cone morphisms from the cone corresponding to a sieve_compatible family to the natural
     cone associated to a sieve `S` and a presheaf `P` are in 1-1 correspondence with amalgamations
@@ -163,10 +154,7 @@ def homEquivAmalgamation : (hx.Cone ⟶ P.mapCone S.arrows.Cocone.op) ≃ { t //
 variable (P S)
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_limit_iff_is_sheaf_for CategoryTheory.Presheaf.isLimit_iff_isSheafForₓ'. -/
 /-- Given sieve `S` and presheaf `P : Cᵒᵖ ⥤ A`, their natural associated cone is a limit cone
     iff `Hom (E, P -)` is a sheaf of types for the sieve `S` and all `E : A`. -/
@@ -190,10 +178,7 @@ theorem isLimit_iff_isSheafFor :
 #align category_theory.presheaf.is_limit_iff_is_sheaf_for CategoryTheory.Presheaf.isLimit_iff_isSheafFor
 
 /- warning: category_theory.presheaf.subsingleton_iff_is_separated_for -> CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.subsingleton_iff_is_separated_for CategoryTheory.Presheaf.subsingleton_iff_isSeparatedForₓ'. -/
 /-- Given sieve `S` and presheaf `P : Cᵒᵖ ⥤ A`, their natural associated cone admits at most one
     morphism from every cone in the same category (i.e. over the same diagram),
@@ -222,10 +207,7 @@ theorem subsingleton_iff_isSeparatedFor :
 #align category_theory.presheaf.subsingleton_iff_is_separated_for CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor
 
 /- warning: category_theory.presheaf.is_sheaf_iff_is_limit -> CategoryTheory.Presheaf.isSheaf_iff_isLimit is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf_iff_is_limit CategoryTheory.Presheaf.isSheaf_iff_isLimitₓ'. -/
 /-- A presheaf `P` is a sheaf for the Grothendieck topology `J` iff for every covering sieve
     `S` of `J`, the natural cone associated to `P` and `S` is a limit cone. -/
@@ -237,10 +219,7 @@ theorem isSheaf_iff_isLimit :
 #align category_theory.presheaf.is_sheaf_iff_is_limit CategoryTheory.Presheaf.isSheaf_iff_isLimit
 
 /- warning: category_theory.presheaf.is_separated_iff_subsingleton -> CategoryTheory.Presheaf.isSeparated_iff_subsingleton is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_separated_iff_subsingleton CategoryTheory.Presheaf.isSeparated_iff_subsingletonₓ'. -/
 /-- A presheaf `P` is separated for the Grothendieck topology `J` iff for every covering sieve
     `S` of `J`, the natural cone associated to `P` and `S` admits at most one morphism from every
@@ -253,10 +232,7 @@ theorem isSeparated_iff_subsingleton :
 #align category_theory.presheaf.is_separated_iff_subsingleton CategoryTheory.Presheaf.isSeparated_iff_subsingleton
 
 /- warning: category_theory.presheaf.is_limit_iff_is_sheaf_for_presieve -> CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_limit_iff_is_sheaf_for_presieve CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieveₓ'. -/
 /-- Given presieve `R` and presheaf `P : Cᵒᵖ ⥤ A`, the natural cone associated to `P` and
     the sieve `sieve.generate R` generated by `R` is a limit cone iff `Hom (E, P -)` is a
@@ -268,10 +244,7 @@ theorem isLimit_iff_isSheafFor_presieve :
 #align category_theory.presheaf.is_limit_iff_is_sheaf_for_presieve CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve
 
 /- warning: category_theory.presheaf.is_sheaf_iff_is_limit_pretopology -> CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf_iff_is_limit_pretopology CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopologyₓ'. -/
 /-- A presheaf `P` is a sheaf for the Grothendieck topology generated by a pretopology `K`
     iff for every covering presieve `R` of `K`, the natural cone associated to `P` and
@@ -293,10 +266,7 @@ end LimitSheafCondition
 variable {J}
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf.amalgamate CategoryTheory.Presheaf.IsSheaf.amalgamateₓ'. -/
 /-- This is a wrapper around `presieve.is_sheaf_for.amalgamate` to be used below.
   If `P`s a sheaf, `S` is a cover of `X`, and `x` is a collection of morphisms from `E`
@@ -310,10 +280,7 @@ def IsSheaf.amalgamate {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X :
 #align category_theory.presheaf.is_sheaf.amalgamate CategoryTheory.Presheaf.IsSheaf.amalgamate
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf.amalgamate_map CategoryTheory.Presheaf.IsSheaf.amalgamate_mapₓ'. -/
 @[simp, reassoc]
 theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
@@ -328,10 +295,7 @@ theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{max v₁ u₁} A] {E :
 #align category_theory.presheaf.is_sheaf.amalgamate_map CategoryTheory.Presheaf.IsSheaf.amalgamate_map
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf.hom_ext CategoryTheory.Presheaf.IsSheaf.hom_extₓ'. -/
 theorem IsSheaf.hom_ext {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
     (hP : Presheaf.IsSheaf J P) (S : J.cover X) (e₁ e₂ : E ⟶ P.obj (op X))
@@ -555,10 +519,7 @@ instance : Zero (P ⟶ Q) where zero := Sheaf.Hom.mk 0
 instance : Add (P ⟶ Q) where add f g := Sheaf.Hom.mk <| f.1 + g.1
 
 /- warning: category_theory.Sheaf.hom.add_app -> CategoryTheory.Sheaf.Hom.add_app is a dubious translation:
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u4} A _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) A _inst_2 (CategoryTheory.Sheaf.val.{u1, u2, u3, u4} C _inst_1 J A _inst_2 P)) U) (Prefunctor.obj.{succ u1, succ u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} A (CategoryTheory.Category.toCategoryStruct.{u2, u4} A _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) A _inst_2 (CategoryTheory.Sheaf.val.{u1, u2, u3, u4} C _inst_1 J A _inst_2 Q)) U)) (CategoryTheory.Preadditive.homGroup.{u2, u4} A _inst_2 _inst_3 (Prefunctor.obj.{succ u1, succ u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} A (CategoryTheory.Category.toCategoryStruct.{u2, u4} A _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) A _inst_2 (CategoryTheory.Sheaf.val.{u1, u2, u3, u4} C _inst_1 J A _inst_2 P)) U) (Prefunctor.obj.{succ u1, succ u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u1, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} A (CategoryTheory.Category.toCategoryStruct.{u2, u4} A _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) A _inst_2 (CategoryTheory.Sheaf.val.{u1, u2, u3, u4} C _inst_1 J A _inst_2 Q)) U)))))))) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) A _inst_2 (CategoryTheory.Sheaf.val.{u1, u2, u3, u4} C _inst_1 J A _inst_2 P) (CategoryTheory.Sheaf.val.{u1, u2, u3, u4} C _inst_1 J A _inst_2 Q) (CategoryTheory.Sheaf.Hom.val.{u1, u2, u3, u4} C _inst_1 J A _inst_2 P Q f) U) (CategoryTheory.NatTrans.app.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) A _inst_2 (CategoryTheory.Sheaf.val.{u1, u2, u3, u4} C _inst_1 J A _inst_2 P) (CategoryTheory.Sheaf.val.{u1, u2, u3, u4} C _inst_1 J A _inst_2 Q) (CategoryTheory.Sheaf.Hom.val.{u1, u2, u3, u4} C _inst_1 J A _inst_2 P Q g) U))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.Sheaf.hom.add_app CategoryTheory.Sheaf.Hom.add_appₓ'. -/
 @[simp]
 theorem Sheaf.Hom.add_app (f g : P ⟶ Q) (U) : (f + g).1.app U = f.1.app U + g.1.app U :=

2efd2423

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -315,7 +315,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {J : CategoryTheory.GrothendieckTopology.{u1, u2} C _inst_1} {A : Type.{u3}} [_inst_3 : CategoryTheory.Category.{max u1 u2, u3} A] {E : A} {X : C} {P : CategoryTheory.Functor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3} (hP : CategoryTheory.Presheaf.IsSheaf.{u1, max u2 u1, u2, u3} C _inst_1 A _inst_3 J P) (S : CategoryTheory.GrothendieckTopology.Cover.{u1, u2} C _inst_1 J X) (x : forall (I : CategoryTheory.GrothendieckTopology.Cover.Arrow.{u1, u2} C _inst_1 X J S), Quiver.Hom.{max (succ u2) (succ u1), u3} A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) E (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u1, u2} C _inst_1 X J S I)))) (hx : forall (I : CategoryTheory.GrothendieckTopology.Cover.Relation.{u1, u2} C _inst_1 X J S), Eq.{max (succ u2) (succ u1)} (Quiver.Hom.{succ (max u2 u1), u3} A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) E (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Relation.Z.{u1, u2} C _inst_1 X J S I)))) (CategoryTheory.CategoryStruct.comp.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3) E (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u1, u2} C _inst_1 X J S (CategoryTheory.GrothendieckTopology.Cover.Relation.fst.{u1, u2} C _inst_1 X J S I)))) (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Relation.Z.{u1, u2} C _inst_1 X J S I))) (x (CategoryTheory.GrothendieckTopology.Cover.Relation.fst.{u1, u2} C _inst_1 X J S I)) (Prefunctor.map.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u1, u2} C _inst_1 X J S (CategoryTheory.GrothendieckTopology.Cover.Relation.fst.{u1, u2} C _inst_1 X J S I))) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Relation.Z.{u1, u2} C _inst_1 X J S I)) (Quiver.Hom.op.{u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Relation.Z.{u1, u2} C _inst_1 X J S I) (CategoryTheory.GrothendieckTopology.Cover.Relation.Y₁.{u1, u2} C _inst_1 X J S I) (CategoryTheory.GrothendieckTopology.Cover.Relation.g₁.{u1, u2} C _inst_1 X J S I)))) (CategoryTheory.CategoryStruct.comp.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3) E (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u1, u2} C _inst_1 X J S (CategoryTheory.GrothendieckTopology.Cover.Relation.snd.{u1, u2} C _inst_1 X J S I)))) (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Relation.Z.{u1, u2} C _inst_1 X J S I))) (x (CategoryTheory.GrothendieckTopology.Cover.Relation.snd.{u1, u2} C _inst_1 X J S I)) (Prefunctor.map.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u1, u2} C _inst_1 X J S (CategoryTheory.GrothendieckTopology.Cover.Relation.snd.{u1, u2} C _inst_1 X J S I))) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Relation.Z.{u1, u2} C _inst_1 X J S I)) (Quiver.Hom.op.{u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Relation.Z.{u1, u2} C _inst_1 X J S I) (CategoryTheory.GrothendieckTopology.Cover.Relation.Y₂.{u1, u2} C _inst_1 X J S I) (CategoryTheory.GrothendieckTopology.Cover.Relation.g₂.{u1, u2} C _inst_1 X J S I))))) (I : CategoryTheory.GrothendieckTopology.Cover.Arrow.{u1, u2} C _inst_1 X J S), Eq.{max (succ u2) (succ u1)} (Quiver.Hom.{succ (max u2 u1), u3} A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) E (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u1, u2} C _inst_1 X J S I)))) (CategoryTheory.CategoryStruct.comp.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3) E (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C X)) (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u1, u2} C _inst_1 X J S I))) (CategoryTheory.Presheaf.IsSheaf.amalgamate.{u1, u2, u3} C _inst_1 J A _inst_3 E X P hP S x hx) (Prefunctor.map.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_3 P) (Opposite.op.{succ u2} C X) (Opposite.op.{succ u2} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u1, u2} C _inst_1 X J S I)) (Quiver.Hom.op.{u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u1, u2} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u1, u2} C _inst_1 X J S I)))) (x I)
 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf.amalgamate_map CategoryTheory.Presheaf.IsSheaf.amalgamate_mapₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
     (hP : Presheaf.IsSheaf J P) (S : J.cover X) (x : ∀ I : S.arrow, E ⟶ P.obj (op I.y))
     (hx : ∀ I : S.Relation, x I.fst ≫ P.map I.g₁.op = x I.snd ≫ P.map I.g₂.op) (I : S.arrow) :

