category_theory.sites.sieves | 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

239d882c

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

f4758115

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -877,7 +877,8 @@ theorem image_mem_functorPushforward (R : Sieve X) {V} {f : V ⟶ X} (h : R f) :
 
 #print CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion /-
 /-- When `F` is essentially surjective and full, the galois connection is a galois insertion. -/
-def essSurjFullFunctorGaloisInsertion [EssSurj F] [Full F] (X : C) :
+def essSurjFullFunctorGaloisInsertion [CategoryTheory.Functor.EssSurj F]
+    [CategoryTheory.Functor.Full F] (X : C) :
     GaloisInsertion (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
       (Sieve.functorPullback F) :=
   by
@@ -890,7 +891,8 @@ def essSurjFullFunctorGaloisInsertion [EssSurj F] [Full F] (X : C) :
 
 #print CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertion /-
 /-- When `F` is fully faithful, the galois connection is a galois coinsertion. -/
-def fullyFaithfulFunctorGaloisCoinsertion [Full F] [Faithful F] (X : C) :
+def fullyFaithfulFunctorGaloisCoinsertion [CategoryTheory.Functor.Full F]
+    [CategoryTheory.Functor.Faithful F] (X : C) :
     GaloisCoinsertion (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
       (Sieve.functorPullback F) :=
   by

f4758115

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, E. W. Ayers
 -/
 import Order.CompleteLattice
-import CategoryTheory.Over
+import CategoryTheory.Comma.Over
 import CategoryTheory.Yoneda
 import CategoryTheory.Limits.Shapes.Pullbacks
 import Data.Set.Lattice

f4758115

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -656,7 +656,7 @@ def galoisCoinsertionOfMono (f : Y ⟶ X) [Mono f] :
   by
   apply (GaloisConnection f).toGaloisCoinsertion
   rintro S Z g ⟨g₁, hf, hg₁⟩
-  rw [cancel_mono f] at hf 
+  rw [cancel_mono f] at hf
   rwa [← hf]
 #align category_theory.sieve.galois_coinsertion_of_mono CategoryTheory.Sieve.galoisCoinsertionOfMono
 -/
@@ -896,7 +896,7 @@ def fullyFaithfulFunctorGaloisCoinsertion [Full F] [Faithful F] (X : C) :
   by
   apply (functor_galois_connection F X).toGaloisCoinsertion
   rintro S Y f ⟨Z, g, h, h₁, h₂⟩
-  rw [← F.image_preimage h, ← F.map_comp] at h₂ 
+  rw [← F.image_preimage h, ← F.map_comp] at h₂
   rw [F.map_injective h₂]
   exact S.downward_closed h₁ _
 #align category_theory.sieve.fully_faithful_functor_galois_coinsertion CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertion

f4758115

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 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, E. W. Ayers
 -/
-import Mathbin.Order.CompleteLattice
-import Mathbin.CategoryTheory.Over
-import Mathbin.CategoryTheory.Yoneda
-import Mathbin.CategoryTheory.Limits.Shapes.Pullbacks
-import Mathbin.Data.Set.Lattice
+import Order.CompleteLattice
+import CategoryTheory.Over
+import CategoryTheory.Yoneda
+import CategoryTheory.Limits.Shapes.Pullbacks
+import Data.Set.Lattice
 
 #align_import category_theory.sites.sieves from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"

f4758115

bump to nightly-2023-08-02-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

7aca3f15

Diff

@@ -249,7 +249,7 @@ theorem functorPushforward_comp (R : Presieve X) :
   ext x f
   constructor
   · rintro ⟨X, f₁, g₁, h₁, rfl⟩; exact ⟨F.obj X, F.map f₁, g₁, ⟨X, f₁, 𝟙 _, h₁, by simp⟩, rfl⟩
-  · rintro ⟨X, f₁, g₁, ⟨X', f₂, g₂, h₁, rfl⟩, rfl⟩; use ⟨X', f₂, g₁ ≫ G.map g₂, h₁, by simp⟩
+  · rintro ⟨X, f₁, g₁, ⟨X', f₂, g₂, h₁, rfl⟩, rfl⟩; use⟨X', f₂, g₁ ≫ G.map g₂, h₁, by simp⟩
 #align category_theory.presieve.functor_pushforward_comp CategoryTheory.Presieve.functorPushforward_comp
 -/

f4758115

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 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, E. W. Ayers
-
-! This file was ported from Lean 3 source module category_theory.sites.sieves
-! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Order.CompleteLattice
 import Mathbin.CategoryTheory.Over
@@ -14,6 +9,8 @@ import Mathbin.CategoryTheory.Yoneda
 import Mathbin.CategoryTheory.Limits.Shapes.Pullbacks
 import Mathbin.Data.Set.Lattice
 
+#align_import category_theory.sites.sieves from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # Theory of sieves

f4758115

bump to nightly-2023-06-20-01

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

9b351f8c

Diff

@@ -130,7 +130,7 @@ inductive pullbackArrows [HasPullbacks C] (R : Presieve X) : Presieve Y
 theorem pullback_singleton [HasPullbacks C] (g : Z ⟶ X) :
     pullbackArrows f (singleton g) = singleton (pullback.snd : pullback g f ⟶ _) :=
   by
-  ext (W h)
+  ext W h
   constructor
   · rintro ⟨W, _, _, _⟩
     exact singleton.mk
@@ -149,7 +149,7 @@ inductive ofArrows {ι : Type _} (Y : ι → C) (f : ∀ i, Y i ⟶ X) : Presiev
 #print CategoryTheory.Presieve.ofArrows_pUnit /-
 theorem ofArrows_pUnit : (ofArrows _ fun _ : PUnit => f) = singleton f :=
   by
-  ext (Y g)
+  ext Y g
   constructor
   · rintro ⟨_⟩
     apply singleton.mk
@@ -163,7 +163,7 @@ theorem ofArrows_pullback [HasPullbacks C] {ι : Type _} (Z : ι → C) (g : ∀
     (ofArrows (fun i => pullback (g i) f) fun i => pullback.snd) =
       pullbackArrows f (ofArrows Z g) :=
   by
-  ext (T h)
+  ext T h
   constructor
   · rintro ⟨hk⟩
     exact pullback_arrows.mk _ _ (of_arrows.mk hk)
@@ -181,7 +181,7 @@ theorem ofArrows_bind {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
       ofArrows (fun i : Σ i, j _ (ofArrows.mk i) => W (g i.1) _ i.2) fun ij =>
         k (g ij.1) _ ij.2 ≫ g ij.1 :=
   by
-  ext (Y f)
+  ext Y f
   constructor
   · rintro ⟨_, _, _, ⟨i⟩, ⟨i'⟩, rfl⟩
     exact of_arrows.mk (Sigma.mk _ _)
@@ -249,7 +249,7 @@ noncomputable def getFunctorPushforwardStructure {F : C ⥤ D} {S : Presieve X}
 theorem functorPushforward_comp (R : Presieve X) :
     R.functorPushforward (F ⋙ G) = (R.functorPushforward F).functorPushforward G :=
   by
-  ext (x f)
+  ext x f
   constructor
   · rintro ⟨X, f₁, g₁, h₁, rfl⟩; exact ⟨F.obj X, F.map f₁, g₁, ⟨X, f₁, 𝟙 _, h₁, by simp⟩, rfl⟩
   · rintro ⟨X, f₁, g₁, ⟨X', f₂, g₂, h₁, rfl⟩, rfl⟩; use ⟨X', f₂, g₁ ≫ G.map g₂, h₁, by simp⟩
@@ -679,7 +679,7 @@ def galoisInsertionOfIsSplitEpi (f : Y ⟶ X) [IsSplitEpi f] :
 theorem pullbackArrows_comm [HasPullbacks C] {X Y : C} (f : Y ⟶ X) (R : Presieve X) :
     Sieve.generate (R.pullbackArrows f) = (Sieve.generate R).pullback f :=
   by
-  ext (Z g)
+  ext Z g
   constructor
   · rintro ⟨_, h, k, hk, rfl⟩
     cases' hk with W g hg
@@ -734,7 +734,7 @@ theorem functorPullback_comp (R : Sieve ((F ⋙ G).obj X)) :
 theorem functorPushforward_extend_eq {R : Presieve X} :
     (generate R).arrows.functorPushforward F = R.functorPushforward F :=
   by
-  ext (Y f); constructor
+  ext Y f; constructor
   · rintro ⟨X', g, f', ⟨X'', g', f'', h₁, rfl⟩, rfl⟩
     exact ⟨X'', f'', f' ≫ F.map g', h₁, by simp⟩
   · rintro ⟨X', g, f', h₁, h₂⟩; exact ⟨X', g, f', le_generate R _ h₁, h₂⟩
@@ -757,7 +757,7 @@ def functorPushforward (R : Sieve X) : Sieve (F.obj X)
 @[simp]
 theorem functorPushforward_id (R : Sieve X) : R.functorPushforward (𝟭 _) = R :=
   by
-  ext (X f)
+  ext X f
   constructor
   · intro hf
     obtain ⟨X, g, h, hg, rfl⟩ := hf
@@ -943,7 +943,7 @@ theorem natTransOfLe_comm {S T : Sieve X} (h : S ≤ T) :
 #print CategoryTheory.Sieve.functorInclusion_is_mono /-
 /-- The presheaf induced by a sieve is a subobject of the yoneda embedding. -/
 instance functorInclusion_is_mono : Mono S.functorInclusion :=
-  ⟨fun Z f g h => by ext (Y y); apply congr_fun (nat_trans.congr_app h Y) y⟩
+  ⟨fun Z f g h => by ext Y y; apply congr_fun (nat_trans.congr_app h Y) y⟩
 #align category_theory.sieve.functor_inclusion_is_mono CategoryTheory.Sieve.functorInclusion_is_mono
 -/

f4758115

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -56,18 +56,22 @@ namespace Presieve
 instance : Inhabited (Presieve X) :=
   ⟨⊤⟩
 
+#print CategoryTheory.Presieve.diagram /-
 /-- Given a sieve `S` on `X : C`, its associated diagram `S.diagram` is defined to be
     the natural functor from the full subcategory of the over category `C/X` consisting
     of arrows in `S` to `C`. -/
 abbrev diagram (S : Presieve X) : (FullSubcategory fun f : Over X => S f.Hom) ⥤ C :=
   fullSubcategoryInclusion _ ⋙ Over.forget X
 #align category_theory.presieve.diagram CategoryTheory.Presieve.diagram
+-/
 
+#print CategoryTheory.Presieve.cocone /-
 /-- Given a sieve `S` on `X : C`, its associated cocone `S.cocone` is defined to be
     the natural cocone over the diagram defined above with cocone point `X`. -/
 abbrev cocone (S : Presieve X) : Cocone S.diagram :=
   (Over.forgetCocone X).whisker (fullSubcategoryInclusion _)
 #align category_theory.presieve.cocone CategoryTheory.Presieve.cocone
+-/
 
