category_theory.sites.closed | 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

4cfc30e3

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

599fffe7

bump to nightly-2024-04-25-08

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

ad7a2212

Diff

@@ -246,7 +246,7 @@ theorem classifier_isSheaf : Presieve.IsSheaf J₁ (Functor.closedSieves J₁) :
       apply congr_arg Subtype.val ((hM₂ g hg).trans (hN₂ g hg).symm)
     have MSNS : M ⊓ S = N ⊓ S := by
       ext Z g
-      rw [sieve.inter_apply, sieve.inter_apply, and_comm' (N g), and_comm']
+      rw [sieve.inter_apply, sieve.inter_apply, and_comm (N g), and_comm]
       apply and_congr_right
       intro hg
       rw [sieve.pullback_eq_top_iff_mem, sieve.pullback_eq_top_iff_mem, q g hg]

599fffe7

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 -/
-import CategoryTheory.Sites.SheafOfTypes
+import CategoryTheory.Sites.IsSheafFor
 import Order.Closure
 
 #align_import category_theory.sites.closed from "leanprover-community/mathlib"@"599fffe78f0e11eb6a034e834ec51882167b9688"

599fffe7

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -262,7 +262,7 @@ theorem classifier_isSheaf : Presieve.IsSheaf J₁ (Functor.closedSieves J₁) :
       rw [MSNS]
       apply J₁.arrow_intersect f N S hf (J₁.pullback_stable _ hS)
   · intro x hx
-    rw [presieve.compatible_iff_sieve_compatible] at hx 
+    rw [presieve.compatible_iff_sieve_compatible] at hx
     let M := sieve.bind S fun Y f hf => (x f hf).1
     have : ∀ ⦃Y⦄ (f : Y ⟶ X) (hf : S f), M.pullback f = (x f hf).1 :=
       by
@@ -297,7 +297,7 @@ theorem le_topology_of_closedSieves_isSheaf {J₁ J₂ : GrothendieckTopology C}
     trivial
   suffices (⟨J₂.close S, J₂.close_is_closed S⟩ : Subtype _) = ⟨⊤, this⟩
     by
-    rw [Subtype.ext_iff] at this 
+    rw [Subtype.ext_iff] at this
     exact this
   apply (h S hS).IsSeparatedFor.ext
   · intro Y f hf
@@ -342,10 +342,10 @@ def topologyOfClosureOperator (c : ∀ X : C, ClosureOperator (Sieve X))
   sieves X := {S | c X S = ⊤}
   top_mem' X := top_unique ((c X).le_closure _)
   pullback_stable' X Y S f hS := by
-    rw [Set.mem_setOf_eq] at hS 
+    rw [Set.mem_setOf_eq] at hS
     rw [Set.mem_setOf_eq, hc, hS, sieve.pullback_top]
   transitive' X S hS R hR := by
-    rw [Set.mem_setOf_eq] at hS 
+    rw [Set.mem_setOf_eq] at hS
     rw [Set.mem_setOf_eq, ← (c X).idempotent, eq_top_iff, ← hS]
     apply (c X).Monotone fun Y f hf => _
     rw [sieve.pullback_eq_top_iff_mem, ← hc]

599fffe7

bump to nightly-2023-12-22-06

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

485b2c6c

Diff

@@ -204,12 +204,12 @@ def closureOperator (X : C) : ClosureOperator (Sieve X) :=
 #align category_theory.grothendieck_topology.closure_operator CategoryTheory.GrothendieckTopology.closureOperator
 -/
 
-#print CategoryTheory.GrothendieckTopology.closed_iff_closed /-
+#print CategoryTheory.GrothendieckTopology.closureOperator_isClosed /-
 @[simp]
-theorem closed_iff_closed {X : C} (S : Sieve X) :
+theorem closureOperator_isClosed {X : C} (S : Sieve X) :
     S ∈ (J₁.ClosureOperator X).closed ↔ J₁.IsClosed S :=
   (J₁.isClosed_iff_close_eq_self S).symm
-#align category_theory.grothendieck_topology.closed_iff_closed CategoryTheory.GrothendieckTopology.closed_iff_closed
+#align category_theory.grothendieck_topology.closed_iff_closed CategoryTheory.GrothendieckTopology.closureOperator_isClosed
 -/
 
 end GrothendieckTopology

599fffe7

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 -/
-import Mathbin.CategoryTheory.Sites.SheafOfTypes
-import Mathbin.Order.Closure
+import CategoryTheory.Sites.SheafOfTypes
+import Order.Closure
 
 #align_import category_theory.sites.closed from "leanprover-community/mathlib"@"599fffe78f0e11eb6a034e834ec51882167b9688"