2efd2423

bump to nightly-2023-04-09-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228

32290448

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module category_theory.sites.sheaf
-! leanprover-community/mathlib commit 75be6b616681ab6ca66d798ead117e75cd64f125
+! leanprover-community/mathlib commit 2efd2423f8d25fa57cf7a179f5d8652ab4d0df44
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -569,11 +569,9 @@ instance : AddCommGroup (P ⟶ Q) :=
   Function.Injective.addCommGroup (fun f : Sheaf.Hom P Q => f.1) (fun _ _ h => Sheaf.Hom.ext _ _ h)
     rfl (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl)
     (fun _ _ => by
-      dsimp at *
       ext
       simpa [*] )
     fun _ _ => by
-    dsimp at *
     ext
     simpa [*]

75be6b61

bump to nightly-2023-04-07-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

3f979973

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module category_theory.sites.sheaf
-! leanprover-community/mathlib commit a67ec23dd8dc08195d77b6df2cd21f9c64989131
+! leanprover-community/mathlib commit 75be6b616681ab6ca66d798ead117e75cd64f125
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.CategoryTheory.Sites.SheafOfTypes
 /-!
 # Sheaves taking values in a category
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 If C is a category with a Grothendieck topology, we define the notion of a sheaf taking values in
 an arbitrary category `A`. We follow the definition in https://stacks.math.columbia.edu/tag/00VR,
 noting that the presheaf of sets "defined above" can be seen in the comments between tags 00VQ and

a67ec23d

bump to nightly-2023-04-05-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0

523f1e96

Diff

@@ -59,6 +59,7 @@ variable {A : Type u₂} [Category.{v₂} A]
 
 variable (J : GrothendieckTopology C)
 
+#print CategoryTheory.Presheaf.IsSheaf /-
 -- We follow https://stacks.math.columbia.edu/tag/00VL definition 00VR
 /-- A sheaf of A is a presheaf P : Cᵒᵖ => A such that for every E : A, the
 presheaf of types given by sending U : C to Hom_{A}(E, P U) is a sheaf of types.
@@ -68,6 +69,7 @@ https://stacks.math.columbia.edu/tag/00VR
 def IsSheaf (P : Cᵒᵖ ⥤ A) : Prop :=
   ∀ E : A, Presieve.IsSheaf J (P ⋙ coyoneda.obj (op E))
 #align category_theory.presheaf.is_sheaf CategoryTheory.Presheaf.IsSheaf
+-/
 
 section LimitSheafCondition
 
@@ -75,6 +77,12 @@ open Presieve Presieve.FamilyOfElements Limits
 
 variable (P : Cᵒᵖ ⥤ A) {X : C} (S : Sieve X) (R : Presieve X) (E : Aᵒᵖ)
 
+/- warning: category_theory.presheaf.cones_equiv_sieve_compatible_family -> CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.cones_equiv_sieve_compatible_family CategoryTheory.Presheaf.conesEquivSieveCompatibleFamilyₓ'. -/
 /-- Given a sieve `S` on `X : C`, a presheaf `P : Cᵒᵖ ⥤ A`, and an object `E` of `A`,
     the cones over the natural diagram `S.arrows.diagram.op ⋙ P` associated to `S` and `P`
     with cone point `E` are in 1-1 correspondence with sieve_compatible family of elements
@@ -114,6 +122,12 @@ def conesEquivSieveCompatibleFamily :
 
 variable {P S E} {x : FamilyOfElements (P ⋙ coyoneda.obj E) S} (hx : x.SieveCompatible)
 
+/- warning: category_theory.presieve.family_of_elements.sieve_compatible.cone -> CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.family_of_elements.sieve_compatible.cone CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.coneₓ'. -/
 /-- The cone corresponding to a sieve_compatible family of elements, dot notation enabled. -/
 @[simp]
 def CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone : Cone (S.arrows.diagram.op ⋙ P)
@@ -122,6 +136,12 @@ def CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone : Cone (S.arro
   π := (conesEquivSieveCompatibleFamily P S E).invFun ⟨x, hx⟩
 #align category_theory.presieve.family_of_elements.sieve_compatible.cone CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone
 
+/- warning: category_theory.presheaf.hom_equiv_amalgamation -> CategoryTheory.Presheaf.homEquivAmalgamation is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.hom_equiv_amalgamation CategoryTheory.Presheaf.homEquivAmalgamationₓ'. -/
 /-- Cone morphisms from the cone corresponding to a sieve_compatible family to the natural
     cone associated to a sieve `S` and a presheaf `P` are in 1-1 correspondence with amalgamations
     of the family. -/
@@ -139,6 +159,12 @@ def homEquivAmalgamation : (hx.Cone ⟶ P.mapCone S.arrows.Cocone.op) ≃ { t //
 
 variable (P S)
 
+/- warning: category_theory.presheaf.is_limit_iff_is_sheaf_for -> CategoryTheory.Presheaf.isLimit_iff_isSheafFor is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_limit_iff_is_sheaf_for CategoryTheory.Presheaf.isLimit_iff_isSheafForₓ'. -/
 /-- Given sieve `S` and presheaf `P : Cᵒᵖ ⥤ A`, their natural associated cone is a limit cone
     iff `Hom (E, P -)` is a sheaf of types for the sieve `S` and all `E : A`. -/
 theorem isLimit_iff_isSheafFor :
@@ -160,6 +186,12 @@ theorem isLimit_iff_isSheafFor :
     exact h _ _ (eqv π).2
 #align category_theory.presheaf.is_limit_iff_is_sheaf_for CategoryTheory.Presheaf.isLimit_iff_isSheafFor
 
+/- warning: category_theory.presheaf.subsingleton_iff_is_separated_for -> CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.subsingleton_iff_is_separated_for CategoryTheory.Presheaf.subsingleton_iff_isSeparatedForₓ'. -/
 /-- Given sieve `S` and presheaf `P : Cᵒᵖ ⥤ A`, their natural associated cone admits at most one
     morphism from every cone in the same category (i.e. over the same diagram),
     iff `Hom (E, P -)`is separated for the sieve `S` and all `E : A`. -/
@@ -186,6 +218,12 @@ theorem subsingleton_iff_isSeparatedFor :
     apply h _ (eqv π).1 <;> exact (eqv' _).2
 #align category_theory.presheaf.subsingleton_iff_is_separated_for CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf_iff_is_limit CategoryTheory.Presheaf.isSheaf_iff_isLimitₓ'. -/
 /-- A presheaf `P` is a sheaf for the Grothendieck topology `J` iff for every covering sieve
     `S` of `J`, the natural cone associated to `P` and `S` is a limit cone. -/
 theorem isSheaf_iff_isLimit :
@@ -195,6 +233,12 @@ theorem isSheaf_iff_isLimit :
     (isLimit_iff_isSheafFor P S).1 (h S hS) (op E)⟩
 #align category_theory.presheaf.is_sheaf_iff_is_limit CategoryTheory.Presheaf.isSheaf_iff_isLimit
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_separated_iff_subsingleton CategoryTheory.Presheaf.isSeparated_iff_subsingletonₓ'. -/
 /-- A presheaf `P` is separated for the Grothendieck topology `J` iff for every covering sieve
     `S` of `J`, the natural cone associated to `P` and `S` admits at most one morphism from every
     cone in the same category. -/
@@ -205,6 +249,12 @@ theorem isSeparated_iff_subsingleton :
     (subsingleton_iff_isSeparatedFor P S).1 (h S hS) (op E)⟩
 #align category_theory.presheaf.is_separated_iff_subsingleton CategoryTheory.Presheaf.isSeparated_iff_subsingleton
 
+/- warning: category_theory.presheaf.is_limit_iff_is_sheaf_for_presieve -> CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_limit_iff_is_sheaf_for_presieve CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieveₓ'. -/
 /-- Given presieve `R` and presheaf `P : Cᵒᵖ ⥤ A`, the natural cone associated to `P` and
     the sieve `sieve.generate R` generated by `R` is a limit cone iff `Hom (E, P -)` is a
     sheaf of types for the presieve `R` and all `E : A`. -/
@@ -214,6 +264,12 @@ theorem isLimit_iff_isSheafFor_presieve :
   (isLimit_iff_isSheafFor P _).trans (forall_congr' fun _ => (isSheafFor_iff_generate _).symm)
 #align category_theory.presheaf.is_limit_iff_is_sheaf_for_presieve CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve
 
+/- warning: category_theory.presheaf.is_sheaf_iff_is_limit_pretopology -> CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopology is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf_iff_is_limit_pretopology CategoryTheory.Presheaf.isSheaf_iff_isLimit_pretopologyₓ'. -/
 /-- A presheaf `P` is a sheaf for the Grothendieck topology generated by a pretopology `K`
     iff for every covering presieve `R` of `K`, the natural cone associated to `P` and
     `sieve.generate R` is a limit cone. -/
@@ -233,6 +289,12 @@ end LimitSheafCondition
 
 variable {J}
 
+/- warning: category_theory.presheaf.is_sheaf.amalgamate -> CategoryTheory.Presheaf.IsSheaf.amalgamate is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf.amalgamate CategoryTheory.Presheaf.IsSheaf.amalgamateₓ'. -/
 /-- This is a wrapper around `presieve.is_sheaf_for.amalgamate` to be used below.
   If `P`s a sheaf, `S` is a cover of `X`, and `x` is a collection of morphisms from `E`
   to `P` evaluated at terms in the cover which are compatible, then we can amalgamate
@@ -244,6 +306,12 @@ def IsSheaf.amalgamate {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X :
     hx ⟨Y₁, Y₂, Z, g₁, g₂, f₁, f₂, h₁, h₂, w⟩
 #align category_theory.presheaf.is_sheaf.amalgamate CategoryTheory.Presheaf.IsSheaf.amalgamate
 