 #print CategoryTheory.Presieve.bind /-
 /-- Given a set of arrows `S` all with codomain `X`, and a set of arrows with codomain `Y` for each
@@ -93,6 +97,7 @@ inductive singleton : Presieve X
   | mk : singleton f
 #align category_theory.presieve.singleton CategoryTheory.Presieve.singletonₓ
 
+#print CategoryTheory.Presieve.singleton_eq_iff_domain /-
 @[simp]
 theorem singleton_eq_iff_domain (f g : Y ⟶ X) : singleton f g ↔ f = g :=
   by
@@ -102,10 +107,13 @@ theorem singleton_eq_iff_domain (f g : Y ⟶ X) : singleton f g ↔ f = g :=
   · rintro rfl
     apply singleton.mk
 #align category_theory.presieve.singleton_eq_iff_domain CategoryTheory.Presieve.singleton_eq_iff_domain
+-/
 
+#print CategoryTheory.Presieve.singleton_self /-
 theorem singleton_self : singleton f f :=
   singleton.mk
 #align category_theory.presieve.singleton_self CategoryTheory.Presieve.singleton_self
+-/
 
 #print CategoryTheory.Presieve.pullbackArrows /-
 /-- Pullback a set of arrows with given codomain along a fixed map, by taking the pullback in the
@@ -118,6 +126,7 @@ inductive pullbackArrows [HasPullbacks C] (R : Presieve X) : Presieve Y
 #align category_theory.presieve.pullback_arrows CategoryTheory.Presieve.pullbackArrows
 -/
 
+#print CategoryTheory.Presieve.pullback_singleton /-
 theorem pullback_singleton [HasPullbacks C] (g : Z ⟶ X) :
     pullbackArrows f (singleton g) = singleton (pullback.snd : pullback g f ⟶ _) :=
   by
@@ -128,6 +137,7 @@ theorem pullback_singleton [HasPullbacks C] (g : Z ⟶ X) :
   · rintro ⟨_⟩
     exact pullback_arrows.mk Z g singleton.mk
 #align category_theory.presieve.pullback_singleton CategoryTheory.Presieve.pullback_singleton
+-/
 
 #print CategoryTheory.Presieve.ofArrows /-
 /-- Construct the presieve given by the family of arrows indexed by `ι`. -/
@@ -136,6 +146,7 @@ inductive ofArrows {ι : Type _} (Y : ι → C) (f : ∀ i, Y i ⟶ X) : Presiev
 #align category_theory.presieve.of_arrows CategoryTheory.Presieve.ofArrows
 -/
 
+#print CategoryTheory.Presieve.ofArrows_pUnit /-
 theorem ofArrows_pUnit : (ofArrows _ fun _ : PUnit => f) = singleton f :=
   by
   ext (Y g)
@@ -145,7 +156,9 @@ theorem ofArrows_pUnit : (ofArrows _ fun _ : PUnit => f) = singleton f :=
   · rintro ⟨_⟩
     exact of_arrows.mk PUnit.unit
 #align category_theory.presieve.of_arrows_punit CategoryTheory.Presieve.ofArrows_pUnit
+-/
 
+#print CategoryTheory.Presieve.ofArrows_pullback /-
 theorem ofArrows_pullback [HasPullbacks C] {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X) :
     (ofArrows (fun i => pullback (g i) f) fun i => pullback.snd) =
       pullbackArrows f (ofArrows Z g) :=
@@ -158,7 +171,9 @@ theorem ofArrows_pullback [HasPullbacks C] {ι : Type _} (Z : ι → C) (g : ∀
     cases' hk₁ with i hi
     apply of_arrows.mk
 #align category_theory.presieve.of_arrows_pullback CategoryTheory.Presieve.ofArrows_pullback
+-/
 
+#print CategoryTheory.Presieve.ofArrows_bind /-
 theorem ofArrows_bind {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
     (j : ∀ ⦃Y⦄ (f : Y ⟶ X), ofArrows Z g f → Type _) (W : ∀ ⦃Y⦄ (f : Y ⟶ X) (H), j f H → C)
     (k : ∀ ⦃Y⦄ (f : Y ⟶ X) (H i), W f H i ⟶ Y) :
@@ -173,16 +188,21 @@ theorem ofArrows_bind {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
   · rintro ⟨i⟩
     exact bind_comp _ (of_arrows.mk _) (of_arrows.mk _)
 #align category_theory.presieve.of_arrows_bind CategoryTheory.Presieve.ofArrows_bind
+-/
 
+#print CategoryTheory.Presieve.functorPullback /-
 /-- Given a presieve on `F(X)`, we can define a presieve on `X` by taking the preimage via `F`. -/
 def functorPullback (R : Presieve (F.obj X)) : Presieve X := fun _ f => R (F.map f)
 #align category_theory.presieve.functor_pullback CategoryTheory.Presieve.functorPullback
+-/
 
+#print CategoryTheory.Presieve.functorPullback_mem /-
 @[simp]
 theorem functorPullback_mem (R : Presieve (F.obj X)) {Y} (f : Y ⟶ X) :
     R.functorPullback F f ↔ R (F.map f) :=
   Iff.rfl
 #align category_theory.presieve.functor_pullback_mem CategoryTheory.Presieve.functorPullback_mem
+-/
 
 #print CategoryTheory.Presieve.functorPullback_id /-
 @[simp]
@@ -195,13 +215,16 @@ section FunctorPushforward
 
 variable {E : Type u₃} [Category.{v₃} E] (G : D ⥤ E)
 
+#print CategoryTheory.Presieve.functorPushforward /-
 /-- Given a presieve on `X`, we can define a presieve on `F(X)` (which is actually a sieve)
 by taking the sieve generated by the image via `F`.
 -/
 def functorPushforward (S : Presieve X) : Presieve (F.obj X) := fun Y f =>
   ∃ (Z : C) (g : Z ⟶ X) (h : Y ⟶ F.obj Z), S g ∧ f = h ≫ F.map g
 #align category_theory.presieve.functor_pushforward CategoryTheory.Presieve.functorPushforward
+-/
 
+#print CategoryTheory.Presieve.FunctorPushforwardStructure /-
 /-- An auxillary definition in order to fix the choice of the preimages between various definitions.
 -/
 @[nolint has_nonempty_instance]
@@ -212,13 +235,17 @@ structure FunctorPushforwardStructure (S : Presieve X) {Y} (f : Y ⟶ F.obj X) w
   cover : S premap
   fac : f = lift ≫ F.map premap
 #align category_theory.presieve.functor_pushforward_structure CategoryTheory.Presieve.FunctorPushforwardStructure
+-/
 
+#print CategoryTheory.Presieve.getFunctorPushforwardStructure /-
 /-- The fixed choice of a preimage. -/
 noncomputable def getFunctorPushforwardStructure {F : C ⥤ D} {S : Presieve X} {Y : D}
     {f : Y ⟶ F.obj X} (h : S.functorPushforward F f) : FunctorPushforwardStructure F S f := by
   choose Z f' g h₁ h using h; exact ⟨Z, f', g, h₁, h⟩
 #align category_theory.presieve.get_functor_pushforward_structure CategoryTheory.Presieve.getFunctorPushforwardStructure
+-/
 
+#print CategoryTheory.Presieve.functorPushforward_comp /-
 theorem functorPushforward_comp (R : Presieve X) :
     R.functorPushforward (F ⋙ G) = (R.functorPushforward F).functorPushforward G :=
   by
@@ -227,11 +254,14 @@ theorem functorPushforward_comp (R : Presieve X) :
   · rintro ⟨X, f₁, g₁, h₁, rfl⟩; exact ⟨F.obj X, F.map f₁, g₁, ⟨X, f₁, 𝟙 _, h₁, by simp⟩, rfl⟩
   · rintro ⟨X, f₁, g₁, ⟨X', f₂, g₂, h₁, rfl⟩, rfl⟩; use ⟨X', f₂, g₁ ≫ G.map g₂, h₁, by simp⟩
 #align category_theory.presieve.functor_pushforward_comp CategoryTheory.Presieve.functorPushforward_comp
+-/
 
+#print CategoryTheory.Presieve.image_mem_functorPushforward /-
 theorem image_mem_functorPushforward (R : Presieve X) {f : Y ⟶ X} (h : R f) :
     R.functorPushforward F (F.map f) :=
   ⟨Y, f, 𝟙 _, h, by simp⟩
 #align category_theory.presieve.image_mem_functor_pushforward CategoryTheory.Presieve.image_mem_functorPushforward
+-/
 
 end FunctorPushforward
 
@@ -257,10 +287,12 @@ initialize_simps_projections Sieve (arrows → apply)
 
 variable {S R : Sieve X}
 
+#print CategoryTheory.Sieve.downward_closed /-
 @[simp]
 theorem downward_closed (S : Sieve X) {f : Y ⟶ X} (hf : S f) (g : Z ⟶ Y) : S (g ≫ f) :=
   S.downward_closed' hf g
 #align category_theory.sieve.downward_closed CategoryTheory.Sieve.downward_closed
+-/
 
 #print CategoryTheory.Sieve.arrows_ext /-
 theorem arrows_ext : ∀ {R S : Sieve X}, R.arrows = S.arrows → R = S
@@ -358,32 +390,42 @@ instance sieveInhabited : Inhabited (Sieve X) :=
 #align category_theory.sieve.sieve_inhabited CategoryTheory.Sieve.sieveInhabited
 -/
 
+#print CategoryTheory.Sieve.sInf_apply /-
 @[simp]
 theorem sInf_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
     sInf Ss f ↔ ∀ (S : Sieve X) (H : S ∈ Ss), S f :=
   Iff.rfl
 #align category_theory.sieve.Inf_apply CategoryTheory.Sieve.sInf_apply
+-/
 
+#print CategoryTheory.Sieve.sSup_apply /-
 @[simp]
 theorem sSup_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
     sSup Ss f ↔ ∃ (S : Sieve X) (H : S ∈ Ss), S f :=
   Iff.rfl
 #align category_theory.sieve.Sup_apply CategoryTheory.Sieve.sSup_apply
+-/
 
+#print CategoryTheory.Sieve.inter_apply /-
 @[simp]
 theorem inter_apply {R S : Sieve X} {Y} (f : Y ⟶ X) : (R ⊓ S) f ↔ R f ∧ S f :=
   Iff.rfl
 #align category_theory.sieve.inter_apply CategoryTheory.Sieve.inter_apply
+-/
 
+#print CategoryTheory.Sieve.union_apply /-
 @[simp]
 theorem union_apply {R S : Sieve X} {Y} (f : Y ⟶ X) : (R ⊔ S) f ↔ R f ∨ S f :=
   Iff.rfl
 #align category_theory.sieve.union_apply CategoryTheory.Sieve.union_apply
+-/
 