599fffe7

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.sites.closed
-! leanprover-community/mathlib commit 599fffe78f0e11eb6a034e834ec51882167b9688
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Sites.SheafOfTypes
 import Mathbin.Order.Closure
 
+#align_import category_theory.sites.closed from "leanprover-community/mathlib"@"599fffe78f0e11eb6a034e834ec51882167b9688"
+
 /-!
 # Closed sieves

599fffe7

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -248,7 +248,7 @@ theorem classifier_isSheaf : Presieve.IsSheaf J₁ (Functor.closedSieves J₁) :
       intro Z g hg
       apply congr_arg Subtype.val ((hM₂ g hg).trans (hN₂ g hg).symm)
     have MSNS : M ⊓ S = N ⊓ S := by
-      ext (Z g)
+      ext Z g
       rw [sieve.inter_apply, sieve.inter_apply, and_comm' (N g), and_comm']
       apply and_congr_right
       intro hg
@@ -363,7 +363,7 @@ The topology given by the closure operator `J.close` on a Grothendieck topology
 theorem topologyOfClosureOperator_self :
     (topologyOfClosureOperator J₁.ClosureOperator fun X Y => J₁.pullback_close) = J₁ :=
   by
-  ext (X S)
+  ext X S
   apply grothendieck_topology.close_eq_top_iff_mem
 #align category_theory.topology_of_closure_operator_self CategoryTheory.topologyOfClosureOperator_self
 -/

599fffe7

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -73,10 +73,12 @@ def close {X : C} (S : Sieve X) : Sieve X
 #align category_theory.grothendieck_topology.close CategoryTheory.GrothendieckTopology.close
 -/
 
+#print CategoryTheory.GrothendieckTopology.le_close /-
 /-- Any sieve is smaller than its closure. -/
 theorem le_close {X : C} (S : Sieve X) : S ≤ J₁.close S := fun Y g hg =>
   J₁.covering_of_eq_top (S.pullback_eq_top_of_mem hg)
 #align category_theory.grothendieck_topology.le_close CategoryTheory.GrothendieckTopology.le_close
+-/
 
 #print CategoryTheory.GrothendieckTopology.IsClosed /-
 /-- A sieve is closed for the Grothendieck topology if it contains every arrow it covers.
@@ -106,12 +108,14 @@ theorem isClosed_pullback {X Y : C} (f : Y ⟶ X) (S : Sieve X) :
 #align category_theory.grothendieck_topology.is_closed_pullback CategoryTheory.GrothendieckTopology.isClosed_pullback
 -/
 
+#print CategoryTheory.GrothendieckTopology.le_close_of_isClosed /-
 /-- The closure of a sieve `S` is the largest closed sieve which contains `S` (justifying the name
 "closure").
 -/
 theorem le_close_of_isClosed {X : C} {S T : Sieve X} (h : S ≤ T) (hT : J₁.IsClosed T) :
     J₁.close S ≤ T := fun Y f hf => hT _ (J₁.superset_covering (Sieve.pullback_monotone f h) hf)
 #align category_theory.grothendieck_topology.le_close_of_is_closed CategoryTheory.GrothendieckTopology.le_close_of_isClosed
+-/
 
 #print CategoryTheory.GrothendieckTopology.close_isClosed /-
 /-- The closure of a sieve is closed. -/
@@ -158,10 +162,12 @@ theorem pullback_close {X Y : C} (f : Y ⟶ X) (S : Sieve X) :
 #align category_theory.grothendieck_topology.pullback_close CategoryTheory.GrothendieckTopology.pullback_close
 -/
 
+#print CategoryTheory.GrothendieckTopology.monotone_close /-
 @[mono]
 theorem monotone_close {X : C} : Monotone (J₁.close : Sieve X → Sieve X) := fun S₁ S₂ h =>
   J₁.le_close_of_isClosed (h.trans (J₁.le_close _)) (J₁.close_isClosed S₂)
 #align category_theory.grothendieck_topology.monotone_close CategoryTheory.GrothendieckTopology.monotone_close
+-/
 
 #print CategoryTheory.GrothendieckTopology.close_close /-
 @[simp]
@@ -171,6 +177,7 @@ theorem close_close {X : C} (S : Sieve X) : J₁.close (J₁.close S) = J₁.clo
 #align category_theory.grothendieck_topology.close_close CategoryTheory.GrothendieckTopology.close_close
 -/
 
+#print CategoryTheory.GrothendieckTopology.close_eq_top_iff_mem /-
 /--
 The sieve `S` is in the topology iff its closure is the maximal sieve. This shows that the closure
 operator determines the topology.
@@ -188,7 +195,9 @@ theorem close_eq_top_iff_mem {X : C} (S : Sieve X) : J₁.close S = ⊤ ↔ S 
     intro Y f hf
     apply J₁.pullback_stable _ hS
 #align category_theory.grothendieck_topology.close_eq_top_iff_mem CategoryTheory.GrothendieckTopology.close_eq_top_iff_mem
+-/
 