+/- warning: category_theory.presheaf.is_sheaf.amalgamate_map -> CategoryTheory.Presheaf.IsSheaf.amalgamate_map is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf.amalgamate_map CategoryTheory.Presheaf.IsSheaf.amalgamate_mapₓ'. -/
 @[simp, reassoc.1]
 theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
     (hP : Presheaf.IsSheaf J P) (S : J.cover X) (x : ∀ I : S.arrow, E ⟶ P.obj (op I.y))
@@ -256,20 +324,34 @@ theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{max v₁ u₁} A] {E :
       (fun Y₁ Y₂ Z g₁ g₂ f₁ f₂ h₁ h₂ w => hx ⟨Y₁, Y₂, Z, g₁, g₂, f₁, f₂, h₁, h₂, w⟩) f hf
 #align category_theory.presheaf.is_sheaf.amalgamate_map CategoryTheory.Presheaf.IsSheaf.amalgamate_map
 
+/- warning: category_theory.presheaf.is_sheaf.hom_ext -> CategoryTheory.Presheaf.IsSheaf.hom_ext is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf.hom_ext CategoryTheory.Presheaf.IsSheaf.hom_extₓ'. -/
 theorem IsSheaf.hom_ext {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
     (hP : Presheaf.IsSheaf J P) (S : J.cover X) (e₁ e₂ : E ⟶ P.obj (op X))
     (h : ∀ I : S.arrow, e₁ ≫ P.map I.f.op = e₂ ≫ P.map I.f.op) : e₁ = e₂ :=
   (hP _ _ S.condition).IsSeparatedFor.ext fun Y f hf => h ⟨Y, f, hf⟩
 #align category_theory.presheaf.is_sheaf.hom_ext CategoryTheory.Presheaf.IsSheaf.hom_ext
 
+#print CategoryTheory.Presheaf.isSheaf_of_iso_iff /-
 theorem isSheaf_of_iso_iff {P P' : Cᵒᵖ ⥤ A} (e : P ≅ P') : IsSheaf J P ↔ IsSheaf J P' :=
   forall_congr' fun a =>
     ⟨Presieve.isSheaf_iso J (isoWhiskerRight e _),
       Presieve.isSheaf_iso J (isoWhiskerRight e.symm _)⟩
 #align category_theory.presheaf.is_sheaf_of_iso_iff CategoryTheory.Presheaf.isSheaf_of_iso_iff
+-/
 
 variable (J)
 
+/- warning: category_theory.presheaf.is_sheaf_of_is_terminal -> CategoryTheory.Presheaf.isSheaf_of_isTerminal is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {A : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} A] (J : CategoryTheory.GrothendieckTopology.{u1, u3} C _inst_1) {X : A}, (CategoryTheory.Limits.IsTerminal.{u2, u4} A _inst_2 X) -> (CategoryTheory.Presheaf.IsSheaf.{u1, u2, u3, u4} C _inst_1 A _inst_2 J (CategoryTheory.Functor.obj.{u2, max u3 u2, u4, max u1 u2 u3 u4} A _inst_2 (CategoryTheory.Functor.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) A _inst_2) (CategoryTheory.Functor.category.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) A _inst_2) (CategoryTheory.Functor.const.{u1, u2, u3, u4} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u1, u3} C _inst_1) A _inst_2) X))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf_of_is_terminal CategoryTheory.Presheaf.isSheaf_of_isTerminalₓ'. -/
 theorem isSheaf_of_isTerminal {X : A} (hX : IsTerminal X) :
     Presheaf.IsSheaf J ((CategoryTheory.Functor.const _).obj X) := fun _ _ _ _ _ _ =>
   ⟨hX.from _, fun _ _ _ => hX.hom_ext _ _, fun _ _ => hX.hom_ext _ _⟩
@@ -283,21 +365,25 @@ variable (J : GrothendieckTopology C)
 
 variable (A : Type u₂) [Category.{v₂} A]
 
+#print CategoryTheory.Sheaf /-
 /-- The category of sheaves taking values in `A` on a grothendieck topology. -/
 structure Sheaf where
   val : Cᵒᵖ ⥤ A
   cond : Presheaf.IsSheaf J val
 #align category_theory.Sheaf CategoryTheory.Sheaf
+-/
 
 namespace Sheaf
 
 variable {J A}
 
+#print CategoryTheory.Sheaf.Hom /-
 /-- Morphisms between sheaves are just morphisms of presheaves. -/
 @[ext]
 structure Hom (X Y : Sheaf J A) where
   val : X.val ⟶ Y.val
 #align category_theory.Sheaf.hom CategoryTheory.Sheaf.Hom
+-/
 
 @[simps]
 instance : Category (Sheaf J A) where
@@ -314,6 +400,7 @@ instance (X : Sheaf J A) : Inhabited (Hom X X) :=
 
 end Sheaf
 
+#print CategoryTheory.sheafToPresheaf /-
 /-- The inclusion functor from sheaves to presheaves. -/
 @[simps]
 def sheafToPresheaf : Sheaf J A ⥤ Cᵒᵖ ⥤ A
@@ -323,28 +410,36 @@ def sheafToPresheaf : Sheaf J A ⥤ Cᵒᵖ ⥤ A
   map_id' X := rfl
   map_comp' X Y Z f g := rfl
 #align category_theory.Sheaf_to_presheaf CategoryTheory.sheafToPresheaf
+-/
 
 instance : Full (sheafToPresheaf J A) where preimage X Y f := ⟨f⟩
 
 instance : Faithful (sheafToPresheaf J A) where
 
+#print CategoryTheory.Sheaf.Hom.mono_of_presheaf_mono /-
 /-- This is stated as a lemma to prevent class search from forming a loop since a sheaf morphism is
 monic if and only if it is monic as a presheaf morphism (under suitable assumption).-/
 theorem Sheaf.Hom.mono_of_presheaf_mono {F G : Sheaf J A} (f : F ⟶ G) [h : Mono f.1] : Mono f :=
   (sheafToPresheaf J A).mono_of_mono_map h
 #align category_theory.Sheaf.hom.mono_of_presheaf_mono CategoryTheory.Sheaf.Hom.mono_of_presheaf_mono
+-/
 
+#print CategoryTheory.Sheaf.Hom.epi_of_presheaf_epi /-
 instance Sheaf.Hom.epi_of_presheaf_epi {F G : Sheaf J A} (f : F ⟶ G) [h : Epi f.1] : Epi f :=
   (sheafToPresheaf J A).epi_of_epi_map h
 #align category_theory.Sheaf.hom.epi_of_presheaf_epi CategoryTheory.Sheaf.Hom.epi_of_presheaf_epi
+-/
 
+#print CategoryTheory.sheafOver /-
 /-- The sheaf of sections guaranteed by the sheaf condition. -/
 @[simps]
 def sheafOver {A : Type u₂} [Category.{v₂} A] {J : GrothendieckTopology C} (ℱ : Sheaf J A) (E : A) :
     SheafOfTypes J :=
   ⟨ℱ.val ⋙ coyoneda.obj (op E), ℱ.cond E⟩
 #align category_theory.sheaf_over CategoryTheory.sheafOver
+-/
 
+#print CategoryTheory.isSheaf_iff_isSheaf_of_type /-
 theorem isSheaf_iff_isSheaf_of_type (P : Cᵒᵖ ⥤ Type w) :
     Presheaf.IsSheaf J P ↔ Presieve.IsSheaf J P :=
   by
@@ -366,7 +461,14 @@ theorem isSheaf_iff_isSheaf_of_type (P : Cᵒᵖ ⥤ Type w) :
       rw [presieve.is_sheaf_for.valid_glue _ _ _ hf, ← hy _ hf]
       rfl
 #align category_theory.is_sheaf_iff_is_sheaf_of_type CategoryTheory.isSheaf_iff_isSheaf_of_type
+-/
 
+/- warning: category_theory.Sheaf_equiv_SheafOfTypes -> CategoryTheory.sheafEquivSheafOfTypes is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1), CategoryTheory.Equivalence.{max u3 u1, max u1 u3, max u3 (succ u1) u2 u1, max u3 u2 (succ u1)} (CategoryTheory.Sheaf.{u2, u1, u3, succ u1} C _inst_1 J Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, u1, u3, succ u1} C _inst_1 J Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.SheafOfTypes.{u1, u2, u3} C _inst_1 J) (CategoryTheory.SheafOfTypes.CategoryTheory.category.{u2, u3, u1} C _inst_1 J)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1), CategoryTheory.Equivalence.{max u3 u1, max u3 u1, max (max (max (succ u1) u3) u1) u2, max (max u3 u2) (succ u1)} (CategoryTheory.Sheaf.{u2, u1, u3, succ u1} C _inst_1 J Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.SheafOfTypes.{u1, u2, u3} C _inst_1 J) (CategoryTheory.Sheaf.instCategorySheaf.{u2, u1, u3, succ u1} C _inst_1 J Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.SheafOfTypes.instCategorySheafOfTypes.{u2, u3, u1} C _inst_1 J)
+Case conversion may be inaccurate. Consider using '#align category_theory.Sheaf_equiv_SheafOfTypes CategoryTheory.sheafEquivSheafOfTypesₓ'. -/
 /-- The category of sheaves taking values in Type is the same as the category of set-valued sheaves.
 -/
 @[simps]
@@ -387,6 +489,12 @@ instance : Inhabited (Sheaf (⊥ : GrothendieckTopology C) (Type w)) :=
 
 variable {J} {A}
 
+/- warning: category_theory.Sheaf.is_terminal_of_bot_cover -> CategoryTheory.Sheaf.isTerminalOfBotCover is a dubious translation:
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 /-- If the empty sieve is a cover of `X`, then `F(X)` is terminal. -/
 def Sheaf.isTerminalOfBotCover (F : Sheaf J A) (X : C) (H : ⊥ ∈ J X) :
     IsTerminal (F.1.obj (op X)) :=
@@ -403,6 +511,7 @@ open Preadditive
 
 variable [Preadditive A] {P Q : Sheaf J A}
 
+#print CategoryTheory.sheafHomHasZsmul /-
 instance sheafHomHasZsmul : SMul ℤ (P ⟶ Q)
     where smul n f :=
     Sheaf.Hom.mk
@@ -418,11 +527,13 @@ instance sheafHomHasZsmul : SMul ℤ (P ⟶ Q)
             simpa only [sub_smul, one_zsmul, comp_sub, nat_trans.naturality, sub_comp,
               sub_left_inj] using ih }
 #align category_theory.Sheaf_hom_has_zsmul CategoryTheory.sheafHomHasZsmul
+-/
 