+#print CategoryTheory.Sieve.top_apply /-
 @[simp]
 theorem top_apply (f : Y ⟶ X) : (⊤ : Sieve X) f :=
   trivial
 #align category_theory.sieve.top_apply CategoryTheory.Sieve.top_apply
+-/
 
 #print CategoryTheory.Sieve.generate /-
 /-- Generate the smallest sieve containing the given set of arrows. -/
@@ -413,13 +455,16 @@ def bind (S : Presieve X) (R : ∀ ⦃Y⦄ ⦃f : Y ⟶ X⦄, S f → Sieve Y) :
 
 open Order Lattice
 
+#print CategoryTheory.Sieve.sets_iff_generate /-
 theorem sets_iff_generate (R : Presieve X) (S : Sieve X) : generate R ≤ S ↔ R ≤ S :=
   ⟨fun H Y g hg => H _ ⟨_, 𝟙 _, _, hg, id_comp _⟩, fun ss Y f =>
     by
     rintro ⟨Z, f, g, hg, rfl⟩
     exact S.downward_closed (ss Z hg) f⟩
 #align category_theory.sieve.sets_iff_generate CategoryTheory.Sieve.sets_iff_generate
+-/
 
+#print CategoryTheory.Sieve.giGenerate /-
 /-- Show that there is a galois insertion (generate, set_over). -/
 def giGenerate : GaloisInsertion (generate : Presieve X → Sieve X) arrows
     where
@@ -428,10 +473,13 @@ def giGenerate : GaloisInsertion (generate : Presieve X → Sieve X) arrows
   choice_eq _ _ := rfl
   le_l_u S Y f hf := ⟨_, 𝟙 _, _, hf, id_comp _⟩
 #align category_theory.sieve.gi_generate CategoryTheory.Sieve.giGenerate
+-/
 
+#print CategoryTheory.Sieve.le_generate /-
 theorem le_generate (R : Presieve X) : R ≤ generate R :=
   giGenerate.gc.le_u_l R
 #align category_theory.sieve.le_generate CategoryTheory.Sieve.le_generate
+-/
 
 #print CategoryTheory.Sieve.generate_sieve /-
 @[simp]
@@ -440,28 +488,36 @@ theorem generate_sieve (S : Sieve X) : generate S = S :=
 #align category_theory.sieve.generate_sieve CategoryTheory.Sieve.generate_sieve
 -/
 
+#print CategoryTheory.Sieve.id_mem_iff_eq_top /-
 /-- If the identity arrow is in a sieve, the sieve is maximal. -/
 theorem id_mem_iff_eq_top : S (𝟙 X) ↔ S = ⊤ :=
   ⟨fun h => top_unique fun Y f _ => by simpa using downward_closed _ h f, fun h => h.symm ▸ trivial⟩
 #align category_theory.sieve.id_mem_iff_eq_top CategoryTheory.Sieve.id_mem_iff_eq_top
+-/
 
+#print CategoryTheory.Sieve.generate_of_contains_isSplitEpi /-
 /-- If an arrow set contains a split epi, it generates the maximal sieve. -/
 theorem generate_of_contains_isSplitEpi {R : Presieve X} (f : Y ⟶ X) [IsSplitEpi f] (hf : R f) :
     generate R = ⊤ := by
   rw [← id_mem_iff_eq_top]
   exact ⟨_, section_ f, f, hf, by simp⟩
 #align category_theory.sieve.generate_of_contains_is_split_epi CategoryTheory.Sieve.generate_of_contains_isSplitEpi
+-/
 
+#print CategoryTheory.Sieve.generate_of_singleton_isSplitEpi /-
 @[simp]
 theorem generate_of_singleton_isSplitEpi (f : Y ⟶ X) [IsSplitEpi f] :
     generate (Presieve.singleton f) = ⊤ :=
   generate_of_contains_isSplitEpi f (Presieve.singleton_self _)
 #align category_theory.sieve.generate_of_singleton_is_split_epi CategoryTheory.Sieve.generate_of_singleton_isSplitEpi
+-/
 
+#print CategoryTheory.Sieve.generate_top /-
 @[simp]
 theorem generate_top : generate (⊤ : Presieve X) = ⊤ :=
   generate_of_contains_isSplitEpi (𝟙 _) ⟨⟩
 #align category_theory.sieve.generate_top CategoryTheory.Sieve.generate_top
+-/
 
 #print CategoryTheory.Sieve.pullback /-
 /-- Given a morphism `h : Y ⟶ X`, send a sieve S on X to a sieve on Y
@@ -481,10 +537,12 @@ theorem pullback_id : S.pullback (𝟙 _) = S := by simp [sieve.ext_iff]
 #align category_theory.sieve.pullback_id CategoryTheory.Sieve.pullback_id
 -/
 
+#print CategoryTheory.Sieve.pullback_top /-
 @[simp]
 theorem pullback_top {f : Y ⟶ X} : (⊤ : Sieve X).pullback f = ⊤ :=
   top_unique fun _ g => id
 #align category_theory.sieve.pullback_top CategoryTheory.Sieve.pullback_top
+-/
 
 #print CategoryTheory.Sieve.pullback_comp /-
 theorem pullback_comp {f : Y ⟶ X} {g : Z ⟶ Y} (S : Sieve X) :
@@ -492,18 +550,24 @@ theorem pullback_comp {f : Y ⟶ X} {g : Z ⟶ Y} (S : Sieve X) :
 #align category_theory.sieve.pullback_comp CategoryTheory.Sieve.pullback_comp
 -/
 
+#print CategoryTheory.Sieve.pullback_inter /-
 @[simp]
 theorem pullback_inter {f : Y ⟶ X} (S R : Sieve X) :
     (S ⊓ R).pullback f = S.pullback f ⊓ R.pullback f := by simp [sieve.ext_iff]
 #align category_theory.sieve.pullback_inter CategoryTheory.Sieve.pullback_inter
+-/
 
+#print CategoryTheory.Sieve.pullback_eq_top_iff_mem /-
 theorem pullback_eq_top_iff_mem (f : Y ⟶ X) : S f ↔ S.pullback f = ⊤ := by
   rw [← id_mem_iff_eq_top, pullback_apply, id_comp]
 #align category_theory.sieve.pullback_eq_top_iff_mem CategoryTheory.Sieve.pullback_eq_top_iff_mem
+-/
 
+#print CategoryTheory.Sieve.pullback_eq_top_of_mem /-
 theorem pullback_eq_top_of_mem (S : Sieve X) {f : Y ⟶ X} : S f → S.pullback f = ⊤ :=
   (pullback_eq_top_iff_mem f).1
 #align category_theory.sieve.pullback_eq_top_of_mem CategoryTheory.Sieve.pullback_eq_top_of_mem
+-/
 
 #print CategoryTheory.Sieve.pushforward /-
 /-- Push a sieve `R` on `Y` forward along an arrow `f : Y ⟶ X`: `gf : Z ⟶ X` is in the sieve if `gf`
@@ -533,45 +597,62 @@ theorem pushforward_comp {f : Y ⟶ X} {g : Z ⟶ Y} (R : Sieve Z) :
 #align category_theory.sieve.pushforward_comp CategoryTheory.Sieve.pushforward_comp
 -/
 
+#print CategoryTheory.Sieve.galoisConnection /-
 theorem galoisConnection (f : Y ⟶ X) : GaloisConnection (Sieve.pushforward f) (Sieve.pullback f) :=
   fun S R => ⟨fun hR Z g hg => hR _ ⟨g, rfl, hg⟩, fun hS Z g ⟨h, hg, hh⟩ => hg ▸ hS h hh⟩
 #align category_theory.sieve.galois_connection CategoryTheory.Sieve.galoisConnection
+-/
 
+#print CategoryTheory.Sieve.pullback_monotone /-
 theorem pullback_monotone (f : Y ⟶ X) : Monotone (Sieve.pullback f) :=
   (galoisConnection f).monotone_u
 #align category_theory.sieve.pullback_monotone CategoryTheory.Sieve.pullback_monotone
+-/
 
+#print CategoryTheory.Sieve.pushforward_monotone /-
 theorem pushforward_monotone (f : Y ⟶ X) : Monotone (Sieve.pushforward f) :=
   (galoisConnection f).monotone_l
 #align category_theory.sieve.pushforward_monotone CategoryTheory.Sieve.pushforward_monotone
+-/
 
+#print CategoryTheory.Sieve.le_pushforward_pullback /-
 theorem le_pushforward_pullback (f : Y ⟶ X) (R : Sieve Y) : R ≤ (R.pushforward f).pullback f :=
   (galoisConnection f).le_u_l _
 #align category_theory.sieve.le_pushforward_pullback CategoryTheory.Sieve.le_pushforward_pullback
+-/
 
+#print CategoryTheory.Sieve.pullback_pushforward_le /-
 theorem pullback_pushforward_le (f : Y ⟶ X) (R : Sieve X) : (R.pullback f).pushforward f ≤ R :=
   (galoisConnection f).l_u_le _
 #align category_theory.sieve.pullback_pushforward_le CategoryTheory.Sieve.pullback_pushforward_le
+-/
 
+#print CategoryTheory.Sieve.pushforward_union /-
 theorem pushforward_union {f : Y ⟶ X} (S R : Sieve Y) :
     (S ⊔ R).pushforward f = S.pushforward f ⊔ R.pushforward f :=
   (galoisConnection f).l_sup
 #align category_theory.sieve.pushforward_union CategoryTheory.Sieve.pushforward_union
+-/
 
+#print CategoryTheory.Sieve.pushforward_le_bind_of_mem /-
 theorem pushforward_le_bind_of_mem (S : Presieve X) (R : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄, S f → Sieve Y)
     (f : Y ⟶ X) (h : S f) : (R h).pushforward f ≤ bind S R :=
   by
   rintro Z _ ⟨g, rfl, hg⟩
   exact ⟨_, g, f, h, hg, rfl⟩
 #align category_theory.sieve.pushforward_le_bind_of_mem CategoryTheory.Sieve.pushforward_le_bind_of_mem
+-/
 
+#print CategoryTheory.Sieve.le_pullback_bind /-
 theorem le_pullback_bind (S : Presieve X) (R : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄, S f → Sieve Y) (f : Y ⟶ X)
     (h : S f) : R h ≤ (bind S R).pullback f :=
   by
   rw [← GaloisConnection f]
   apply pushforward_le_bind_of_mem
 #align category_theory.sieve.le_pullback_bind CategoryTheory.Sieve.le_pullback_bind
+-/
 
+#print CategoryTheory.Sieve.galoisCoinsertionOfMono /-
 /-- If `f` is a monomorphism, the pushforward-pullback adjunction on sieves is coreflective. -/
 def galoisCoinsertionOfMono (f : Y ⟶ X) [Mono f] :
     GaloisCoinsertion (Sieve.pushforward f) (Sieve.pullback f) :=
@@ -581,7 +662,9 @@ def galoisCoinsertionOfMono (f : Y ⟶ X) [Mono f] :
   rw [cancel_mono f] at hf 
   rwa [← hf]
 #align category_theory.sieve.galois_coinsertion_of_mono CategoryTheory.Sieve.galoisCoinsertionOfMono
+-/
 