+#print CategoryTheory.GrothendieckTopology.closureOperator /-
 /-- A Grothendieck topology induces a natural family of closure operators on sieves. -/
 @[simps (config := { rhsMd := semireducible })]
 def closureOperator (X : C) : ClosureOperator (Sieve X) :=
@@ -196,6 +205,7 @@ def closureOperator (X : C) : ClosureOperator (Sieve X) :=
     (fun S₁ S₂ h => J₁.le_close_of_isClosed (h.trans (J₁.le_close _)) (J₁.close_isClosed S₂))
     J₁.le_close fun S => J₁.le_close_of_isClosed le_rfl (J₁.close_isClosed S)
 #align category_theory.grothendieck_topology.closure_operator CategoryTheory.GrothendieckTopology.closureOperator
+-/
 
 #print CategoryTheory.GrothendieckTopology.closed_iff_closed /-
 @[simp]
@@ -322,6 +332,7 @@ theorem topology_eq_iff_same_sheaves {J₁ J₂ : GrothendieckTopology C} :
 #align category_theory.topology_eq_iff_same_sheaves CategoryTheory.topology_eq_iff_same_sheaves
 -/
 
+#print CategoryTheory.topologyOfClosureOperator /-
 /--
 A closure (increasing, inflationary and idempotent) operation on sieves that commutes with pullback
 induces a Grothendieck topology.
@@ -343,6 +354,7 @@ def topologyOfClosureOperator (c : ∀ X : C, ClosureOperator (Sieve X))
     rw [sieve.pullback_eq_top_iff_mem, ← hc]
     apply hR hf
 #align category_theory.topology_of_closure_operator CategoryTheory.topologyOfClosureOperator
+-/
 
 #print CategoryTheory.topologyOfClosureOperator_self /-
 /--
@@ -356,6 +368,7 @@ theorem topologyOfClosureOperator_self :
 #align category_theory.topology_of_closure_operator_self CategoryTheory.topologyOfClosureOperator_self
 -/
 
+#print CategoryTheory.topologyOfClosureOperator_close /-
 theorem topologyOfClosureOperator_close (c : ∀ X : C, ClosureOperator (Sieve X))
     (pb : ∀ ⦃X Y : C⦄ (f : Y ⟶ X) (S : Sieve X), c Y (S.pullback f) = (c X S).pullback f) (X : C)
     (S : Sieve X) : (topologyOfClosureOperator c pb).close S = c X S :=
@@ -364,6 +377,7 @@ theorem topologyOfClosureOperator_close (c : ∀ X : C, ClosureOperator (Sieve X
   change c _ (sieve.pullback f S) = ⊤ ↔ c _ S f
   rw [pb, sieve.pullback_eq_top_iff_mem]
 #align category_theory.topology_of_closure_operator_close CategoryTheory.topologyOfClosureOperator_close
+-/
 
 end CategoryTheory

599fffe7

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -331,7 +331,7 @@ In fact, such operations are in bijection with Grothendieck topologies.
 def topologyOfClosureOperator (c : ∀ X : C, ClosureOperator (Sieve X))
     (hc : ∀ ⦃X Y : C⦄ (f : Y ⟶ X) (S : Sieve X), c _ (S.pullback f) = (c _ S).pullback f) :
     GrothendieckTopology C where
-  sieves X := { S | c X S = ⊤ }
+  sieves X := {S | c X S = ⊤}
   top_mem' X := top_unique ((c X).le_closure _)
   pullback_stable' X Y S f hS := by
     rw [Set.mem_setOf_eq] at hS

599fffe7

bump to nightly-2023-06-02-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/34ebaffc1d1e8e783fc05438ec2e70af87275ac9

c039be4e

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 
 ! This file was ported from Lean 3 source module category_theory.sites.closed
-! leanprover-community/mathlib commit 4cfc30e317caad46858393f1a7a33f609296cc30
+! leanprover-community/mathlib commit 599fffe78f0e11eb6a034e834ec51882167b9688
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Order.Closure
 /-!
 # Closed sieves
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A natural closure operator on sieves is a closure operator on `sieve X` for each `X` which commutes
 with pullback.
 We show that a Grothendieck topology `J` induces a natural closure operator, and define what the