 instance : Sub (P ⟶ Q) where sub f g := Sheaf.Hom.mk <| f.1 - g.1
 
 instance : Neg (P ⟶ Q) where neg f := Sheaf.Hom.mk <| -f.1
 
+#print CategoryTheory.sheafHomHasNsmul /-
 instance sheafHomHasNsmul : SMul ℕ (P ⟶ Q)
     where smul n f :=
     Sheaf.Hom.mk
@@ -434,11 +545,18 @@ instance sheafHomHasNsmul : SMul ℕ (P ⟶ Q)
             simp only [Nat.succ_eq_add_one, add_smul, ih, one_nsmul, comp_add, nat_trans.naturality,
               add_comp] }
 #align category_theory.Sheaf_hom_has_nsmul CategoryTheory.sheafHomHasNsmul
+-/
 
 instance : Zero (P ⟶ Q) where zero := Sheaf.Hom.mk 0
 
 instance : Add (P ⟶ Q) where add f g := Sheaf.Hom.mk <| f.1 + g.1
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.Sheaf.hom.add_app CategoryTheory.Sheaf.Hom.add_appₓ'. -/
 @[simp]
 theorem Sheaf.Hom.add_app (f g : P ⟶ Q) (U) : (f + g).1.app U = f.1.app U + g.1.app U :=
   rfl
@@ -491,6 +609,7 @@ variable (P : Cᵒᵖ ⥤ A)
 
 section MultiequalizerConditions
 
+#print CategoryTheory.Presheaf.isLimitOfIsSheaf /-
 /-- When `P` is a sheaf and `S` is a cover, the associated multifork is a limit. -/
 def isLimitOfIsSheaf {X : C} (S : J.cover X) (hP : IsSheaf J P) : IsLimit (S.Multifork P)
     where
@@ -510,7 +629,9 @@ def isLimitOfIsSheaf {X : C} (S : J.cover X) (hP : IsSheaf J P) : IsLimit (S.Mul
     symm
     apply hP.amalgamate_map
 #align category_theory.presheaf.is_limit_of_is_sheaf CategoryTheory.Presheaf.isLimitOfIsSheaf
+-/
 
+#print CategoryTheory.Presheaf.isSheaf_iff_multifork /-
 theorem isSheaf_iff_multifork :
     IsSheaf J P ↔ ∀ (X : C) (S : J.cover X), Nonempty (IsLimit (S.Multifork P)) :=
   by
@@ -532,7 +653,14 @@ theorem isSheaf_iff_multifork :
       congr 1
       apply he
 #align category_theory.presheaf.is_sheaf_iff_multifork CategoryTheory.Presheaf.isSheaf_iff_multifork
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.is_sheaf_iff_multiequalizer CategoryTheory.Presheaf.isSheaf_iff_multiequalizerₓ'. -/
 theorem isSheaf_iff_multiequalizer [∀ (X : C) (S : J.cover X), HasMultiequalizer (S.index P)] :
     IsSheaf J P ↔ ∀ (X : C) (S : J.cover X), IsIso (S.toMultiequalizer P) :=
   by
@@ -558,6 +686,7 @@ section
 
 variable [HasProducts.{max u₁ v₁} A]
 
+#print CategoryTheory.Presheaf.firstObj /-
 /--
 The middle object of the fork diagram given in Equation (3) of [MM92], as well as the fork diagram
 of <https://stacks.math.columbia.edu/tag/00VM>.
@@ -565,7 +694,14 @@ of <https://stacks.math.columbia.edu/tag/00VM>.
 def firstObj : A :=
   ∏ fun f : ΣV, { f : V ⟶ U // R f } => P.obj (op f.1)
 #align category_theory.presheaf.first_obj CategoryTheory.Presheaf.firstObj
+-/
 
+/- warning: category_theory.presheaf.fork_map -> CategoryTheory.Presheaf.forkMap is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.fork_map CategoryTheory.Presheaf.forkMapₓ'. -/
 /--
 The left morphism of the fork diagram given in Equation (3) of [MM92], as well as the fork diagram
 of <https://stacks.math.columbia.edu/tag/00VM>.
@@ -576,6 +712,7 @@ def forkMap : P.obj (op U) ⟶ firstObj R P :=
 
 variable [HasPullbacks C]
 
+#print CategoryTheory.Presheaf.secondObj /-
 /-- The rightmost object of the fork diagram of https://stacks.math.columbia.edu/tag/00VM, which
 contains the data used to check a family of elements for a presieve is compatible.
 -/
@@ -583,17 +720,28 @@ def secondObj : A :=
   ∏ fun fg : (ΣV, { f : V ⟶ U // R f }) × ΣW, { g : W ⟶ U // R g } =>
     P.obj (op (pullback fg.1.2.1 fg.2.2.1))
 #align category_theory.presheaf.second_obj CategoryTheory.Presheaf.secondObj
+-/
 
+#print CategoryTheory.Presheaf.firstMap /-
 /-- The map `pr₀*` of <https://stacks.math.columbia.edu/tag/00VM>. -/
 def firstMap : firstObj R P ⟶ secondObj R P :=
   Pi.lift fun fg => Pi.π _ _ ≫ P.map pullback.fst.op
 #align category_theory.presheaf.first_map CategoryTheory.Presheaf.firstMap
+-/
 
+#print CategoryTheory.Presheaf.secondMap /-
 /-- The map `pr₁*` of <https://stacks.math.columbia.edu/tag/00VM>. -/
 def secondMap : firstObj R P ⟶ secondObj R P :=
   Pi.lift fun fg => Pi.π _ _ ≫ P.map pullback.snd.op
 #align category_theory.presheaf.second_map CategoryTheory.Presheaf.secondMap
+-/
 
+/- warning: category_theory.presheaf.w -> CategoryTheory.Presheaf.w is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {A : Type.{u3}} [_inst_2 : CategoryTheory.Category.{max u1 u2, u3} A] {U : C} (R : CategoryTheory.Presieve.{u1, u2} C _inst_1 U) (P : CategoryTheory.Functor.{u1, max u1 u2, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_2) [_inst_3 : CategoryTheory.Limits.HasProducts.{max u2 u1, max u1 u2, u3} A _inst_2] [_inst_4 : CategoryTheory.Limits.HasPullbacks.{u1, u2} C _inst_1], Eq.{succ (max u1 u2)} (Quiver.Hom.{succ (max u1 u2), u3} A (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, u3} A (CategoryTheory.Category.toCategoryStruct.{max u1 u2, u3} A _inst_2)) (CategoryTheory.Functor.obj.{u1, max u1 u2, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_2 P (Opposite.op.{succ u2} C U)) (CategoryTheory.Presheaf.secondObj.{u1, u2, u3} C _inst_1 A _inst_2 U R P (CategoryTheory.Presheaf.firstMap._proof_2.{u2, u3, u1} A _inst_2 (fun (J : Type.{max u2 u1}) => _inst_3 J)) _inst_4)) (CategoryTheory.CategoryStruct.comp.{max u1 u2, u3} A (CategoryTheory.Category.toCategoryStruct.{max u1 u2, u3} A _inst_2) (CategoryTheory.Functor.obj.{u1, max u1 u2, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_2 P (Opposite.op.{succ u2} C U)) (CategoryTheory.Presheaf.firstObj.{u1, u2, u3} C _inst_1 A _inst_2 U R P (CategoryTheory.Presheaf.forkMap._proof_1.{u2, u3, u1} A _inst_2 (fun (J : Type.{max u2 u1}) => _inst_3 J))) (CategoryTheory.Presheaf.secondObj.{u1, u2, u3} C _inst_1 A _inst_2 U R P (CategoryTheory.Presheaf.firstMap._proof_2.{u2, u3, u1} A _inst_2 (fun (J : Type.{max u2 u1}) => _inst_3 J)) _inst_4) (CategoryTheory.Presheaf.forkMap.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J)) (CategoryTheory.Presheaf.firstMap.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J) _inst_4)) (CategoryTheory.CategoryStruct.comp.{max u1 u2, u3} A (CategoryTheory.Category.toCategoryStruct.{max u1 u2, u3} A _inst_2) (CategoryTheory.Functor.obj.{u1, max u1 u2, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_2 P (Opposite.op.{succ u2} C U)) (CategoryTheory.Presheaf.firstObj.{u1, u2, u3} C _inst_1 A _inst_2 U R P (CategoryTheory.Presheaf.forkMap._proof_1.{u2, u3, u1} A _inst_2 (fun (J : Type.{max u2 u1}) => _inst_3 J))) (CategoryTheory.Presheaf.secondObj.{u1, u2, u3} C _inst_1 A _inst_2 U R P (CategoryTheory.Presheaf.firstMap._proof_2.{u2, u3, u1} A _inst_2 (fun (J : Type.{max u2 u1}) => _inst_3 J)) _inst_4) (CategoryTheory.Presheaf.forkMap.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J)) (CategoryTheory.Presheaf.secondMap.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J) _inst_4))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {A : Type.{u3}} [_inst_2 : CategoryTheory.Category.{max u1 u2, u3} A] {U : C} (R : CategoryTheory.Presieve.{u1, u2} C _inst_1 U) (P : CategoryTheory.Functor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_2) [_inst_3 : CategoryTheory.Limits.HasProducts.{max u2 u1, max u2 u1, u3} A _inst_2] [_inst_4 : CategoryTheory.Limits.HasPullbacks.{u1, u2} C _inst_1], Eq.{max (succ u2) (succ u1)} (Quiver.Hom.{succ (max u2 u1), u3} A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_2)) (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_2 P) (Opposite.op.{succ u2} C U)) (CategoryTheory.Presheaf.secondObj.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J) _inst_4)) (CategoryTheory.CategoryStruct.comp.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_2) (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_2 P) (Opposite.op.{succ u2} C U)) (CategoryTheory.Presheaf.firstObj.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J)) (CategoryTheory.Presheaf.secondObj.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J) _inst_4) (CategoryTheory.Presheaf.forkMap.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J)) (CategoryTheory.Presheaf.firstMap.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J) _inst_4)) (CategoryTheory.CategoryStruct.comp.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_2) (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, u3} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) A (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, u3} A (CategoryTheory.Category.toCategoryStruct.{max u2 u1, u3} A _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, u3} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) A _inst_2 P) (Opposite.op.{succ u2} C U)) (CategoryTheory.Presheaf.firstObj.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J)) (CategoryTheory.Presheaf.secondObj.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J) _inst_4) (CategoryTheory.Presheaf.forkMap.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J)) (CategoryTheory.Presheaf.secondMap.{u1, u2, u3} C _inst_1 A _inst_2 U R P (fun (J : Type.{max u2 u1}) => _inst_3 J) _inst_4))
+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf.w CategoryTheory.Presheaf.wₓ'. -/
 theorem w : forkMap R P ≫ firstMap R P = forkMap R P ≫ secondMap R P :=
   by
   apply limit.hom_ext
@@ -604,13 +752,16 @@ theorem w : forkMap R P ≫ firstMap R P = forkMap R P ≫ secondMap R P :=
   simp
 #align category_theory.presheaf.w CategoryTheory.Presheaf.w
 