+#print CategoryTheory.Sieve.galoisInsertionOfIsSplitEpi /-
 /-- If `f` is a split epi, the pushforward-pullback adjunction on sieves is reflective. -/
 def galoisInsertionOfIsSplitEpi (f : Y ⟶ X) [IsSplitEpi f] :
     GaloisInsertion (Sieve.pushforward f) (Sieve.pullback f) :=
@@ -590,6 +673,7 @@ def galoisInsertionOfIsSplitEpi (f : Y ⟶ X) [IsSplitEpi f] :
   intro S Z g hg
   refine' ⟨g ≫ section_ f, by simpa⟩
 #align category_theory.sieve.galois_insertion_of_is_split_epi CategoryTheory.Sieve.galoisInsertionOfIsSplitEpi
+-/
 
 #print CategoryTheory.Sieve.pullbackArrows_comm /-
 theorem pullbackArrows_comm [HasPullbacks C] {X Y : C} (f : Y ⟶ X) (R : Presieve X) :
@@ -611,6 +695,7 @@ section Functor
 
 variable {E : Type u₃} [Category.{v₃} E] (G : D ⥤ E)
 
+#print CategoryTheory.Sieve.functorPullback /-
 /--
 If `R` is a sieve, then the `category_theory.presieve.functor_pullback` of `R` is actually a sieve.
 -/
@@ -623,12 +708,15 @@ def functorPullback (R : Sieve (F.obj X)) : Sieve X
     rw [F.map_comp]
     exact R.downward_closed hf (F.map g)
 #align category_theory.sieve.functor_pullback CategoryTheory.Sieve.functorPullback
+-/
 
+#print CategoryTheory.Sieve.functorPullback_arrows /-
 @[simp]
 theorem functorPullback_arrows (R : Sieve (F.obj X)) :
     (R.functorPullback F).arrows = R.arrows.functorPullback F :=
   rfl
 #align category_theory.sieve.functor_pullback_arrows CategoryTheory.Sieve.functorPullback_arrows
+-/
 
 #print CategoryTheory.Sieve.functorPullback_id /-
 @[simp]
@@ -636,10 +724,13 @@ theorem functorPullback_id (R : Sieve X) : R.functorPullback (𝟭 _) = R := by
 #align category_theory.sieve.functor_pullback_id CategoryTheory.Sieve.functorPullback_id
 -/
 
+#print CategoryTheory.Sieve.functorPullback_comp /-
 theorem functorPullback_comp (R : Sieve ((F ⋙ G).obj X)) :
     R.functorPullback (F ⋙ G) = (R.functorPullback G).functorPullback F := by ext; rfl
 #align category_theory.sieve.functor_pullback_comp CategoryTheory.Sieve.functorPullback_comp
+-/
 
+#print CategoryTheory.Sieve.functorPushforward_extend_eq /-
 theorem functorPushforward_extend_eq {R : Presieve X} :
     (generate R).arrows.functorPushforward F = R.functorPushforward F :=
   by
@@ -648,7 +739,9 @@ theorem functorPushforward_extend_eq {R : Presieve X} :
     exact ⟨X'', f'', f' ≫ F.map g', h₁, by simp⟩
   · rintro ⟨X', g, f', h₁, h₂⟩; exact ⟨X', g, f', le_generate R _ h₁, h₂⟩
 #align category_theory.sieve.functor_pushforward_extend_eq CategoryTheory.Sieve.functorPushforward_extend_eq
+-/
 
+#print CategoryTheory.Sieve.functorPushforward /-
 /-- The sieve generated by the image of `R` under `F`. -/
 @[simps]
 def functorPushforward (R : Sieve X) : Sieve (F.obj X)
@@ -658,7 +751,9 @@ def functorPushforward (R : Sieve X) : Sieve (F.obj X)
     obtain ⟨X, α, β, hα, rfl⟩ := h
     exact ⟨X, α, g ≫ β, hα, by simp⟩
 #align category_theory.sieve.functor_pushforward CategoryTheory.Sieve.functorPushforward
+-/
 
+#print CategoryTheory.Sieve.functorPushforward_id /-
 @[simp]
 theorem functorPushforward_id (R : Sieve X) : R.functorPushforward (𝟭 _) = R :=
   by
@@ -670,12 +765,16 @@ theorem functorPushforward_id (R : Sieve X) : R.functorPushforward (𝟭 _) = R
   · intro hf
     exact ⟨X, f, 𝟙 _, hf, by simp⟩
 #align category_theory.sieve.functor_pushforward_id CategoryTheory.Sieve.functorPushforward_id
+-/
 
+#print CategoryTheory.Sieve.functorPushforward_comp /-
 theorem functorPushforward_comp (R : Sieve X) :
     R.functorPushforward (F ⋙ G) = (R.functorPushforward F).functorPushforward G := by ext;
   simpa [R.arrows.functor_pushforward_comp F G]
 #align category_theory.sieve.functor_pushforward_comp CategoryTheory.Sieve.functorPushforward_comp
+-/
 
+#print CategoryTheory.Sieve.functor_galoisConnection /-
 theorem functor_galoisConnection (X : C) :
     GaloisConnection (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
       (Sieve.functorPullback F) :=
@@ -690,47 +789,65 @@ theorem functor_galoisConnection (X : C) :
     apply sieve.downward_closed S
     exact hle g hg
 #align category_theory.sieve.functor_galois_connection CategoryTheory.Sieve.functor_galoisConnection
+-/
 
+#print CategoryTheory.Sieve.functorPullback_monotone /-
 theorem functorPullback_monotone (X : C) :
     Monotone (Sieve.functorPullback F : Sieve (F.obj X) → Sieve X) :=
   (functor_galoisConnection F X).monotone_u
 #align category_theory.sieve.functor_pullback_monotone CategoryTheory.Sieve.functorPullback_monotone
+-/
 
+#print CategoryTheory.Sieve.functorPushforward_monotone /-
 theorem functorPushforward_monotone (X : C) :
     Monotone (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X)) :=
   (functor_galoisConnection F X).monotone_l
 #align category_theory.sieve.functor_pushforward_monotone CategoryTheory.Sieve.functorPushforward_monotone
+-/
 
+#print CategoryTheory.Sieve.le_functorPushforward_pullback /-
 theorem le_functorPushforward_pullback (R : Sieve X) :
     R ≤ (R.functorPushforward F).functorPullback F :=
   (functor_galoisConnection F X).le_u_l _
 #align category_theory.sieve.le_functor_pushforward_pullback CategoryTheory.Sieve.le_functorPushforward_pullback
+-/
 
+#print CategoryTheory.Sieve.functorPullback_pushforward_le /-
 theorem functorPullback_pushforward_le (R : Sieve (F.obj X)) :
     (R.functorPullback F).functorPushforward F ≤ R :=
   (functor_galoisConnection F X).l_u_le _
 #align category_theory.sieve.functor_pullback_pushforward_le CategoryTheory.Sieve.functorPullback_pushforward_le
+-/
 
+#print CategoryTheory.Sieve.functorPushforward_union /-
 theorem functorPushforward_union (S R : Sieve X) :
     (S ⊔ R).functorPushforward F = S.functorPushforward F ⊔ R.functorPushforward F :=
   (functor_galoisConnection F X).l_sup
 #align category_theory.sieve.functor_pushforward_union CategoryTheory.Sieve.functorPushforward_union
+-/
 
+#print CategoryTheory.Sieve.functorPullback_union /-
 theorem functorPullback_union (S R : Sieve (F.obj X)) :
     (S ⊔ R).functorPullback F = S.functorPullback F ⊔ R.functorPullback F :=
   rfl
 #align category_theory.sieve.functor_pullback_union CategoryTheory.Sieve.functorPullback_union
+-/
 
+#print CategoryTheory.Sieve.functorPullback_inter /-
 theorem functorPullback_inter (S R : Sieve (F.obj X)) :
     (S ⊓ R).functorPullback F = S.functorPullback F ⊓ R.functorPullback F :=
   rfl
 #align category_theory.sieve.functor_pullback_inter CategoryTheory.Sieve.functorPullback_inter
+-/
 
+#print CategoryTheory.Sieve.functorPushforward_bot /-
 @[simp]
 theorem functorPushforward_bot (F : C ⥤ D) (X : C) : (⊥ : Sieve X).functorPushforward F = ⊥ :=
   (functor_galoisConnection F X).l_bot
 #align category_theory.sieve.functor_pushforward_bot CategoryTheory.Sieve.functorPushforward_bot
+-/
 
+#print CategoryTheory.Sieve.functorPushforward_top /-
 @[simp]
 theorem functorPushforward_top (F : C ⥤ D) (X : C) : (⊤ : Sieve X).functorPushforward F = ⊤ :=
   by
@@ -738,22 +855,30 @@ theorem functorPushforward_top (F : C ⥤ D) (X : C) : (⊤ : Sieve X).functorPu
   apply generate_of_contains_is_split_epi (𝟙 (F.obj X))
   refine' ⟨X, 𝟙 _, 𝟙 _, trivial, by simp⟩
 #align category_theory.sieve.functor_pushforward_top CategoryTheory.Sieve.functorPushforward_top
+-/
 
+#print CategoryTheory.Sieve.functorPullback_bot /-
 @[simp]
 theorem functorPullback_bot (F : C ⥤ D) (X : C) : (⊥ : Sieve (F.obj X)).functorPullback F = ⊥ :=
   rfl
 #align category_theory.sieve.functor_pullback_bot CategoryTheory.Sieve.functorPullback_bot
+-/
 
+#print CategoryTheory.Sieve.functorPullback_top /-
 @[simp]
 theorem functorPullback_top (F : C ⥤ D) (X : C) : (⊤ : Sieve (F.obj X)).functorPullback F = ⊤ :=
   rfl
 #align category_theory.sieve.functor_pullback_top CategoryTheory.Sieve.functorPullback_top
+-/
 
+#print CategoryTheory.Sieve.image_mem_functorPushforward /-
 theorem image_mem_functorPushforward (R : Sieve X) {V} {f : V ⟶ X} (h : R f) :
     R.functorPushforward F (F.map f) :=
   ⟨V, f, 𝟙 _, h, by simp⟩
 #align category_theory.sieve.image_mem_functor_pushforward CategoryTheory.Sieve.image_mem_functorPushforward
+-/
 
+#print CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion /-
 /-- When `F` is essentially surjective and full, the galois connection is a galois insertion. -/
 def essSurjFullFunctorGaloisInsertion [EssSurj F] [Full F] (X : C) :
     GaloisInsertion (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
@@ -764,7 +889,9 @@ def essSurjFullFunctorGaloisInsertion [EssSurj F] [Full F] (X : C) :
   refine' ⟨_, F.preimage ((F.obj_obj_preimage_iso Y).Hom ≫ f), (F.obj_obj_preimage_iso Y).inv, _⟩
   simpa using S.downward_closed hf _
 #align category_theory.sieve.ess_surj_full_functor_galois_insertion CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion
+-/
 