4cfc30e3

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -252,7 +252,7 @@ theorem classifier_isSheaf : Presieve.IsSheaf J₁ (Functor.closedSieves J₁) :
       rw [MSNS]
       apply J₁.arrow_intersect f N S hf (J₁.pullback_stable _ hS)
   · intro x hx
-    rw [presieve.compatible_iff_sieve_compatible] at hx
+    rw [presieve.compatible_iff_sieve_compatible] at hx 
     let M := sieve.bind S fun Y f hf => (x f hf).1
     have : ∀ ⦃Y⦄ (f : Y ⟶ X) (hf : S f), M.pullback f = (x f hf).1 :=
       by
@@ -287,7 +287,7 @@ theorem le_topology_of_closedSieves_isSheaf {J₁ J₂ : GrothendieckTopology C}
     trivial
   suffices (⟨J₂.close S, J₂.close_is_closed S⟩ : Subtype _) = ⟨⊤, this⟩
     by
-    rw [Subtype.ext_iff] at this
+    rw [Subtype.ext_iff] at this 
     exact this
   apply (h S hS).IsSeparatedFor.ext
   · intro Y f hf
@@ -331,10 +331,10 @@ def topologyOfClosureOperator (c : ∀ X : C, ClosureOperator (Sieve X))
   sieves X := { S | c X S = ⊤ }
   top_mem' X := top_unique ((c X).le_closure _)
   pullback_stable' X Y S f hS := by
-    rw [Set.mem_setOf_eq] at hS
+    rw [Set.mem_setOf_eq] at hS 
     rw [Set.mem_setOf_eq, hc, hS, sieve.pullback_top]
   transitive' X S hS R hR := by
-    rw [Set.mem_setOf_eq] at hS
+    rw [Set.mem_setOf_eq] at hS 
     rw [Set.mem_setOf_eq, ← (c X).idempotent, eq_top_iff, ← hS]
     apply (c X).Monotone fun Y f hf => _
     rw [sieve.pullback_eq_top_iff_mem, ← hc]

4cfc30e3

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -60,6 +60,7 @@ variable (J₁ J₂ : GrothendieckTopology C)
 
 namespace GrothendieckTopology
 
+#print CategoryTheory.GrothendieckTopology.close /-
 /-- The `J`-closure of a sieve is the collection of arrows which it covers. -/
 @[simps]
 def close {X : C} (S : Sieve X) : Sieve X
@@ -67,12 +68,14 @@ def close {X : C} (S : Sieve X) : Sieve X
   arrows Y f := J₁.Covers S f
   downward_closed' Y Z f hS := J₁.arrow_stable _ _ hS
 #align category_theory.grothendieck_topology.close CategoryTheory.GrothendieckTopology.close
+-/
 
 /-- Any sieve is smaller than its closure. -/
 theorem le_close {X : C} (S : Sieve X) : S ≤ J₁.close S := fun Y g hg =>
   J₁.covering_of_eq_top (S.pullback_eq_top_of_mem hg)
 #align category_theory.grothendieck_topology.le_close CategoryTheory.GrothendieckTopology.le_close
 
+#print CategoryTheory.GrothendieckTopology.IsClosed /-
 /-- A sieve is closed for the Grothendieck topology if it contains every arrow it covers.
 In the case of the usual topology on a topological space, this means that the open cover contains
 every open set which it covers.
@@ -82,18 +85,23 @@ Note this has no relation to a closed subset of a topological space.
 def IsClosed {X : C} (S : Sieve X) : Prop :=
   ∀ ⦃Y : C⦄ (f : Y ⟶ X), J₁.Covers S f → S f
 #align category_theory.grothendieck_topology.is_closed CategoryTheory.GrothendieckTopology.IsClosed
+-/
 
+#print CategoryTheory.GrothendieckTopology.covers_iff_mem_of_isClosed /-
 /-- If `S` is `J₁`-closed, then `S` covers exactly the arrows it contains. -/
-theorem covers_iff_mem_of_closed {X : C} {S : Sieve X} (h : J₁.IsClosed S) {Y : C} (f : Y ⟶ X) :
+theorem covers_iff_mem_of_isClosed {X : C} {S : Sieve X} (h : J₁.IsClosed S) {Y : C} (f : Y ⟶ X) :
     J₁.Covers S f ↔ S f :=
   ⟨h _, J₁.arrow_max _ _⟩
-#align category_theory.grothendieck_topology.covers_iff_mem_of_closed CategoryTheory.GrothendieckTopology.covers_iff_mem_of_closed
+#align category_theory.grothendieck_topology.covers_iff_mem_of_closed CategoryTheory.GrothendieckTopology.covers_iff_mem_of_isClosed
+-/
 
+#print CategoryTheory.GrothendieckTopology.isClosed_pullback /-
 /-- Being `J`-closed is stable under pullback. -/
 theorem isClosed_pullback {X Y : C} (f : Y ⟶ X) (S : Sieve X) :
     J₁.IsClosed S → J₁.IsClosed (S.pullback f) := fun hS Z g hg =>
   hS (g ≫ f) (by rwa [J₁.covers_iff, sieve.pullback_comp])
 #align category_theory.grothendieck_topology.is_closed_pullback CategoryTheory.GrothendieckTopology.isClosed_pullback
+-/
 