+#print CategoryTheory.Presheaf.IsSheaf' /-
 /-- An alternative definition of the sheaf condition in terms of equalizers. This is shown to be
 equivalent in `category_theory.presheaf.is_sheaf_iff_is_sheaf'`.
 -/
 def IsSheaf' (P : Cᵒᵖ ⥤ A) : Prop :=
   ∀ (U : C) (R : Presieve U) (hR : generate R ∈ J U), Nonempty (IsLimit (Fork.ofι _ (w R P)))
 #align category_theory.presheaf.is_sheaf' CategoryTheory.Presheaf.IsSheaf'
+-/
 
+#print CategoryTheory.Presheaf.isSheafForIsSheafFor' /-
 /-- (Implementation). An auxiliary lemma to convert between sheaf conditions. -/
 def isSheafForIsSheafFor' (P : Cᵒᵖ ⥤ A) (s : A ⥤ Type max v₁ u₁)
     [∀ J, PreservesLimitsOfShape (Discrete.{max v₁ u₁} J) s] (U : C) (R : Presieve U) :
@@ -638,7 +789,9 @@ def isSheafForIsSheafFor' (P : Cᵒᵖ ⥤ A) (s : A ⥤ Type max v₁ u₁)
     dsimp [equalizer.fork_map, fork_map]
     simp [fork.ι]
 #align category_theory.presheaf.is_sheaf_for_is_sheaf_for' CategoryTheory.Presheaf.isSheafForIsSheafFor'
+-/
 
+#print CategoryTheory.Presheaf.isSheaf_iff_isSheaf' /-
 /-- The equalizer definition of a sheaf given by `is_sheaf'` is equivalent to `is_sheaf`. -/
 theorem isSheaf_iff_isSheaf' : IsSheaf J P ↔ IsSheaf' J P :=
   by
@@ -661,6 +814,7 @@ theorem isSheaf_iff_isSheaf' : IsSheaf J P ↔ IsSheaf' J P :=
     apply Classical.choice (h _ S _)
     simpa
 #align category_theory.presheaf.is_sheaf_iff_is_sheaf' CategoryTheory.Presheaf.isSheaf_iff_isSheaf'
+-/
 
 end
 
@@ -668,6 +822,7 @@ section Concrete
 
 variable [HasPullbacks C]
 
+#print CategoryTheory.Presheaf.isSheaf_iff_isSheaf_forget /-
 /--
 For a concrete category `(A, s)` where the forgetful functor `s : A ⥤ Type v` preserves limits and
 reflects isomorphisms, and `A` has limits, an `A`-valued presheaf `P : Cᵒᵖ ⥤ A` is a sheaf iff its
@@ -693,6 +848,7 @@ theorem isSheaf_iff_isSheaf_forget (s : A ⥤ Type max v₁ u₁) [HasLimits A]
   · haveI := reflects_smallest_limits_of_reflects_limits s
     exact Nonempty.map fun t => is_limit_of_reflects s t
 #align category_theory.presheaf.is_sheaf_iff_is_sheaf_forget CategoryTheory.Presheaf.isSheaf_iff_isSheaf_forget
+-/
 
 end Concrete

a67ec23d

bump to nightly-2023-03-09-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

a3ca2eeb

Diff

@@ -459,10 +459,10 @@ instance : AddCommGroup (P ⟶ Q) :=
 instance : Preadditive (Sheaf J A)
     where
   homGroup P Q := inferInstance
-  add_comp' P Q R f f' g := by
+  add_comp P Q R f f' g := by
     ext
     simp
-  comp_add' P Q R f g g' := by
+  comp_add P Q R f g g' := by
     ext
     simp

a67ec23d

bump to nightly-2023-02-28-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

1fb1623f

Diff

@@ -118,7 +118,7 @@ variable {P S E} {x : FamilyOfElements (P ⋙ coyoneda.obj E) S} (hx : x.SieveCo
 @[simp]
 def CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone : Cone (S.arrows.diagram.op ⋙ P)
     where
-  x := E.unop
+  pt := E.unop
   π := (conesEquivSieveCompatibleFamily P S E).invFun ⟨x, hx⟩
 #align category_theory.presieve.family_of_elements.sieve_compatible.cone CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone

a67ec23d

bump to nightly-2023-02-27-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

91d8c210

Diff

@@ -495,14 +495,14 @@ section MultiequalizerConditions
 def isLimitOfIsSheaf {X : C} (S : J.cover X) (hP : IsSheaf J P) : IsLimit (S.Multifork P)
     where
   lift := fun E : Multifork _ => hP.amalgamate S (fun I => E.ι _) fun I => E.condition _
-  fac' := by
+  fac := by
     rintro (E : multifork _) (a | b)
     · apply hP.amalgamate_map
     · rw [← E.w (walking_multicospan.hom.fst b), ←
         (S.multifork P).w (walking_multicospan.hom.fst b), ← assoc]
       congr 1
       apply hP.amalgamate_map
-  uniq' := by
+  uniq := by
     rintro (E : multifork _) m hm
     apply hP.hom_ext S
     intro I

a67ec23d

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

2efd2423

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

@@ -312,6 +312,14 @@ instance (X : Sheaf J A) : Inhabited (Hom X X) :=
 lemma hom_ext {X Y : Sheaf J A} (x y : X ⟶ Y) (h : x.val = y.val) : x = y :=
   Sheaf.Hom.ext _ _ h
 
+/-- The bijection `(X ⟶ Y) ≃ (X.val ⟶ Y.val)` when `X` and `Y` are sheaves. -/
+@[simps]
+def homEquiv {X Y : Sheaf J A} : (X ⟶ Y) ≃ (X.val ⟶ Y.val) where
+  toFun f := f.val
+  invFun f := ⟨f⟩
+  left_inv _ := rfl
+  right_inv _ := rfl
+
 end Sheaf
 
 /-- The inclusion functor from sheaves to presheaves. -/
@@ -327,7 +335,7 @@ set_option linter.uppercaseLean3 false in
 /-- The sections of a sheaf (i.e. evaluation as a presheaf on `C`). -/
 abbrev sheafSections : Cᵒᵖ ⥤ Sheaf J A ⥤ A := (sheafToPresheaf J A).flip
 
-instance : (sheafToPresheaf J A).Full where preimage f := ⟨f⟩
+instance : (sheafToPresheaf J A).Full where map_surjective f := ⟨⟨f⟩, rfl⟩
 
 instance : (sheafToPresheaf J A).Faithful where

2efd2423

chore: replace refine' that already have a ?_ (#12261)

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

94b44d32

Diff

@@ -394,7 +394,7 @@ variable {J} {A}
 /-- If the empty sieve is a cover of `X`, then `F(X)` is terminal. -/
 def Sheaf.isTerminalOfBotCover (F : Sheaf J A) (X : C) (H : ⊥ ∈ J X) :
     IsTerminal (F.1.obj (op X)) := by
-  refine' @IsTerminal.ofUnique _ _ _ ?_
+  refine @IsTerminal.ofUnique _ _ _ ?_
   intro Y
   choose t h using F.2 Y _ H (by tauto) (by tauto)
   exact ⟨⟨t⟩, fun a => h.2 a (by tauto)⟩

2efd2423

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

@@ -327,9 +327,9 @@ set_option linter.uppercaseLean3 false in
 /-- The sections of a sheaf (i.e. evaluation as a presheaf on `C`). -/
 abbrev sheafSections : Cᵒᵖ ⥤ Sheaf J A ⥤ A := (sheafToPresheaf J A).flip
 
-instance : Full (sheafToPresheaf J A) where preimage f := ⟨f⟩
+instance : (sheafToPresheaf J A).Full where preimage f := ⟨f⟩
 
-instance : Faithful (sheafToPresheaf J A) where
+instance : (sheafToPresheaf J A).Faithful where
 
 /-- This is stated as a lemma to prevent class search from forming a loop since a sheaf morphism is
 monic if and only if it is monic as a presheaf morphism (under suitable assumption). -/
@@ -670,7 +670,7 @@ theorem isSheaf_comp_of_isSheaf (s : A ⥤ B) [PreservesLimitsOfSize.{v₁, max
   apply fun X S hS ↦ (h S hS).map fun t ↦ isLimitOfPreserves s t
 
 theorem isSheaf_iff_isSheaf_comp (s : A ⥤ B) [HasLimitsOfSize.{v₁, max v₁ u₁} A]
-    [PreservesLimitsOfSize.{v₁, max v₁ u₁} s] [ReflectsIsomorphisms s] :
+    [PreservesLimitsOfSize.{v₁, max v₁ u₁} s] [s.ReflectsIsomorphisms] :
     IsSheaf J P ↔ IsSheaf J (P ⋙ s) := by
   letI : ReflectsLimitsOfSize s := reflectsLimitsOfReflectsIsomorphisms
   exact ⟨isSheaf_comp_of_isSheaf J P s, isSheaf_of_isSheaf_comp J P s⟩
@@ -685,7 +685,7 @@ for the category of topological spaces, topological rings, etc since reflecting
 hold.
 -/
 theorem isSheaf_iff_isSheaf_forget (s : A' ⥤ Type max v₁ u₁) [HasLimits A'] [PreservesLimits s]
-    [ReflectsIsomorphisms s] : IsSheaf J P' ↔ IsSheaf J (P' ⋙ s) := by
+    [s.ReflectsIsomorphisms] : IsSheaf J P' ↔ IsSheaf J (P' ⋙ s) := by
   have : HasLimitsOfSize.{v₁, max v₁ u₁} A' := hasLimitsOfSizeShrink.{_, _, u₁, 0} A'
   have : PreservesLimitsOfSize.{v₁, max v₁ u₁} s := preservesLimitsOfSizeShrink.{_, 0, _, u₁} s
   apply isSheaf_iff_isSheaf_comp

2efd2423

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -332,7 +332,7 @@ instance : Full (sheafToPresheaf J A) where preimage f := ⟨f⟩
 instance : Faithful (sheafToPresheaf J A) where
 
 /-- This is stated as a lemma to prevent class search from forming a loop since a sheaf morphism is
-monic if and only if it is monic as a presheaf morphism (under suitable assumption).-/
+monic if and only if it is monic as a presheaf morphism (under suitable assumption). -/
 theorem Sheaf.Hom.mono_of_presheaf_mono {F G : Sheaf J A} (f : F ⟶ G) [h : Mono f.1] : Mono f :=
   (sheafToPresheaf J A).mono_of_mono_map h
 set_option linter.uppercaseLean3 false in

2efd2423

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

@@ -64,9 +64,7 @@ open Opposite CategoryTheory Category Limits Sieve
 namespace Presheaf
 
 variable {C : Type u₁} [Category.{v₁} C]
-
 variable {A : Type u₂} [Category.{v₂} A]
-
 variable (J : GrothendieckTopology C)
 
 -- We follow https://stacks.math.columbia.edu/tag/00VL definition 00VR
@@ -272,9 +270,7 @@ theorem isSheaf_of_isTerminal {X : A} (hX : IsTerminal X) :
 end Presheaf
 
 variable {C : Type u₁} [Category.{v₁} C]
-
 variable (J : GrothendieckTopology C)
-
 variable (A : Type u₂) [Category.{v₂} A]
 
 /-- The category of sheaves taking values in `A` on a grothendieck topology. -/
@@ -483,11 +479,8 @@ variable {C : Type u₁} [Category.{v₁} C]
 variable {A : Type u₂} [Category.{v₂} A]
 variable {A' : Type u₂} [Category.{max v₁ u₁} A']
 variable {B : Type u₃} [Category.{v₃} B]
-
 variable (J : GrothendieckTopology C)
-
 variable {U : C} (R : Presieve U)
-
 variable (P : Cᵒᵖ ⥤ A) (P' : Cᵒᵖ ⥤ A')
 
 section MultiequalizerConditions

2efd2423

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".