+#print CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertion /-
 /-- When `F` is fully faithful, the galois connection is a galois coinsertion. -/
 def fullyFaithfulFunctorGaloisCoinsertion [Full F] [Faithful F] (X : C) :
     GaloisCoinsertion (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
@@ -776,6 +903,7 @@ def fullyFaithfulFunctorGaloisCoinsertion [Full F] [Faithful F] (X : C) :
   rw [F.map_injective h₂]
   exact S.downward_closed h₁ _
 #align category_theory.sieve.fully_faithful_functor_galois_coinsertion CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertion
+-/
 
 end Functor
 
@@ -789,28 +917,37 @@ def functor (S : Sieve X) : Cᵒᵖ ⥤ Type v₁
 #align category_theory.sieve.functor CategoryTheory.Sieve.functor
 -/
 
+#print CategoryTheory.Sieve.natTransOfLe /-
 /-- If a sieve S is contained in a sieve T, then we have a morphism of presheaves on their induced
 presheaves.
 -/
 @[simps]
 def natTransOfLe {S T : Sieve X} (h : S ≤ T) : S.Functor ⟶ T.Functor where app Y f := ⟨f.1, h _ f.2⟩
 #align category_theory.sieve.nat_trans_of_le CategoryTheory.Sieve.natTransOfLe
+-/
 
+#print CategoryTheory.Sieve.functorInclusion /-
 /-- The natural inclusion from the functor induced by a sieve to the yoneda embedding. -/
 @[simps]
 def functorInclusion (S : Sieve X) : S.Functor ⟶ yoneda.obj X where app Y f := f.1
 #align category_theory.sieve.functor_inclusion CategoryTheory.Sieve.functorInclusion
+-/
 
+#print CategoryTheory.Sieve.natTransOfLe_comm /-
 theorem natTransOfLe_comm {S T : Sieve X} (h : S ≤ T) :
     natTransOfLe h ≫ functorInclusion _ = functorInclusion _ :=
   rfl
 #align category_theory.sieve.nat_trans_of_le_comm CategoryTheory.Sieve.natTransOfLe_comm
+-/
 
+#print CategoryTheory.Sieve.functorInclusion_is_mono /-
 /-- The presheaf induced by a sieve is a subobject of the yoneda embedding. -/
 instance functorInclusion_is_mono : Mono S.functorInclusion :=
   ⟨fun Z f g h => by ext (Y y); apply congr_fun (nat_trans.congr_app h Y) y⟩
 #align category_theory.sieve.functor_inclusion_is_mono CategoryTheory.Sieve.functorInclusion_is_mono
+-/
 
+#print CategoryTheory.Sieve.sieveOfSubfunctor /-
 -- TODO: Show that when `f` is mono, this is right inverse to `functor_inclusion` up to isomorphism.
 /-- A natural transformation to a representable functor induces a sieve. This is the left inverse of
 `functor_inclusion`, shown in `sieve_of_functor_inclusion`.
@@ -825,6 +962,7 @@ def sieveOfSubfunctor {R} (f : R ⟶ yoneda.obj X) : Sieve X
     rw [functor_to_types.naturality _ _ f]
     simp
 #align category_theory.sieve.sieve_of_subfunctor CategoryTheory.Sieve.sieveOfSubfunctor
+-/
 
 #print CategoryTheory.Sieve.sieveOfSubfunctor_functorInclusion /-
 theorem sieveOfSubfunctor_functorInclusion : sieveOfSubfunctor S.functorInclusion = S :=
@@ -839,9 +977,11 @@ theorem sieveOfSubfunctor_functorInclusion : sieveOfSubfunctor S.functorInclusio
 #align category_theory.sieve.sieve_of_subfunctor_functor_inclusion CategoryTheory.Sieve.sieveOfSubfunctor_functorInclusion
 -/
 
+#print CategoryTheory.Sieve.functorInclusion_top_isIso /-
 instance functorInclusion_top_isIso : IsIso (⊤ : Sieve X).functorInclusion :=
   ⟨⟨{ app := fun Y a => ⟨a, ⟨⟩⟩ }, by tidy⟩⟩
 #align category_theory.sieve.functor_inclusion_top_is_iso CategoryTheory.Sieve.functorInclusion_top_isIso
+-/
 
 end Sieve

f4758115

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -287,7 +287,7 @@ open Lattice
 /-- The supremum of a collection of sieves: the union of them all. -/
 protected def sup (𝒮 : Set (Sieve X)) : Sieve X
     where
-  arrows Y := { f | ∃ S ∈ 𝒮, Sieve.arrows S f }
+  arrows Y := {f | ∃ S ∈ 𝒮, Sieve.arrows S f}
   downward_closed' Y Z f := by rintro ⟨S, hS, hf⟩ g; exact ⟨S, hS, S.downward_closed hf _⟩
 #align category_theory.sieve.Sup CategoryTheory.Sieve.sup
 -/
@@ -296,7 +296,7 @@ protected def sup (𝒮 : Set (Sieve X)) : Sieve X
 /-- The infimum of a collection of sieves: the intersection of them all. -/
 protected def inf (𝒮 : Set (Sieve X)) : Sieve X
     where
-  arrows Y := { f | ∀ S ∈ 𝒮, Sieve.arrows S f }
+  arrows Y := {f | ∀ S ∈ 𝒮, Sieve.arrows S f}
   downward_closed' Y Z f hf g S H := S.downward_closed (hf S H) g
 #align category_theory.sieve.Inf CategoryTheory.Sieve.inf
 -/

f4758115

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -46,7 +46,8 @@ variable {X Y Z : C} (f : Y ⟶ X)
 #print CategoryTheory.Presieve /-
 /-- A set of arrows all with codomain `X`. -/
 def Presieve (X : C) :=
-  ∀ ⦃Y⦄, Set (Y ⟶ X)deriving CompleteLattice
+  ∀ ⦃Y⦄, Set (Y ⟶ X)
+deriving CompleteLattice
 #align category_theory.presieve CategoryTheory.Presieve
 -/
 
@@ -74,7 +75,7 @@ abbrev cocone (S : Presieve X) : Cocone S.diagram :=
 `{ g ≫ f | (f : Y ⟶ X) ∈ S, (g : Z ⟶ Y) ∈ R f }`.
 -/
 def bind (S : Presieve X) (R : ∀ ⦃Y⦄ ⦃f : Y ⟶ X⦄, S f → Presieve Y) : Presieve X := fun Z h =>
-  ∃ (Y : C)(g : Z ⟶ Y)(f : Y ⟶ X)(H : S f), R H g ∧ g ≫ f = h
+  ∃ (Y : C) (g : Z ⟶ Y) (f : Y ⟶ X) (H : S f), R H g ∧ g ≫ f = h
 #align category_theory.presieve.bind CategoryTheory.Presieve.bind
 -/
 
@@ -162,7 +163,7 @@ theorem ofArrows_bind {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
     (j : ∀ ⦃Y⦄ (f : Y ⟶ X), ofArrows Z g f → Type _) (W : ∀ ⦃Y⦄ (f : Y ⟶ X) (H), j f H → C)
     (k : ∀ ⦃Y⦄ (f : Y ⟶ X) (H i), W f H i ⟶ Y) :
     ((ofArrows Z g).bind fun Y f H => ofArrows (W f H) (k f H)) =
-      ofArrows (fun i : Σi, j _ (ofArrows.mk i) => W (g i.1) _ i.2) fun ij =>
+      ofArrows (fun i : Σ i, j _ (ofArrows.mk i) => W (g i.1) _ i.2) fun ij =>
         k (g ij.1) _ ij.2 ≫ g ij.1 :=
   by
   ext (Y f)
@@ -198,7 +199,7 @@ variable {E : Type u₃} [Category.{v₃} E] (G : D ⥤ E)
 by taking the sieve generated by the image via `F`.
 -/
 def functorPushforward (S : Presieve X) : Presieve (F.obj X) := fun Y f =>
-  ∃ (Z : C)(g : Z ⟶ X)(h : Y ⟶ F.obj Z), S g ∧ f = h ≫ F.map g
+  ∃ (Z : C) (g : Z ⟶ X) (h : Y ⟶ F.obj Z), S g ∧ f = h ≫ F.map g
 #align category_theory.presieve.functor_pushforward CategoryTheory.Presieve.functorPushforward
 
 /-- An auxillary definition in order to fix the choice of the preimages between various definitions.
@@ -365,7 +366,7 @@ theorem sInf_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
 
 @[simp]
 theorem sSup_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
-    sSup Ss f ↔ ∃ (S : Sieve X)(H : S ∈ Ss), S f :=
+    sSup Ss f ↔ ∃ (S : Sieve X) (H : S ∈ Ss), S f :=
   Iff.rfl
 #align category_theory.sieve.Sup_apply CategoryTheory.Sieve.sSup_apply
 
@@ -389,7 +390,7 @@ theorem top_apply (f : Y ⟶ X) : (⊤ : Sieve X) f :=
 @[simps]
 def generate (R : Presieve X) : Sieve X
     where
-  arrows Z f := ∃ (Y : _)(h : Z ⟶ Y)(g : Y ⟶ X), R g ∧ h ≫ g = f
+  arrows Z f := ∃ (Y : _) (h : Z ⟶ Y) (g : Y ⟶ X), R g ∧ h ≫ g = f
   downward_closed' := by
     rintro Y Z _ ⟨W, g, f, hf, rfl⟩ h
     exact ⟨_, h ≫ g, _, hf, by simp⟩
@@ -577,7 +578,7 @@ def galoisCoinsertionOfMono (f : Y ⟶ X) [Mono f] :
   by
   apply (GaloisConnection f).toGaloisCoinsertion
   rintro S Z g ⟨g₁, hf, hg₁⟩
-  rw [cancel_mono f] at hf
+  rw [cancel_mono f] at hf 
   rwa [← hf]
 #align category_theory.sieve.galois_coinsertion_of_mono CategoryTheory.Sieve.galoisCoinsertionOfMono
 
@@ -771,7 +772,7 @@ def fullyFaithfulFunctorGaloisCoinsertion [Full F] [Faithful F] (X : C) :
   by
   apply (functor_galois_connection F X).toGaloisCoinsertion
   rintro S Y f ⟨Z, g, h, h₁, h₂⟩
-  rw [← F.image_preimage h, ← F.map_comp] at h₂
+  rw [← F.image_preimage h, ← F.map_comp] at h₂ 
   rw [F.map_injective h₂]
   exact S.downward_closed h₁ _
 #align category_theory.sieve.fully_faithful_functor_galois_coinsertion CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertion

f4758115

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -55,12 +55,6 @@ namespace Presieve
 instance : Inhabited (Presieve X) :=
   ⟨⊤⟩
 