 /-- The closure of a sieve `S` is the largest closed sieve which contains `S` (justifying the name
 "closure").
@@ -102,11 +110,14 @@ theorem le_close_of_isClosed {X : C} {S T : Sieve X} (h : S ≤ T) (hT : J₁.Is
     J₁.close S ≤ T := fun Y f hf => hT _ (J₁.superset_covering (Sieve.pullback_monotone f h) hf)
 #align category_theory.grothendieck_topology.le_close_of_is_closed CategoryTheory.GrothendieckTopology.le_close_of_isClosed
 
+#print CategoryTheory.GrothendieckTopology.close_isClosed /-
 /-- The closure of a sieve is closed. -/
 theorem close_isClosed {X : C} (S : Sieve X) : J₁.IsClosed (J₁.close S) := fun Y g hg =>
   J₁.arrow_trans g _ S hg fun Z h hS => hS
 #align category_theory.grothendieck_topology.close_is_closed CategoryTheory.GrothendieckTopology.close_isClosed
+-/
 
+#print CategoryTheory.GrothendieckTopology.isClosed_iff_close_eq_self /-
 /-- The sieve `S` is closed iff its closure is equal to itself. -/
 theorem isClosed_iff_close_eq_self {X : C} (S : Sieve X) : J₁.IsClosed S ↔ J₁.close S = S :=
   by
@@ -121,11 +132,15 @@ theorem isClosed_iff_close_eq_self {X : C} (S : Sieve X) : J₁.IsClosed S ↔ J
     rw [← e]
     apply J₁.close_is_closed
 #align category_theory.grothendieck_topology.is_closed_iff_close_eq_self CategoryTheory.GrothendieckTopology.isClosed_iff_close_eq_self
+-/
 
+#print CategoryTheory.GrothendieckTopology.close_eq_self_of_isClosed /-
 theorem close_eq_self_of_isClosed {X : C} {S : Sieve X} (hS : J₁.IsClosed S) : J₁.close S = S :=
   (J₁.isClosed_iff_close_eq_self S).1 hS
 #align category_theory.grothendieck_topology.close_eq_self_of_is_closed CategoryTheory.GrothendieckTopology.close_eq_self_of_isClosed
+-/
 
+#print CategoryTheory.GrothendieckTopology.pullback_close /-
 /-- Closing under `J` is stable under pullback. -/
 theorem pullback_close {X Y : C} (f : Y ⟶ X) (S : Sieve X) :
     J₁.close (S.pullback f) = (J₁.close S).pullback f :=
@@ -138,17 +153,20 @@ theorem pullback_close {X Y : C} (f : Y ⟶ X) (S : Sieve X) :
     rw [← sieve.pullback_comp]
     apply hg
 #align category_theory.grothendieck_topology.pullback_close CategoryTheory.GrothendieckTopology.pullback_close
+-/
 
 @[mono]
 theorem monotone_close {X : C} : Monotone (J₁.close : Sieve X → Sieve X) := fun S₁ S₂ h =>
   J₁.le_close_of_isClosed (h.trans (J₁.le_close _)) (J₁.close_isClosed S₂)
 #align category_theory.grothendieck_topology.monotone_close CategoryTheory.GrothendieckTopology.monotone_close
 
+#print CategoryTheory.GrothendieckTopology.close_close /-
 @[simp]
 theorem close_close {X : C} (S : Sieve X) : J₁.close (J₁.close S) = J₁.close S :=
   le_antisymm (J₁.le_close_of_isClosed le_rfl (J₁.close_isClosed S))
     (J₁.monotone_close (J₁.le_close _))
 #align category_theory.grothendieck_topology.close_close CategoryTheory.GrothendieckTopology.close_close
+-/
 
 /--
 The sieve `S` is in the topology iff its closure is the maximal sieve. This shows that the closure
@@ -176,14 +194,17 @@ def closureOperator (X : C) : ClosureOperator (Sieve X) :=
     J₁.le_close fun S => J₁.le_close_of_isClosed le_rfl (J₁.close_isClosed S)
 #align category_theory.grothendieck_topology.closure_operator CategoryTheory.GrothendieckTopology.closureOperator
 