8be0b69c

Diff

@@ -311,7 +311,7 @@ instance instCategorySheaf : Category (Sheaf J A) where
 instance (X : Sheaf J A) : Inhabited (Hom X X) :=
   ⟨𝟙 X⟩
 
--- porting note: added because `Sheaf.Hom.ext` was not triggered automatically
+-- Porting note: added because `Sheaf.Hom.ext` was not triggered automatically
 @[ext]
 lemma hom_ext {X Y : Sheaf J A} (x y : X ⟶ Y) (h : x.val = y.val) : x = y :=
   Sheaf.Hom.ext _ _ h

2efd2423

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.

ea36aa7d

Diff

@@ -359,7 +359,7 @@ theorem isSheaf_iff_isSheaf_of_type (P : Cᵒᵖ ⥤ Type w) :
   constructor
   · intro hP
     refine' Presieve.isSheaf_iso J _ (hP PUnit)
-    refine' isoWhiskerLeft _ Coyoneda.punitIso ≪≫ P.rightUnitor
+    exact isoWhiskerLeft _ Coyoneda.punitIso ≪≫ P.rightUnitor
   · intro hP X Y S hS z hz
     refine' ⟨fun x => (hP S hS).amalgamate (fun Z f hf => z f hf x) _, _, _⟩
     · intro Y₁ Y₂ Z g₁ g₂ f₁ f₂ hf₁ hf₂ h

2efd2423

chore: Nsmul -> NSMul, Zpow -> ZPow, etc (#9067)

Normalising to naming convention rule number 6.

9b2f0dca

Diff

@@ -411,7 +411,7 @@ open Preadditive
 
 variable [Preadditive A] {P Q : Sheaf J A}
 
-instance sheafHomHasZsmul : SMul ℤ (P ⟶ Q) where
+instance sheafHomHasZSMul : SMul ℤ (P ⟶ Q) where
   smul n f :=
     Sheaf.Hom.mk
       { app := fun U => n • f.1.app U
@@ -423,13 +423,13 @@ instance sheafHomHasZsmul : SMul ℤ (P ⟶ Q) where
           · simpa only [sub_smul, one_zsmul, comp_sub, NatTrans.naturality, sub_comp,
               sub_left_inj] using ih }
 set_option linter.uppercaseLean3 false in
-#align category_theory.Sheaf_hom_has_zsmul CategoryTheory.sheafHomHasZsmul
+#align category_theory.Sheaf_hom_has_zsmul CategoryTheory.sheafHomHasZSMul
 
 instance : Sub (P ⟶ Q) where sub f g := Sheaf.Hom.mk <| f.1 - g.1
 
 instance : Neg (P ⟶ Q) where neg f := Sheaf.Hom.mk <| -f.1
 
-instance sheafHomHasNsmul : SMul ℕ (P ⟶ Q) where
+instance sheafHomHasNSMul : SMul ℕ (P ⟶ Q) where
   smul n f :=
     Sheaf.Hom.mk
       { app := fun U => n • f.1.app U
@@ -439,7 +439,7 @@ instance sheafHomHasNsmul : SMul ℕ (P ⟶ Q) where
           · simp only [Nat.succ_eq_add_one, add_smul, ih, one_nsmul, comp_add,
               NatTrans.naturality, add_comp] }
 set_option linter.uppercaseLean3 false in
-#align category_theory.Sheaf_hom_has_nsmul CategoryTheory.sheafHomHasNsmul
+#align category_theory.Sheaf_hom_has_nsmul CategoryTheory.sheafHomHasNSMul
 
 instance : Zero (P ⟶ Q) where zero := Sheaf.Hom.mk 0

2efd2423

feat(Condensed): discrete-underlying adjunction (#8270)

We define a functor, associating to an object of a concrete category with nice properties, a "discrete" condensed object, and prove that this functor is left adjoint to the forgetful functor from Condensed C to C.

e72b7012

Diff

@@ -328,6 +328,9 @@ def sheafToPresheaf : Sheaf J A ⥤ Cᵒᵖ ⥤ A where
 set_option linter.uppercaseLean3 false in
 #align category_theory.Sheaf_to_presheaf CategoryTheory.sheafToPresheaf
 
+/-- The sections of a sheaf (i.e. evaluation as a presheaf on `C`). -/
+abbrev sheafSections : Cᵒᵖ ⥤ Sheaf J A ⥤ A := (sheafToPresheaf J A).flip
+
 instance : Full (sheafToPresheaf J A) where preimage f := ⟨f⟩
 
 instance : Faithful (sheafToPresheaf J A) where

2efd2423

chore: split `CategoryTheory/Sites/SheafOfTypes (#7854)

I was planning to add some stuff to this file which was already over 1000 lines long.

The explicit sheaf condition for a sieve/presieve IsSheafFor is now in CategoryTheory/Sites/IsSheafFor.
The sheaf condition for a sieve/presieve in terms of equalizer diagrams is now in CategoryTheory/Sites/EqualizerSheafCondition
Only things related to IsSheaf/IsSeparated are left in the file CategoryTheory/Sites/SheafOfTypes.

1391538c

Diff

@@ -8,6 +8,7 @@ import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products
 import Mathlib.CategoryTheory.Limits.Yoneda
 import Mathlib.CategoryTheory.Preadditive.FunctorCategory
 import Mathlib.CategoryTheory.Sites.SheafOfTypes
+import Mathlib.CategoryTheory.Sites.EqualizerSheafCondition
 
 #align_import category_theory.sites.sheaf from "leanprover-community/mathlib"@"2efd2423f8d25fa57cf7a179f5d8652ab4d0df44"

2efd2423

feat: universe generalizations in UniqueGluing and Forget (#7654)

Add a criterion isLimit_iff for a cone to be a limit in Limits/Types.lean.
Use the criterion to show the equivalence between the UniqueGluing and PairwiseIntersection sheaf conditions without going through EqualizerProducts, thereby generalize the universes.
Remove theorems/def that are now unnecessary. (cc @justus-springer)
Generalize isSheaf_iff_isSheaf_forget for sheaves on sites using isSheaf_iff_isLimit; use it to prove and generalize the result on topological spaces, removing a large chunk of code.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

dac8099a

Diff

@@ -26,6 +26,8 @@ and `A` live in the same universe.
   are all sheaves of sets, see `CategoryTheory.Presheaf.IsSheaf`.
 * When `A = Type`, this recovers the basic definition of sheaves of sets, see
   `CategoryTheory.isSheaf_iff_isSheaf_of_type`.
+* A alternate definition in terms of limits, unconditionally equivalent to the original one:
+  see `CategoryTheory.Presheaf.isSheaf_iff_isLimit`.
 * An alternate definition when `C` is small, has pullbacks and `A` has products is given by an
   equalizer condition `CategoryTheory.Presheaf.IsSheaf'`. This is equivalent to the earlier
   definition, shown in `CategoryTheory.Presheaf.isSheaf_iff_isSheaf'`.
@@ -50,7 +52,7 @@ inequalities this can be changed.
 -/
 
 
-universe w v₁ v₂ u₁ u₂
+universe w v₁ v₂ v₃ u₁ u₂ u₃
 
 noncomputable section
 
@@ -476,6 +478,7 @@ variable {C : Type u₁} [Category.{v₁} C]
 -- instead.
 variable {A : Type u₂} [Category.{v₂} A]
 variable {A' : Type u₂} [Category.{max v₁ u₁} A']
+variable {B : Type u₃} [Category.{v₃} B]
 
 variable (J : GrothendieckTopology C)
 
@@ -631,8 +634,8 @@ def isSheafForIsSheafFor' (P : Cᵒᵖ ⥤ A) (s : A ⥤ Type max v₁ u₁)
     simp [Fork.ι]
 #align category_theory.presheaf.is_sheaf_for_is_sheaf_for' CategoryTheory.Presheaf.isSheafForIsSheafFor'
 
--- Remark : this lemma and the next use `A'` not `A`; `A'` is `A` but with a universe
--- restriction. Can they be generalised?
+-- Remark : this lemma uses `A'` not `A`; `A'` is `A` but with a universe
+-- restriction. Can it be generalised?
 /-- The equalizer definition of a sheaf given by `isSheaf'` is equivalent to `isSheaf`. -/
 theorem isSheaf_iff_isSheaf' : IsSheaf J P' ↔ IsSheaf' J P' := by
   constructor
@@ -659,7 +662,21 @@ end
 
 section Concrete
 
-variable [HasPullbacks C]
+theorem isSheaf_of_isSheaf_comp (s : A ⥤ B) [ReflectsLimitsOfSize.{v₁, max v₁ u₁} s]
+    (h : IsSheaf J (P ⋙ s)) : IsSheaf J P := by
+  rw [isSheaf_iff_isLimit] at h ⊢
+  exact fun X S hS ↦ (h S hS).map fun t ↦ isLimitOfReflects s t
+
+theorem isSheaf_comp_of_isSheaf (s : A ⥤ B) [PreservesLimitsOfSize.{v₁, max v₁ u₁} s]
+    (h : IsSheaf J P) : IsSheaf J (P ⋙ s) := by
+  rw [isSheaf_iff_isLimit] at h ⊢
+  apply fun X S hS ↦ (h S hS).map fun t ↦ isLimitOfPreserves s t
+
+theorem isSheaf_iff_isSheaf_comp (s : A ⥤ B) [HasLimitsOfSize.{v₁, max v₁ u₁} A]
+    [PreservesLimitsOfSize.{v₁, max v₁ u₁} s] [ReflectsIsomorphisms s] :
+    IsSheaf J P ↔ IsSheaf J (P ⋙ s) := by
+  letI : ReflectsLimitsOfSize s := reflectsLimitsOfReflectsIsomorphisms
+  exact ⟨isSheaf_comp_of_isSheaf J P s, isSheaf_of_isSheaf_comp J P s⟩
 