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 /-- Given a sieve `S` on `X : C`, its associated diagram `S.diagram` is defined to be
     the natural functor from the full subcategory of the over category `C/X` consisting
     of arrows in `S` to `C`. -/
@@ -68,12 +62,6 @@ abbrev diagram (S : Presieve X) : (FullSubcategory fun f : Over X => S f.Hom) 
   fullSubcategoryInclusion _ ⋙ Over.forget X
 #align category_theory.presieve.diagram CategoryTheory.Presieve.diagram
 
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 /-- Given a sieve `S` on `X : C`, its associated cocone `S.cocone` is defined to be
     the natural cocone over the diagram defined above with cocone point `X`. -/
 abbrev cocone (S : Presieve X) : Cocone S.diagram :=
@@ -104,12 +92,6 @@ inductive singleton : Presieve X
   | mk : singleton f
 #align category_theory.presieve.singleton CategoryTheory.Presieve.singletonₓ
 
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 @[simp]
 theorem singleton_eq_iff_domain (f g : Y ⟶ X) : singleton f g ↔ f = g :=
   by
@@ -120,12 +102,6 @@ theorem singleton_eq_iff_domain (f g : Y ⟶ X) : singleton f g ↔ f = g :=
     apply singleton.mk
 #align category_theory.presieve.singleton_eq_iff_domain CategoryTheory.Presieve.singleton_eq_iff_domain
 
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 theorem singleton_self : singleton f f :=
   singleton.mk
 #align category_theory.presieve.singleton_self CategoryTheory.Presieve.singleton_self
@@ -141,12 +117,6 @@ inductive pullbackArrows [HasPullbacks C] (R : Presieve X) : Presieve Y
 #align category_theory.presieve.pullback_arrows CategoryTheory.Presieve.pullbackArrows
 -/
 
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 theorem pullback_singleton [HasPullbacks C] (g : Z ⟶ X) :
     pullbackArrows f (singleton g) = singleton (pullback.snd : pullback g f ⟶ _) :=
   by
@@ -165,12 +135,6 @@ inductive ofArrows {ι : Type _} (Y : ι → C) (f : ∀ i, Y i ⟶ X) : Presiev
 #align category_theory.presieve.of_arrows CategoryTheory.Presieve.ofArrows
 -/
 
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 theorem ofArrows_pUnit : (ofArrows _ fun _ : PUnit => f) = singleton f :=
   by
   ext (Y g)
@@ -181,12 +145,6 @@ theorem ofArrows_pUnit : (ofArrows _ fun _ : PUnit => f) = singleton f :=
     exact of_arrows.mk PUnit.unit
 #align category_theory.presieve.of_arrows_punit CategoryTheory.Presieve.ofArrows_pUnit
 
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 theorem ofArrows_pullback [HasPullbacks C] {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X) :
     (ofArrows (fun i => pullback (g i) f) fun i => pullback.snd) =
       pullbackArrows f (ofArrows Z g) :=
@@ -200,9 +158,6 @@ theorem ofArrows_pullback [HasPullbacks C] {ι : Type _} (Z : ι → C) (g : ∀
     apply of_arrows.mk
 #align category_theory.presieve.of_arrows_pullback CategoryTheory.Presieve.ofArrows_pullback
 
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 theorem ofArrows_bind {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
     (j : ∀ ⦃Y⦄ (f : Y ⟶ X), ofArrows Z g f → Type _) (W : ∀ ⦃Y⦄ (f : Y ⟶ X) (H), j f H → C)
     (k : ∀ ⦃Y⦄ (f : Y ⟶ X) (H i), W f H i ⟶ Y) :
@@ -218,22 +173,10 @@ theorem ofArrows_bind {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
     exact bind_comp _ (of_arrows.mk _) (of_arrows.mk _)
 #align category_theory.presieve.of_arrows_bind CategoryTheory.Presieve.ofArrows_bind
 
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 /-- Given a presieve on `F(X)`, we can define a presieve on `X` by taking the preimage via `F`. -/
 def functorPullback (R : Presieve (F.obj X)) : Presieve X := fun _ f => R (F.map f)
 #align category_theory.presieve.functor_pullback CategoryTheory.Presieve.functorPullback
 
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 @[simp]
 theorem functorPullback_mem (R : Presieve (F.obj X)) {Y} (f : Y ⟶ X) :
     R.functorPullback F f ↔ R (F.map f) :=
@@ -251,12 +194,6 @@ section FunctorPushforward
 
 variable {E : Type u₃} [Category.{v₃} E] (G : D ⥤ E)
 
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 /-- Given a presieve on `X`, we can define a presieve on `F(X)` (which is actually a sieve)
 by taking the sieve generated by the image via `F`.
 -/
@@ -264,12 +201,6 @@ def functorPushforward (S : Presieve X) : Presieve (F.obj X) := fun Y f =>
   ∃ (Z : C)(g : Z ⟶ X)(h : Y ⟶ F.obj Z), S g ∧ f = h ≫ F.map g
 #align category_theory.presieve.functor_pushforward CategoryTheory.Presieve.functorPushforward
 
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 /-- An auxillary definition in order to fix the choice of the preimages between various definitions.
 -/
 @[nolint has_nonempty_instance]
@@ -281,24 +212,12 @@ structure FunctorPushforwardStructure (S : Presieve X) {Y} (f : Y ⟶ F.obj X) w
   fac : f = lift ≫ F.map premap
 #align category_theory.presieve.functor_pushforward_structure CategoryTheory.Presieve.FunctorPushforwardStructure
 
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 /-- The fixed choice of a preimage. -/
 noncomputable def getFunctorPushforwardStructure {F : C ⥤ D} {S : Presieve X} {Y : D}
     {f : Y ⟶ F.obj X} (h : S.functorPushforward F f) : FunctorPushforwardStructure F S f := by
   choose Z f' g h₁ h using h; exact ⟨Z, f', g, h₁, h⟩
 #align category_theory.presieve.get_functor_pushforward_structure CategoryTheory.Presieve.getFunctorPushforwardStructure
 
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 theorem functorPushforward_comp (R : Presieve X) :
     R.functorPushforward (F ⋙ G) = (R.functorPushforward F).functorPushforward G :=
   by
@@ -308,12 +227,6 @@ theorem functorPushforward_comp (R : Presieve X) :
   · rintro ⟨X, f₁, g₁, ⟨X', f₂, g₂, h₁, rfl⟩, rfl⟩; use ⟨X', f₂, g₁ ≫ G.map g₂, h₁, by simp⟩
 #align category_theory.presieve.functor_pushforward_comp CategoryTheory.Presieve.functorPushforward_comp
 
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 theorem image_mem_functorPushforward (R : Presieve X) {f : Y ⟶ X} (h : R f) :
     R.functorPushforward F (F.map f) :=
   ⟨Y, f, 𝟙 _, h, by simp⟩
@@ -343,12 +256,6 @@ initialize_simps_projections Sieve (arrows → apply)
 
 variable {S R : Sieve X}
 
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 @[simp]
 theorem downward_closed (S : Sieve X) {f : Y ⟶ X} (hf : S f) (g : Z ⟶ Y) : S (g ≫ f) :=
   S.downward_closed' hf g
@@ -450,58 +357,28 @@ instance sieveInhabited : Inhabited (Sieve X) :=
 #align category_theory.sieve.sieve_inhabited CategoryTheory.Sieve.sieveInhabited
 -/
 
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 @[simp]
 theorem sInf_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
     sInf Ss f ↔ ∀ (S : Sieve X) (H : S ∈ Ss), S f :=
   Iff.rfl
 #align category_theory.sieve.Inf_apply CategoryTheory.Sieve.sInf_apply
 
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 @[simp]
 theorem sSup_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
     sSup Ss f ↔ ∃ (S : Sieve X)(H : S ∈ Ss), S f :=
   Iff.rfl
 #align category_theory.sieve.Sup_apply CategoryTheory.Sieve.sSup_apply
 
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 @[simp]
 theorem inter_apply {R S : Sieve X} {Y} (f : Y ⟶ X) : (R ⊓ S) f ↔ R f ∧ S f :=
   Iff.rfl
 #align category_theory.sieve.inter_apply CategoryTheory.Sieve.inter_apply
 
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 @[simp]
 theorem union_apply {R S : Sieve X} {Y} (f : Y ⟶ X) : (R ⊔ S) f ↔ R f ∨ S f :=
   Iff.rfl
 #align category_theory.sieve.union_apply CategoryTheory.Sieve.union_apply
 
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 @[simp]
 theorem top_apply (f : Y ⟶ X) : (⊤ : Sieve X) f :=
   trivial
@@ -535,12 +412,6 @@ def bind (S : Presieve X) (R : ∀ ⦃Y⦄ ⦃f : Y ⟶ X⦄, S f → Sieve Y) :
 
 open Order Lattice
 
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 theorem sets_iff_generate (R : Presieve X) (S : Sieve X) : generate R ≤ S ↔ R ≤ S :=
   ⟨fun H Y g hg => H _ ⟨_, 𝟙 _, _, hg, id_comp _⟩, fun ss Y f =>
     by
@@ -548,12 +419,6 @@ theorem sets_iff_generate (R : Presieve X) (S : Sieve X) : generate R ≤ S ↔
     exact S.downward_closed (ss Z hg) f⟩
 #align category_theory.sieve.sets_iff_generate CategoryTheory.Sieve.sets_iff_generate
 
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 /-- Show that there is a galois insertion (generate, set_over). -/
 def giGenerate : GaloisInsertion (generate : Presieve X → Sieve X) arrows
     where
@@ -563,12 +428,6 @@ def giGenerate : GaloisInsertion (generate : Presieve X → Sieve X) arrows
   le_l_u S Y f hf := ⟨_, 𝟙 _, _, hf, id_comp _⟩
 #align category_theory.sieve.gi_generate CategoryTheory.Sieve.giGenerate
 
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 theorem le_generate (R : Presieve X) : R ≤ generate R :=
   giGenerate.gc.le_u_l R
 #align category_theory.sieve.le_generate CategoryTheory.Sieve.le_generate
@@ -580,23 +439,11 @@ theorem generate_sieve (S : Sieve X) : generate S = S :=
 #align category_theory.sieve.generate_sieve CategoryTheory.Sieve.generate_sieve
 -/
 
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 /-- If the identity arrow is in a sieve, the sieve is maximal. -/
 theorem id_mem_iff_eq_top : S (𝟙 X) ↔ S = ⊤ :=
   ⟨fun h => top_unique fun Y f _ => by simpa using downward_closed _ h f, fun h => h.symm ▸ trivial⟩
 #align category_theory.sieve.id_mem_iff_eq_top CategoryTheory.Sieve.id_mem_iff_eq_top
 