+#print CategoryTheory.GrothendieckTopology.closed_iff_closed /-
 @[simp]
 theorem closed_iff_closed {X : C} (S : Sieve X) :
     S ∈ (J₁.ClosureOperator X).closed ↔ J₁.IsClosed S :=
   (J₁.isClosed_iff_close_eq_self S).symm
 #align category_theory.grothendieck_topology.closed_iff_closed CategoryTheory.GrothendieckTopology.closed_iff_closed
+-/
 
 end GrothendieckTopology
 
+#print CategoryTheory.Functor.closedSieves /-
 /--
 The presheaf sending each object to the set of `J`-closed sieves on it. This presheaf is a `J`-sheaf
 (and will turn out to be a subobject classifier for the category of `J`-sheaves).
@@ -194,7 +215,9 @@ def Functor.closedSieves : Cᵒᵖ ⥤ Type max v u
   obj X := { S : Sieve X.unop // J₁.IsClosed S }
   map X Y f S := ⟨S.1.pullback f.unop, J₁.isClosed_pullback f.unop _ S.2⟩
 #align category_theory.functor.closed_sieves CategoryTheory.Functor.closedSieves
+-/
 
+#print CategoryTheory.classifier_isSheaf /-
 /-- The presheaf of `J`-closed sieves is a `J`-sheaf.
 The proof of this is adapted from [MM92], Chatper III, Section 7, Lemma 1.
 -/
@@ -249,7 +272,9 @@ theorem classifier_isSheaf : Presieve.IsSheaf J₁ (Functor.closedSieves J₁) :
       rw [← J₁.pullback_close, this _ hf]
       apply le_antisymm (J₁.le_close_of_is_closed le_rfl (x f hf).2) (J₁.le_close _)
 #align category_theory.classifier_is_sheaf CategoryTheory.classifier_isSheaf
+-/
 
+#print CategoryTheory.le_topology_of_closedSieves_isSheaf /-
 /-- If presheaf of `J₁`-closed sieves is a `J₂`-sheaf then `J₁ ≤ J₂`. Note the converse is true by
 `classifier_is_sheaf` and `is_sheaf_of_le`.
 -/
@@ -272,7 +297,9 @@ theorem le_topology_of_closedSieves_isSheaf {J₁ J₂ : GrothendieckTopology C}
       J₂.close_eq_top_iff_mem]
     apply J₂.top_mem
 #align category_theory.le_topology_of_closed_sieves_is_sheaf CategoryTheory.le_topology_of_closedSieves_isSheaf
+-/
 
+#print CategoryTheory.topology_eq_iff_same_sheaves /-
 /-- If being a sheaf for `J₁` is equivalent to being a sheaf for `J₂`, then `J₁ = J₂`. -/
 theorem topology_eq_iff_same_sheaves {J₁ J₂ : GrothendieckTopology C} :
     J₁ = J₂ ↔ ∀ P : Cᵒᵖ ⥤ Type max v u, Presieve.IsSheaf J₁ P ↔ Presieve.IsSheaf J₂ P :=
@@ -290,6 +317,7 @@ theorem topology_eq_iff_same_sheaves {J₁ J₂ : GrothendieckTopology C} :
       rw [← h]
       apply classifier_is_sheaf
 #align category_theory.topology_eq_iff_same_sheaves CategoryTheory.topology_eq_iff_same_sheaves
+-/
 
 /--
 A closure (increasing, inflationary and idempotent) operation on sieves that commutes with pullback
@@ -313,6 +341,7 @@ def topologyOfClosureOperator (c : ∀ X : C, ClosureOperator (Sieve X))
     apply hR hf
 #align category_theory.topology_of_closure_operator CategoryTheory.topologyOfClosureOperator
 
+#print CategoryTheory.topologyOfClosureOperator_self /-
 /--
 The topology given by the closure operator `J.close` on a Grothendieck topology is the same as `J`.
 -/
@@ -322,6 +351,7 @@ theorem topologyOfClosureOperator_self :
   ext (X S)
   apply grothendieck_topology.close_eq_top_iff_mem
 #align category_theory.topology_of_closure_operator_self CategoryTheory.topologyOfClosureOperator_self
+-/
 
 theorem topologyOfClosureOperator_close (c : ∀ X : C, ClosureOperator (Sieve X))
     (pb : ∀ ⦃X Y : C⦄ (f : Y ⟶ X) (S : Sieve X), c Y (S.pullback f) = (c X S).pullback f) (X : C)

4cfc30e3

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

4cfc30e3

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

@@ -52,7 +52,6 @@ universe v u
 namespace CategoryTheory
 
 variable {C : Type u} [Category.{v} C]
-
 variable (J₁ J₂ : GrothendieckTopology C)
 
 namespace GrothendieckTopology

4cfc30e3

refactor: Closure predicate for ClosureOperator (#9153)

This PR is the result of two years and a half of pondering.

The only way we ever define closure operators is by having a pre-existing "closedness" predicate and defining the closure of an element x as the infimum of all closed y ≥ x (assuming we're in a complete lattice). In particular, the emphasis is not on the preorder of closed elements, but on the closedness predicate. Morally, this is because a closure operator is the same as a Galois connection to the preorder of closed elements, but without mentioning the preorder of closed elements. That means that if we cared about the preorder of closed elements, we would not have wanted a closure operator in the first place, but a Galois connection.