 /--
 For a concrete category `(A, s)` where the forgetful functor `s : A ⥤ Type v` preserves limits and
@@ -672,17 +689,9 @@ hold.
 -/
 theorem isSheaf_iff_isSheaf_forget (s : A' ⥤ Type max v₁ u₁) [HasLimits A'] [PreservesLimits s]
     [ReflectsIsomorphisms s] : IsSheaf J P' ↔ IsSheaf J (P' ⋙ s) := by
-  rw [isSheaf_iff_isSheaf', isSheaf_iff_isSheaf']
-  refine' forall_congr' (fun U => ball_congr (fun R _ => _))
-  letI : ReflectsLimits s := reflectsLimitsOfReflectsIsomorphisms
-  have : IsLimit (s.mapCone (Fork.ofι _ (w R P'))) ≃ IsLimit (Fork.ofι _ (w R (P' ⋙ s))) :=
-    isSheafForIsSheafFor' P' s U R
-  rw [← Equiv.nonempty_congr this]
-  constructor
-  · haveI := preservesSmallestLimitsOfPreservesLimits s
-    exact Nonempty.map fun t => isLimitOfPreserves s t
-  · haveI := reflectsSmallestLimitsOfReflectsLimits s
-    exact Nonempty.map fun t => isLimitOfReflects s t
+  have : HasLimitsOfSize.{v₁, max v₁ u₁} A' := hasLimitsOfSizeShrink.{_, _, u₁, 0} A'
+  have : PreservesLimitsOfSize.{v₁, max v₁ u₁} s := preservesLimitsOfSizeShrink.{_, 0, _, u₁} s
+  apply isSheaf_iff_isSheaf_comp
 #align category_theory.presheaf.is_sheaf_iff_is_sheaf_forget CategoryTheory.Presheaf.isSheaf_iff_isSheaf_forget
 
 end Concrete

2efd2423

Revert "chore: revert #7703 (#7710)"

This reverts commit f3695eb2.

ab56fa28

Diff

@@ -107,6 +107,10 @@ def conesEquivSieveCompatibleFamily :
   right_inv x := rfl
 #align category_theory.presheaf.cones_equiv_sieve_compatible_family CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily
 
+-- These lemmas have always been bad (#7657), but leanprover/lean4#2644 made `simp` start noticing
+attribute [nolint simpNF] CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily_apply_coe
+  CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily_symm_apply_app
+
 variable {P S E} {x : FamilyOfElements (P ⋙ coyoneda.obj E) S.arrows} (hx : SieveCompatible x)
 
 /-- The cone corresponding to a sieve_compatible family of elements, dot notation enabled. -/

2efd2423

chore: revert #7703 (#7710)

This reverts commit 26eb2b0a.

f3695eb2

Diff

@@ -107,10 +107,6 @@ def conesEquivSieveCompatibleFamily :
   right_inv x := rfl
 #align category_theory.presheaf.cones_equiv_sieve_compatible_family CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily
 
--- These lemmas have always been bad (#7657), but leanprover/lean4#2644 made `simp` start noticing
-attribute [nolint simpNF] CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily_apply_coe
-  CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily_symm_apply_app
-
 variable {P S E} {x : FamilyOfElements (P ⋙ coyoneda.obj E) S.arrows} (hx : SieveCompatible x)
 
 /-- The cone corresponding to a sieve_compatible family of elements, dot notation enabled. -/

2efd2423

chore: bump toolchain to v4.2.0-rc2 (#7703)

This includes all the changes from #7606.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

26eb2b0a

Diff

@@ -107,6 +107,10 @@ def conesEquivSieveCompatibleFamily :
   right_inv x := rfl
 #align category_theory.presheaf.cones_equiv_sieve_compatible_family CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily
 
+-- These lemmas have always been bad (#7657), but leanprover/lean4#2644 made `simp` start noticing
+attribute [nolint simpNF] CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily_apply_coe
+  CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily_symm_apply_app
+
 variable {P S E} {x : FamilyOfElements (P ⋙ coyoneda.obj E) S.arrows} (hx : SieveCompatible x)
 
 /-- The cone corresponding to a sieve_compatible family of elements, dot notation enabled. -/

2efd2423

chore: replace ConeMorphism.Hom by ConeMorphism.hom (#7176)

3e44bb07

Diff

@@ -122,7 +122,7 @@ def _root_.CategoryTheory.Presieve.FamilyOfElements.SieveCompatible.cone :
     of the family. -/
 def homEquivAmalgamation : (hx.cone ⟶ P.mapCone S.arrows.cocone.op) ≃ { t // x.IsAmalgamation t }
     where
-  toFun l := ⟨l.Hom, fun _ f hf => l.w (op ⟨Over.mk f, hf⟩)⟩
+  toFun l := ⟨l.hom, fun _ f hf => l.w (op ⟨Over.mk f, hf⟩)⟩
   invFun t := ⟨t.1, fun f => t.2 f.unop.1.hom f.unop.2⟩
   left_inv _ := rfl
   right_inv _ := rfl

2efd2423

chore: remove unused simps (#6632)

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

916c75c1

Diff

@@ -615,12 +615,11 @@ def isSheafForIsSheafFor' (P : Cᵒᵖ ⥤ A) (s : A ⥤ Type max v₁ u₁)
       · refine' limit.hom_ext (fun j => _)
         dsimp [Equalizer.Presieve.firstMap, firstMap]
         simp only [limit.lift_π, map_lift_piComparison, assoc, Fan.mk_π_app, Functor.map_comp]
-        dsimp [Equalizer.Presieve.firstMap, firstMap]
-        erw [piComparison_comp_π_assoc]
+        rw [piComparison_comp_π_assoc]
       · refine' limit.hom_ext (fun j => _)
         dsimp [Equalizer.Presieve.secondMap, secondMap]
         simp only [limit.lift_π, map_lift_piComparison, assoc, Fan.mk_π_app, Functor.map_comp]
-        erw [piComparison_comp_π_assoc]
+        rw [piComparison_comp_π_assoc]
       · dsimp
         simp
   · refine' Fork.ext (Iso.refl _) _

2efd2423

chore: ensure all instances referred to directly have explicit names (#6423)

Per https://github.com/leanprover/lean4/issues/2343, we are going to need to change the automatic generation of instance names, as they become too long.

This PR ensures that everywhere in Mathlib that refers to an instance by name, that name is given explicitly, rather than being automatically generated.

There are four exceptions, which are now commented, with links to https://github.com/leanprover/lean4/issues/2343.

This was implemented by running Mathlib against a modified Lean that appended _ᾰ to all automatically generated names, and fixing everything.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

65a35f78

Diff

@@ -292,7 +292,7 @@ set_option linter.uppercaseLean3 false in
 #align category_theory.Sheaf.hom CategoryTheory.Sheaf.Hom
 
 @[simps id_val comp_val]
-instance : Category (Sheaf J A) where
+instance instCategorySheaf : Category (Sheaf J A) where
   Hom := Hom
   id _ := ⟨𝟙 _⟩
   comp f g := ⟨f.val ≫ g.val⟩

2efd2423

chore: more universe generalisations / fixes (#5659)

There are changes of two types: first I add some .{w} in some declarations to ensure that universes are in the right order. Secondly I generalise some results from Category.{max u1 v1, u2} to Category.{v2, u2}.

From the Copenhagen workshop.

44692e22

Diff

@@ -37,6 +37,16 @@ and `A` live in the same universe.
   Cf https://stacks.math.columbia.edu/tag/0073, which is a weaker version of this statement (it's
   only over spaces, not sites) and https://stacks.math.columbia.edu/tag/00YR (a), which
   additionally assumes filtered colimits.
+
+## Implementation notes
+
+Occasionally we need to take a limit in `A` of a collection of morphisms of `C` indexed
+by a collection of objects in `C`. This turns out to force the morphisms of `A` to be
+in a sufficiently large universe. Rather than use `UnivLE` we prove some results for
+a category `A'` instead, whose morphism universe of `A'` is defined to be `max u₁ v₁`, where
+`u₁, v₁` are the universes for `C`. Perhaps after we get better at handling universe
+inequalities this can be changed.
+
 -/
 
 
@@ -215,7 +225,7 @@ variable {J}
   If `P`s a sheaf, `S` is a cover of `X`, and `x` is a collection of morphisms from `E`
   to `P` evaluated at terms in the cover which are compatible, then we can amalgamate
   the `x`s to obtain a single morphism `E ⟶ P.obj (op X)`. -/
-def IsSheaf.amalgamate {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
+def IsSheaf.amalgamate {A : Type u₂} [Category.{v₂} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
     (hP : Presheaf.IsSheaf J P) (S : J.Cover X) (x : ∀ I : S.Arrow, E ⟶ P.obj (op I.Y))
     (hx : ∀ I : S.Relation, x I.fst ≫ P.map I.g₁.op = x I.snd ≫ P.map I.g₂.op) : E ⟶ P.obj (op X) :=
   (hP _ _ S.condition).amalgamate (fun Y f hf => x ⟨Y, f, hf⟩) fun Y₁ Y₂ Z g₁ g₂ f₁ f₂ h₁ h₂ w =>
@@ -223,7 +233,7 @@ def IsSheaf.amalgamate {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X :
 #align category_theory.presheaf.is_sheaf.amalgamate CategoryTheory.Presheaf.IsSheaf.amalgamate
 
 @[reassoc (attr := simp)]
-theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
+theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{v₂} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
     (hP : Presheaf.IsSheaf J P) (S : J.Cover X) (x : ∀ I : S.Arrow, E ⟶ P.obj (op I.Y))
     (hx : ∀ I : S.Relation, x I.fst ≫ P.map I.g₁.op = x I.snd ≫ P.map I.g₂.op) (I : S.Arrow) :
     hP.amalgamate S x hx ≫ P.map I.f.op = x _ := by
@@ -233,7 +243,7 @@ theorem IsSheaf.amalgamate_map {A : Type u₂} [Category.{max v₁ u₁} A] {E :
       (fun Y₁ Y₂ Z g₁ g₂ f₁ f₂ h₁ h₂ w => hx ⟨Y₁, Y₂, Z, g₁, g₂, f₁, f₂, h₁, h₂, w⟩) f hf
 #align category_theory.presheaf.is_sheaf.amalgamate_map CategoryTheory.Presheaf.IsSheaf.amalgamate_map
 