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 /-- If an arrow set contains a split epi, it generates the maximal sieve. -/
 theorem generate_of_contains_isSplitEpi {R : Presieve X} (f : Y ⟶ X) [IsSplitEpi f] (hf : R f) :
     generate R = ⊤ := by
@@ -604,24 +451,12 @@ theorem generate_of_contains_isSplitEpi {R : Presieve X} (f : Y ⟶ X) [IsSplitE
   exact ⟨_, section_ f, f, hf, by simp⟩
 #align category_theory.sieve.generate_of_contains_is_split_epi CategoryTheory.Sieve.generate_of_contains_isSplitEpi
 
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 @[simp]
 theorem generate_of_singleton_isSplitEpi (f : Y ⟶ X) [IsSplitEpi f] :
     generate (Presieve.singleton f) = ⊤ :=
   generate_of_contains_isSplitEpi f (Presieve.singleton_self _)
 #align category_theory.sieve.generate_of_singleton_is_split_epi CategoryTheory.Sieve.generate_of_singleton_isSplitEpi
 
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 @[simp]
 theorem generate_top : generate (⊤ : Presieve X) = ⊤ :=
   generate_of_contains_isSplitEpi (𝟙 _) ⟨⟩
@@ -645,12 +480,6 @@ theorem pullback_id : S.pullback (𝟙 _) = S := by simp [sieve.ext_iff]
 #align category_theory.sieve.pullback_id CategoryTheory.Sieve.pullback_id
 -/
 
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 @[simp]
 theorem pullback_top {f : Y ⟶ X} : (⊤ : Sieve X).pullback f = ⊤ :=
   top_unique fun _ g => id
@@ -662,33 +491,15 @@ theorem pullback_comp {f : Y ⟶ X} {g : Z ⟶ Y} (S : Sieve X) :
 #align category_theory.sieve.pullback_comp CategoryTheory.Sieve.pullback_comp
 -/
 
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 @[simp]
 theorem pullback_inter {f : Y ⟶ X} (S R : Sieve X) :
     (S ⊓ R).pullback f = S.pullback f ⊓ R.pullback f := by simp [sieve.ext_iff]
 #align category_theory.sieve.pullback_inter CategoryTheory.Sieve.pullback_inter
 
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 theorem pullback_eq_top_iff_mem (f : Y ⟶ X) : S f ↔ S.pullback f = ⊤ := by
   rw [← id_mem_iff_eq_top, pullback_apply, id_comp]
 #align category_theory.sieve.pullback_eq_top_iff_mem CategoryTheory.Sieve.pullback_eq_top_iff_mem
 
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 theorem pullback_eq_top_of_mem (S : Sieve X) {f : Y ⟶ X} : S f → S.pullback f = ⊤ :=
   (pullback_eq_top_iff_mem f).1
 #align category_theory.sieve.pullback_eq_top_of_mem CategoryTheory.Sieve.pullback_eq_top_of_mem
@@ -721,73 +532,31 @@ theorem pushforward_comp {f : Y ⟶ X} {g : Z ⟶ Y} (R : Sieve Z) :
 #align category_theory.sieve.pushforward_comp CategoryTheory.Sieve.pushforward_comp
 -/
 
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 theorem galoisConnection (f : Y ⟶ X) : GaloisConnection (Sieve.pushforward f) (Sieve.pullback f) :=
   fun S R => ⟨fun hR Z g hg => hR _ ⟨g, rfl, hg⟩, fun hS Z g ⟨h, hg, hh⟩ => hg ▸ hS h hh⟩
 #align category_theory.sieve.galois_connection CategoryTheory.Sieve.galoisConnection
 
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 theorem pullback_monotone (f : Y ⟶ X) : Monotone (Sieve.pullback f) :=
   (galoisConnection f).monotone_u
 #align category_theory.sieve.pullback_monotone CategoryTheory.Sieve.pullback_monotone
 
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 theorem pushforward_monotone (f : Y ⟶ X) : Monotone (Sieve.pushforward f) :=
   (galoisConnection f).monotone_l
 #align category_theory.sieve.pushforward_monotone CategoryTheory.Sieve.pushforward_monotone
 
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 theorem le_pushforward_pullback (f : Y ⟶ X) (R : Sieve Y) : R ≤ (R.pushforward f).pullback f :=
   (galoisConnection f).le_u_l _
 #align category_theory.sieve.le_pushforward_pullback CategoryTheory.Sieve.le_pushforward_pullback
 
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 theorem pullback_pushforward_le (f : Y ⟶ X) (R : Sieve X) : (R.pullback f).pushforward f ≤ R :=
   (galoisConnection f).l_u_le _
 #align category_theory.sieve.pullback_pushforward_le CategoryTheory.Sieve.pullback_pushforward_le
 
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 theorem pushforward_union {f : Y ⟶ X} (S R : Sieve Y) :
     (S ⊔ R).pushforward f = S.pushforward f ⊔ R.pushforward f :=
   (galoisConnection f).l_sup
 #align category_theory.sieve.pushforward_union CategoryTheory.Sieve.pushforward_union
 
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 theorem pushforward_le_bind_of_mem (S : Presieve X) (R : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄, S f → Sieve Y)
     (f : Y ⟶ X) (h : S f) : (R h).pushforward f ≤ bind S R :=
   by
@@ -795,12 +564,6 @@ theorem pushforward_le_bind_of_mem (S : Presieve X) (R : ∀ ⦃Y : C⦄ ⦃f :
   exact ⟨_, g, f, h, hg, rfl⟩
 #align category_theory.sieve.pushforward_le_bind_of_mem CategoryTheory.Sieve.pushforward_le_bind_of_mem
 
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 theorem le_pullback_bind (S : Presieve X) (R : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄, S f → Sieve Y) (f : Y ⟶ X)
     (h : S f) : R h ≤ (bind S R).pullback f :=
   by
@@ -808,12 +571,6 @@ theorem le_pullback_bind (S : Presieve X) (R : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄
   apply pushforward_le_bind_of_mem
 #align category_theory.sieve.le_pullback_bind CategoryTheory.Sieve.le_pullback_bind
 
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 /-- If `f` is a monomorphism, the pushforward-pullback adjunction on sieves is coreflective. -/
 def galoisCoinsertionOfMono (f : Y ⟶ X) [Mono f] :
     GaloisCoinsertion (Sieve.pushforward f) (Sieve.pullback f) :=
@@ -824,12 +581,6 @@ def galoisCoinsertionOfMono (f : Y ⟶ X) [Mono f] :
   rwa [← hf]
 #align category_theory.sieve.galois_coinsertion_of_mono CategoryTheory.Sieve.galoisCoinsertionOfMono
 
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 /-- If `f` is a split epi, the pushforward-pullback adjunction on sieves is reflective. -/
 def galoisInsertionOfIsSplitEpi (f : Y ⟶ X) [IsSplitEpi f] :
     GaloisInsertion (Sieve.pushforward f) (Sieve.pullback f) :=
@@ -859,12 +610,6 @@ section Functor
 
 variable {E : Type u₃} [Category.{v₃} E] (G : D ⥤ E)
 
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 /--
 If `R` is a sieve, then the `category_theory.presieve.functor_pullback` of `R` is actually a sieve.
 -/
@@ -878,12 +623,6 @@ def functorPullback (R : Sieve (F.obj X)) : Sieve X
     exact R.downward_closed hf (F.map g)
 #align category_theory.sieve.functor_pullback CategoryTheory.Sieve.functorPullback
 
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 @[simp]
 theorem functorPullback_arrows (R : Sieve (F.obj X)) :
     (R.functorPullback F).arrows = R.arrows.functorPullback F :=
@@ -896,22 +635,10 @@ theorem functorPullback_id (R : Sieve X) : R.functorPullback (𝟭 _) = R := by
 #align category_theory.sieve.functor_pullback_id CategoryTheory.Sieve.functorPullback_id
 -/
 
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 theorem functorPullback_comp (R : Sieve ((F ⋙ G).obj X)) :
     R.functorPullback (F ⋙ G) = (R.functorPullback G).functorPullback F := by ext; rfl
 #align category_theory.sieve.functor_pullback_comp CategoryTheory.Sieve.functorPullback_comp
 
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 theorem functorPushforward_extend_eq {R : Presieve X} :
     (generate R).arrows.functorPushforward F = R.functorPushforward F :=
   by
@@ -921,12 +648,6 @@ theorem functorPushforward_extend_eq {R : Presieve X} :
   · rintro ⟨X', g, f', h₁, h₂⟩; exact ⟨X', g, f', le_generate R _ h₁, h₂⟩
 #align category_theory.sieve.functor_pushforward_extend_eq CategoryTheory.Sieve.functorPushforward_extend_eq
 
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 /-- The sieve generated by the image of `R` under `F`. -/
 @[simps]
 def functorPushforward (R : Sieve X) : Sieve (F.obj X)
@@ -937,12 +658,6 @@ def functorPushforward (R : Sieve X) : Sieve (F.obj X)
     exact ⟨X, α, g ≫ β, hα, by simp⟩
 #align category_theory.sieve.functor_pushforward CategoryTheory.Sieve.functorPushforward
 
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 @[simp]
 theorem functorPushforward_id (R : Sieve X) : R.functorPushforward (𝟭 _) = R :=
   by
@@ -955,23 +670,11 @@ theorem functorPushforward_id (R : Sieve X) : R.functorPushforward (𝟭 _) = R
     exact ⟨X, f, 𝟙 _, hf, by simp⟩
 #align category_theory.sieve.functor_pushforward_id CategoryTheory.Sieve.functorPushforward_id
 
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 theorem functorPushforward_comp (R : Sieve X) :
     R.functorPushforward (F ⋙ G) = (R.functorPushforward F).functorPushforward G := by ext;
   simpa [R.arrows.functor_pushforward_comp F G]
 #align category_theory.sieve.functor_pushforward_comp CategoryTheory.Sieve.functorPushforward_comp
 
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 theorem functor_galoisConnection (X : C) :
     GaloisConnection (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
       (Sieve.functorPullback F) :=
@@ -987,100 +690,46 @@ theorem functor_galoisConnection (X : C) :
     exact hle g hg
 #align category_theory.sieve.functor_galois_connection CategoryTheory.Sieve.functor_galoisConnection
 
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 theorem functorPullback_monotone (X : C) :
     Monotone (Sieve.functorPullback F : Sieve (F.obj X) → Sieve X) :=
   (functor_galoisConnection F X).monotone_u
 #align category_theory.sieve.functor_pullback_monotone CategoryTheory.Sieve.functorPullback_monotone
 
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 theorem functorPushforward_monotone (X : C) :
     Monotone (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X)) :=
   (functor_galoisConnection F X).monotone_l
 #align category_theory.sieve.functor_pushforward_monotone CategoryTheory.Sieve.functorPushforward_monotone
 
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 theorem le_functorPushforward_pullback (R : Sieve X) :
     R ≤ (R.functorPushforward F).functorPullback F :=
   (functor_galoisConnection F X).le_u_l _
 #align category_theory.sieve.le_functor_pushforward_pullback CategoryTheory.Sieve.le_functorPushforward_pullback
 