All this said, here's what this PR does

Add an IsClosed predicate to ClosureOperator. This redundant field is here to fix definitional equalities.
Remove the set closeds. This is mostly replaced by the predicate, except in the map toCloseds, so we...
... Introduce an abbrev Closeds for the order of closed elements
Rename toClosed to toCloseds to match.
Rename the constructor mk₃ to the more sexy ofPred. This is virtually the only useful constructor. Maybe it should even be taken as the definition, but I haven't gone that far.
Rename the old ofPred to ofCompletePred. ofCompletePred is a specialisation of ofPred to the case where we are in a complete lattice.
Remove a bunch of lemmas that are junk now that the definitional equality for IsClosed can be controlled.
Golf existing uses of ClosureOperator. The diff here, I think, truly demonstrates that this PR is a step forward.

I am not extending the refactor to LowerAdjoint because:

I am still not sure we want LowerAdjoint to even exist
The rationale of preferring the closedness predicate over the preorder of closed elements is less strong here.
I am lazy.

It is however easy to do the same refactor if wanted.

a4a7700f

Diff

@@ -104,18 +104,17 @@ theorem close_isClosed {X : C} (S : Sieve X) : J₁.IsClosed (J₁.close S) :=
   fun _ g hg => J₁.arrow_trans g _ S hg fun _ hS => hS
 #align category_theory.grothendieck_topology.close_is_closed CategoryTheory.GrothendieckTopology.close_isClosed
 
+/-- A Grothendieck topology induces a natural family of closure operators on sieves. -/
+@[simps! isClosed]
+def closureOperator (X : C) : ClosureOperator (Sieve X) :=
+  .ofPred J₁.close J₁.IsClosed J₁.le_close J₁.close_isClosed fun _ _ ↦ J₁.le_close_of_isClosed
+#align category_theory.grothendieck_topology.closure_operator CategoryTheory.GrothendieckTopology.closureOperator
+
+#align category_theory.grothendieck_topology.closed_iff_closed CategoryTheory.GrothendieckTopology.closureOperator_isClosed
+
 /-- The sieve `S` is closed iff its closure is equal to itself. -/
-theorem isClosed_iff_close_eq_self {X : C} (S : Sieve X) : J₁.IsClosed S ↔ J₁.close S = S := by
-  constructor
-  · intro h
-    apply le_antisymm
-    · intro Y f hf
-      rw [← J₁.covers_iff_mem_of_isClosed h]
-      apply hf
-    · apply J₁.le_close
-  · intro e
-    rw [← e]
-    apply J₁.close_isClosed
+theorem isClosed_iff_close_eq_self {X : C} (S : Sieve X) : J₁.IsClosed S ↔ J₁.close S = S :=
+  (J₁.closureOperator _).isClosed_iff
 #align category_theory.grothendieck_topology.is_closed_iff_close_eq_self CategoryTheory.GrothendieckTopology.isClosed_iff_close_eq_self
 
 theorem close_eq_self_of_isClosed {X : C} {S : Sieve X} (hS : J₁.IsClosed S) : J₁.close S = S :=
@@ -136,13 +135,12 @@ theorem pullback_close {X Y : C} (f : Y ⟶ X) (S : Sieve X) :
 
 @[mono]
 theorem monotone_close {X : C} : Monotone (J₁.close : Sieve X → Sieve X) :=
-  fun _ S₂ h => J₁.le_close_of_isClosed (h.trans (J₁.le_close _)) (J₁.close_isClosed S₂)
+  (J₁.closureOperator _).monotone
 #align category_theory.grothendieck_topology.monotone_close CategoryTheory.GrothendieckTopology.monotone_close
 
 @[simp]
 theorem close_close {X : C} (S : Sieve X) : J₁.close (J₁.close S) = J₁.close S :=
-  le_antisymm (J₁.le_close_of_isClosed le_rfl (J₁.close_isClosed S))
-    (J₁.monotone_close (J₁.le_close _))
+  (J₁.closureOperator _).idempotent _
 #align category_theory.grothendieck_topology.close_close CategoryTheory.GrothendieckTopology.close_close
 
 /--
@@ -162,20 +160,6 @@ theorem close_eq_top_iff_mem {X : C} (S : Sieve X) : J₁.close S = ⊤ ↔ S 
     apply J₁.pullback_stable _ hS
 #align category_theory.grothendieck_topology.close_eq_top_iff_mem CategoryTheory.GrothendieckTopology.close_eq_top_iff_mem
 