-theorem IsSheaf.hom_ext {A : Type u₂} [Category.{max v₁ u₁} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
+theorem IsSheaf.hom_ext {A : Type u₂} [Category.{v₂} A] {E : A} {X : C} {P : Cᵒᵖ ⥤ A}
     (hP : Presheaf.IsSheaf J P) (S : J.Cover X) (e₁ e₂ : E ⟶ P.obj (op X))
     (h : ∀ I : S.Arrow, e₁ ≫ P.map I.f.op = e₂ ≫ P.map I.f.op) : e₁ = e₂ :=
   (hP _ _ S.condition).isSeparatedFor.ext fun Y f hf => h ⟨Y, f, hf⟩
@@ -454,13 +464,20 @@ namespace Presheaf
 -- between 00VQ and 00VR.
 variable {C : Type u₁} [Category.{v₁} C]
 
-variable {A : Type u₂} [Category.{max v₁ u₁} A]
+-- `A` is a general category; `A'` is a variant where the morphisms live in a large enough
+-- universe to guarantee that we can take limits in A of things coming from C.
+-- I would have liked to use something like `UnivLE.{max v₁ u₁, v₂}` as a hypothesis on
+-- `A`'s morphism universe rather than introducing `A'` but I can't get it to work.
+-- So, for now, results which need max v₁ u₁ ≤ v₂ are just stated for `A'` and `P' : Cᵒᵖ ⥤ A'`
+-- instead.
+variable {A : Type u₂} [Category.{v₂} A]
+variable {A' : Type u₂} [Category.{max v₁ u₁} A']
 
 variable (J : GrothendieckTopology C)
 
 variable {U : C} (R : Presieve U)
 
-variable (P : Cᵒᵖ ⥤ A)
+variable (P : Cᵒᵖ ⥤ A) (P' : Cᵒᵖ ⥤ A')
 
 section MultiequalizerConditions
 
@@ -527,6 +544,7 @@ end MultiequalizerConditions
 section
 
 variable [HasProducts.{max u₁ v₁} A]
+variable [HasProducts.{max u₁ v₁} A']
 
 /--
 The middle object of the fork diagram given in Equation (3) of [MM92], as well as the fork diagram
@@ -580,6 +598,8 @@ def IsSheaf' (P : Cᵒᵖ ⥤ A) : Prop :=
   ∀ (U : C) (R : Presieve U) (_ : generate R ∈ J U), Nonempty (IsLimit (Fork.ofι _ (w R P)))
 #align category_theory.presheaf.is_sheaf' CategoryTheory.Presheaf.IsSheaf'
 
+-- Again I wonder whether `UnivLE` can somehow be used to allow `s` to take
+-- values in a more general universe.
 /-- (Implementation). An auxiliary lemma to convert between sheaf conditions. -/
 def isSheafForIsSheafFor' (P : Cᵒᵖ ⥤ A) (s : A ⥤ Type max v₁ u₁)
     [∀ J, PreservesLimitsOfShape (Discrete.{max v₁ u₁} J) s] (U : C) (R : Presieve U) :
@@ -608,14 +628,16 @@ def isSheafForIsSheafFor' (P : Cᵒᵖ ⥤ A) (s : A ⥤ Type max v₁ u₁)
     simp [Fork.ι]
 #align category_theory.presheaf.is_sheaf_for_is_sheaf_for' CategoryTheory.Presheaf.isSheafForIsSheafFor'
 
+-- Remark : this lemma and the next use `A'` not `A`; `A'` is `A` but with a universe
+-- restriction. Can they be generalised?
 /-- The equalizer definition of a sheaf given by `isSheaf'` is equivalent to `isSheaf`. -/
-theorem isSheaf_iff_isSheaf' : IsSheaf J P ↔ IsSheaf' J P := by
+theorem isSheaf_iff_isSheaf' : IsSheaf J P' ↔ IsSheaf' J P' := by
   constructor
   · intro h U R hR
     refine' ⟨_⟩
     apply coyonedaJointlyReflectsLimits
     intro X
-    have q : Presieve.IsSheafFor (P ⋙ coyoneda.obj X) _ := h X.unop _ hR
+    have q : Presieve.IsSheafFor (P' ⋙ coyoneda.obj X) _ := h X.unop _ hR
     rw [← Presieve.isSheafFor_iff_generate] at q
     rw [Equalizer.Presieve.sheaf_condition] at q
     replace q := Classical.choice q
@@ -645,13 +667,13 @@ Note this lemma applies for "algebraic" categories, eg groups, abelian groups an
 for the category of topological spaces, topological rings, etc since reflecting isomorphisms doesn't
 hold.
 -/
-theorem isSheaf_iff_isSheaf_forget (s : A ⥤ Type max v₁ u₁) [HasLimits A] [PreservesLimits s]
-    [ReflectsIsomorphisms s] : IsSheaf J P ↔ IsSheaf J (P ⋙ s) := by
+theorem isSheaf_iff_isSheaf_forget (s : A' ⥤ Type max v₁ u₁) [HasLimits A'] [PreservesLimits s]
+    [ReflectsIsomorphisms s] : IsSheaf J P' ↔ IsSheaf J (P' ⋙ s) := by
   rw [isSheaf_iff_isSheaf', isSheaf_iff_isSheaf']
   refine' forall_congr' (fun U => ball_congr (fun R _ => _))
   letI : ReflectsLimits s := reflectsLimitsOfReflectsIsomorphisms
-  have : IsLimit (s.mapCone (Fork.ofι _ (w R P))) ≃ IsLimit (Fork.ofι _ (w R (P ⋙ s))) :=
-    isSheafForIsSheafFor' P s U R
+  have : IsLimit (s.mapCone (Fork.ofι _ (w R P'))) ≃ IsLimit (Fork.ofι _ (w R (P' ⋙ s))) :=
+    isSheafForIsSheafFor' P' s U R
   rw [← Equiv.nonempty_congr this]
   constructor
   · haveI := preservesSmallestLimitsOfPreservesLimits s

2efd2423

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Kevin Buzzard, Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.sites.sheaf
-! leanprover-community/mathlib commit 2efd2423f8d25fa57cf7a179f5d8652ab4d0df44
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers
 import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products
@@ -14,6 +9,8 @@ import Mathlib.CategoryTheory.Limits.Yoneda
 import Mathlib.CategoryTheory.Preadditive.FunctorCategory
 import Mathlib.CategoryTheory.Sites.SheafOfTypes
 
+#align_import category_theory.sites.sheaf from "leanprover-community/mathlib"@"2efd2423f8d25fa57cf7a179f5d8652ab4d0df44"
+
 /-!
 # Sheaves taking values in a category

2efd2423

chore: review of automation in category theory (#4793)

Clean up of automation in the category theory library. Leaving out unnecessary proof steps, or fields done by aesop_cat, and making more use of available autoparameters.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

5b958613

Diff

@@ -368,8 +368,8 @@ def sheafEquivSheafOfTypes : Sheaf J (Type w) ≌ SheafOfTypes J where
   inverse :=
     { obj := fun S => ⟨S.val, (isSheaf_iff_isSheaf_of_type _ _).2 S.2⟩
       map := fun f => ⟨f.val⟩ }
-  unitIso := NatIso.ofComponents (fun X => Iso.refl _) (by aesop_cat)
-  counitIso := NatIso.ofComponents (fun X => Iso.refl _) (by aesop_cat)
+  unitIso := NatIso.ofComponents fun X => Iso.refl _
+  counitIso := NatIso.ofComponents fun X => Iso.refl _
 set_option linter.uppercaseLean3 false in
 #align category_theory.Sheaf_equiv_SheafOfTypes CategoryTheory.sheafEquivSheafOfTypes
 
@@ -441,14 +441,6 @@ instance Sheaf.Hom.addCommGroup : AddCommGroup (P ⟶ Q) :=
 
 instance : Preadditive (Sheaf J A) where
   homGroup P Q := Sheaf.Hom.addCommGroup
-  add_comp P Q R f f' g := by
-    ext
-    dsimp
-    simp
-  comp_add P Q R f g g' := by
-    ext
-    dsimp
-    simp
 
 end Preadditive

2efd2423

chore: made Opposite a structure (#3193)

The opposite category is no longer a type synonym, but a structure.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net>

d090d0a8

Diff

@@ -84,11 +84,10 @@ def conesEquivSieveCompatibleFamily :
     (S.arrows.diagram.op ⋙ P).cones.obj E ≃
       { x : FamilyOfElements (P ⋙ coyoneda.obj E) (S : Presieve X) // x.SieveCompatible } where
   toFun π :=
-    ⟨fun Y f h => π.app (op ⟨Over.mk f, h⟩), fun _ => by
-      intros
+    ⟨fun Y f h => π.app (op ⟨Over.mk f, h⟩), fun X Y f g hf => by
       apply (id_comp _).symm.trans
       dsimp
-      convert π.naturality (Quiver.Hom.op (Over.homMk _ _)) <;> rfl⟩
+      exact π.naturality (Quiver.Hom.op (Over.homMk _ (by rfl)))⟩
   invFun x :=
     { app := fun f => x.1 f.unop.1.hom f.unop.2
       naturality := fun f f' g => by
@@ -96,7 +95,7 @@ def conesEquivSieveCompatibleFamily :
         dsimp
         rw [id_comp]
         convert rfl
-        rw [Over.w g.unop] }
+        rw [Over.w] }
   left_inv π := rfl
   right_inv x := rfl
 #align category_theory.presheaf.cones_equiv_sieve_compatible_family CategoryTheory.Presheaf.conesEquivSieveCompatibleFamily

2efd2423

chore: forward port mathlib#17611, 18742, 18198, 18520 (#3389)

SHA-only updates:

leanprover-community/mathlib#17611 – CategoryTheory.Sites.Sheaf already uses aesop_cat at this location, nothing to port.
leanprover-community/mathlib#18742 – fiber spelling, which is all of the changes to Topology.FiberBundle.Trivialization, is already in mathlib4.
leanprover-community/mathlib#18198 – FunLike change to Data.PEquiv is already in mathlib4.

Substantative forward port:

leanprover-community/mathlib#18520

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

84169f45

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module category_theory.sites.sheaf
-! leanprover-community/mathlib commit a67ec23dd8dc08195d77b6df2cd21f9c64989131
+! leanprover-community/mathlib commit 2efd2423f8d25fa57cf7a179f5d8652ab4d0df44
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

a67ec23d

feat: port CategoryTheory.Sites.Sheaf (#3244)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

50dc55de

`category_theory.sites.sheaf` ⟷ `Mathlib.CategoryTheory.Sites.Sheaf`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 313

category_theory.sites.sheaf ⟷ Mathlib.CategoryTheory.Sites.Sheaf

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 313

`category_theory.sites.sheaf` ⟷ `Mathlib.CategoryTheory.Sites.Sheaf`