-/-- A Grothendieck topology induces a natural family of closure operators on sieves. -/
-@[simps!]
-def closureOperator (X : C) : ClosureOperator (Sieve X) :=
-  ClosureOperator.mk' J₁.close
-    (fun _ S₂ h => J₁.le_close_of_isClosed (h.trans (J₁.le_close _)) (J₁.close_isClosed S₂))
-    J₁.le_close fun S => J₁.le_close_of_isClosed le_rfl (J₁.close_isClosed S)
-#align category_theory.grothendieck_topology.closure_operator CategoryTheory.GrothendieckTopology.closureOperator
-
-@[simp]
-theorem closed_iff_closed {X : C} (S : Sieve X) :
-    S ∈ (J₁.closureOperator X).closed ↔ J₁.IsClosed S :=
-  (J₁.isClosed_iff_close_eq_self S).symm
-#align category_theory.grothendieck_topology.closed_iff_closed CategoryTheory.GrothendieckTopology.closed_iff_closed
-
 end GrothendieckTopology
 
 /--

4cfc30e3

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.sites.closed
-! leanprover-community/mathlib commit 4cfc30e317caad46858393f1a7a33f609296cc30
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Sites.SheafOfTypes
 import Mathlib.Order.Closure
 
+#align_import category_theory.sites.closed from "leanprover-community/mathlib"@"4cfc30e317caad46858393f1a7a33f609296cc30"
+
 /-!
 # Closed sieves

4cfc30e3

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -313,7 +313,7 @@ The topology given by the closure operator `J.close` on a Grothendieck topology
 -/
 theorem topologyOfClosureOperator_self :
     (topologyOfClosureOperator J₁.closureOperator fun X Y => J₁.pullback_close) = J₁ := by
-  ext (X S)
+  ext X S
   apply GrothendieckTopology.close_eq_top_iff_mem
 #align category_theory.topology_of_closure_operator_self CategoryTheory.topologyOfClosureOperator_self

4cfc30e3

chore: bump Std4 (#5219)

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

59c36da5

Diff

@@ -200,15 +200,13 @@ theorem classifier_isSheaf : Presieve.IsSheaf J₁ (Functor.closedSieves J₁) :
   refine' ⟨_, _⟩
   · rintro x ⟨M, hM⟩ ⟨N, hN⟩ hM₂ hN₂
     simp only [Functor.closedSieves_obj]
-    ext Y
-    intro f
+    ext Y f
     dsimp only [Subtype.coe_mk]
     rw [← J₁.covers_iff_mem_of_isClosed hM, ← J₁.covers_iff_mem_of_isClosed hN]
     have q : ∀ ⦃Z : C⦄ (g : Z ⟶ X) (_ : S g), M.pullback g = N.pullback g :=
       fun Z g hg => congr_arg Subtype.val ((hM₂ g hg).trans (hN₂ g hg).symm)
     have MSNS : M ⊓ S = N ⊓ S := by
-      ext Z
-      intro g
+      ext Z g
       rw [Sieve.inter_apply, Sieve.inter_apply]
       simp only [and_comm]
       apply and_congr_right
@@ -322,8 +320,7 @@ theorem topologyOfClosureOperator_self :
 theorem topologyOfClosureOperator_close (c : ∀ X : C, ClosureOperator (Sieve X))
     (pb : ∀ ⦃X Y : C⦄ (f : Y ⟶ X) (S : Sieve X), c Y (S.pullback f) = (c X S).pullback f) (X : C)
     (S : Sieve X) : (topologyOfClosureOperator c pb).close S = c X S := by
-  ext Y
-  intro f
+  ext Y f
   change c _ (Sieve.pullback f S) = ⊤ ↔ c _ S f
   rw [pb, Sieve.pullback_eq_top_iff_mem]
 #align category_theory.topology_of_closure_operator_close CategoryTheory.topologyOfClosureOperator_close

4cfc30e3

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -192,7 +192,7 @@ def Functor.closedSieves : Cᵒᵖ ⥤ Type max v u where
 #align category_theory.functor.closed_sieves CategoryTheory.Functor.closedSieves
 
 /-- The presheaf of `J`-closed sieves is a `J`-sheaf.
-The proof of this is adapted from [MM92], Chatper III, Section 7, Lemma 1.
+The proof of this is adapted from [MM92], Chapter III, Section 7, Lemma 1.
 -/
 theorem classifier_isSheaf : Presieve.IsSheaf J₁ (Functor.closedSieves J₁) := by
   intro X S hS

4cfc30e3

feat: port CategoryTheory.Sites.Closed (#3356)

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>

0cbb9b87

`category_theory.sites.closed` ⟷ `Mathlib.CategoryTheory.Sites.Closed`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 2 + 261

category_theory.sites.closed ⟷ Mathlib.CategoryTheory.Sites.Closed

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 2 + 261

`category_theory.sites.closed` ⟷ `Mathlib.CategoryTheory.Sites.Closed`