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 theorem functorPullback_pushforward_le (R : Sieve (F.obj X)) :
     (R.functorPullback F).functorPushforward F ≤ R :=
   (functor_galoisConnection F X).l_u_le _
 #align category_theory.sieve.functor_pullback_pushforward_le CategoryTheory.Sieve.functorPullback_pushforward_le
 
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 theorem functorPushforward_union (S R : Sieve X) :
     (S ⊔ R).functorPushforward F = S.functorPushforward F ⊔ R.functorPushforward F :=
   (functor_galoisConnection F X).l_sup
 #align category_theory.sieve.functor_pushforward_union CategoryTheory.Sieve.functorPushforward_union
 
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 theorem functorPullback_union (S R : Sieve (F.obj X)) :
     (S ⊔ R).functorPullback F = S.functorPullback F ⊔ R.functorPullback F :=
   rfl
 #align category_theory.sieve.functor_pullback_union CategoryTheory.Sieve.functorPullback_union
 
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 theorem functorPullback_inter (S R : Sieve (F.obj X)) :
     (S ⊓ R).functorPullback F = S.functorPullback F ⊓ R.functorPullback F :=
   rfl
 #align category_theory.sieve.functor_pullback_inter CategoryTheory.Sieve.functorPullback_inter
 
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 @[simp]
 theorem functorPushforward_bot (F : C ⥤ D) (X : C) : (⊥ : Sieve X).functorPushforward F = ⊥ :=
   (functor_galoisConnection F X).l_bot
 #align category_theory.sieve.functor_pushforward_bot CategoryTheory.Sieve.functorPushforward_bot
 
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 @[simp]
 theorem functorPushforward_top (F : C ⥤ D) (X : C) : (⊤ : Sieve X).functorPushforward F = ⊤ :=
   by
@@ -1089,45 +738,21 @@ theorem functorPushforward_top (F : C ⥤ D) (X : C) : (⊤ : Sieve X).functorPu
   refine' ⟨X, 𝟙 _, 𝟙 _, trivial, by simp⟩
 #align category_theory.sieve.functor_pushforward_top CategoryTheory.Sieve.functorPushforward_top
 
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 @[simp]
 theorem functorPullback_bot (F : C ⥤ D) (X : C) : (⊥ : Sieve (F.obj X)).functorPullback F = ⊥ :=
   rfl
 #align category_theory.sieve.functor_pullback_bot CategoryTheory.Sieve.functorPullback_bot
 
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 @[simp]
 theorem functorPullback_top (F : C ⥤ D) (X : C) : (⊤ : Sieve (F.obj X)).functorPullback F = ⊤ :=
   rfl
 #align category_theory.sieve.functor_pullback_top CategoryTheory.Sieve.functorPullback_top
 
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 theorem image_mem_functorPushforward (R : Sieve X) {V} {f : V ⟶ X} (h : R f) :
     R.functorPushforward F (F.map f) :=
   ⟨V, f, 𝟙 _, h, by simp⟩
 #align category_theory.sieve.image_mem_functor_pushforward CategoryTheory.Sieve.image_mem_functorPushforward
 
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 /-- When `F` is essentially surjective and full, the galois connection is a galois insertion. -/
 def essSurjFullFunctorGaloisInsertion [EssSurj F] [Full F] (X : C) :
     GaloisInsertion (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
@@ -1139,12 +764,6 @@ def essSurjFullFunctorGaloisInsertion [EssSurj F] [Full F] (X : C) :
   simpa using S.downward_closed hf _
 #align category_theory.sieve.ess_surj_full_functor_galois_insertion CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion
 
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 /-- When `F` is fully faithful, the galois connection is a galois coinsertion. -/
 def fullyFaithfulFunctorGaloisCoinsertion [Full F] [Faithful F] (X : C) :
     GaloisCoinsertion (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
@@ -1169,12 +788,6 @@ def functor (S : Sieve X) : Cᵒᵖ ⥤ Type v₁
 #align category_theory.sieve.functor CategoryTheory.Sieve.functor
 -/
 
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 /-- If a sieve S is contained in a sieve T, then we have a morphism of presheaves on their induced
 presheaves.
 -/
@@ -1182,45 +795,21 @@ presheaves.
 def natTransOfLe {S T : Sieve X} (h : S ≤ T) : S.Functor ⟶ T.Functor where app Y f := ⟨f.1, h _ f.2⟩
 #align category_theory.sieve.nat_trans_of_le CategoryTheory.Sieve.natTransOfLe
 
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 /-- The natural inclusion from the functor induced by a sieve to the yoneda embedding. -/
 @[simps]
 def functorInclusion (S : Sieve X) : S.Functor ⟶ yoneda.obj X where app Y f := f.1
 #align category_theory.sieve.functor_inclusion CategoryTheory.Sieve.functorInclusion
 
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 theorem natTransOfLe_comm {S T : Sieve X} (h : S ≤ T) :
     natTransOfLe h ≫ functorInclusion _ = functorInclusion _ :=
   rfl
 #align category_theory.sieve.nat_trans_of_le_comm CategoryTheory.Sieve.natTransOfLe_comm
 
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 /-- The presheaf induced by a sieve is a subobject of the yoneda embedding. -/
 instance functorInclusion_is_mono : Mono S.functorInclusion :=
   ⟨fun Z f g h => by ext (Y y); apply congr_fun (nat_trans.congr_app h Y) y⟩
 #align category_theory.sieve.functor_inclusion_is_mono CategoryTheory.Sieve.functorInclusion_is_mono
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.sieve.sieve_of_subfunctor CategoryTheory.Sieve.sieveOfSubfunctorₓ'. -/
 -- TODO: Show that when `f` is mono, this is right inverse to `functor_inclusion` up to isomorphism.
 /-- A natural transformation to a representable functor induces a sieve. This is the left inverse of
 `functor_inclusion`, shown in `sieve_of_functor_inclusion`.
@@ -1249,12 +838,6 @@ theorem sieveOfSubfunctor_functorInclusion : sieveOfSubfunctor S.functorInclusio
 #align category_theory.sieve.sieve_of_subfunctor_functor_inclusion CategoryTheory.Sieve.sieveOfSubfunctor_functorInclusion
 -/
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_inclusion_top_is_iso CategoryTheory.Sieve.functorInclusion_top_isIsoₓ'. -/
 instance functorInclusion_top_isIso : IsIso (⊤ : Sieve X).functorInclusion :=
   ⟨⟨{ app := fun Y a => ⟨a, ⟨⟩⟩ }, by tidy⟩⟩
 #align category_theory.sieve.functor_inclusion_top_is_iso CategoryTheory.Sieve.functorInclusion_top_isIso

f4758115

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -289,10 +289,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.presieve.get_functor_pushforward_structure CategoryTheory.Presieve.getFunctorPushforwardStructureₓ'. -/
 /-- The fixed choice of a preimage. -/
 noncomputable def getFunctorPushforwardStructure {F : C ⥤ D} {S : Presieve X} {Y : D}
-    {f : Y ⟶ F.obj X} (h : S.functorPushforward F f) : FunctorPushforwardStructure F S f :=
-  by
-  choose Z f' g h₁ h using h
-  exact ⟨Z, f', g, h₁, h⟩
+    {f : Y ⟶ F.obj X} (h : S.functorPushforward F f) : FunctorPushforwardStructure F S f := by
+  choose Z f' g h₁ h using h; exact ⟨Z, f', g, h₁, h⟩
 #align category_theory.presieve.get_functor_pushforward_structure CategoryTheory.Presieve.getFunctorPushforwardStructure
 
 /- warning: category_theory.presieve.functor_pushforward_comp -> CategoryTheory.Presieve.functorPushforward_comp is a dubious translation:
@@ -306,10 +304,8 @@ theorem functorPushforward_comp (R : Presieve X) :
   by
   ext (x f)
   constructor
-  · rintro ⟨X, f₁, g₁, h₁, rfl⟩
-    exact ⟨F.obj X, F.map f₁, g₁, ⟨X, f₁, 𝟙 _, h₁, by simp⟩, rfl⟩
-  · rintro ⟨X, f₁, g₁, ⟨X', f₂, g₂, h₁, rfl⟩, rfl⟩
-    use ⟨X', f₂, g₁ ≫ G.map g₂, h₁, by simp⟩
+  · rintro ⟨X, f₁, g₁, h₁, rfl⟩; exact ⟨F.obj X, F.map f₁, g₁, ⟨X, f₁, 𝟙 _, h₁, by simp⟩, rfl⟩
+  · rintro ⟨X, f₁, g₁, ⟨X', f₂, g₂, h₁, rfl⟩, rfl⟩; use ⟨X', f₂, g₁ ≫ G.map g₂, h₁, by simp⟩
 #align category_theory.presieve.functor_pushforward_comp CategoryTheory.Presieve.functorPushforward_comp
 
 /- warning: category_theory.presieve.image_mem_functor_pushforward -> CategoryTheory.Presieve.image_mem_functorPushforward is a dubious translation:
@@ -384,9 +380,7 @@ open Lattice
 protected def sup (𝒮 : Set (Sieve X)) : Sieve X
     where
   arrows Y := { f | ∃ S ∈ 𝒮, Sieve.arrows S f }
-  downward_closed' Y Z f := by
-    rintro ⟨S, hS, hf⟩ g
-    exact ⟨S, hS, S.downward_closed hf _⟩
+  downward_closed' Y Z f := by rintro ⟨S, hS, hf⟩ g; exact ⟨S, hS, S.downward_closed hf _⟩
 #align category_theory.sieve.Sup CategoryTheory.Sieve.sup
 -/
 
@@ -413,9 +407,7 @@ protected def union (S R : Sieve X) : Sieve X
 protected def inter (S R : Sieve X) : Sieve X
     where
   arrows Y f := S f ∧ R f
-  downward_closed' := by
-    rintro Y Z f ⟨h₁, h₂⟩ g
-    simp [h₁, h₂]
+  downward_closed' := by rintro Y Z f ⟨h₁, h₂⟩ g; simp [h₁, h₂]
 #align category_theory.sieve.inter CategoryTheory.Sieve.inter
 -/
 
@@ -439,9 +431,7 @@ instance : CompleteLattice (Sieve X)
   sSup := Sieve.sup
   sInf := Sieve.inf
   le_sup 𝒮 S hS Y f hf := ⟨S, hS, hf⟩
-  sup_le ℰ S hS Y f := by
-    rintro ⟨R, hR, hf⟩
-    apply hS R hR _ hf
+  sup_le ℰ S hS Y f := by rintro ⟨R, hR, hf⟩; apply hS R hR _ hf
   inf_le _ _ hS _ _ h := h _ hS
   le_inf _ _ hS _ _ hf _ hR := hS _ hR _ hf
   le_sup_left _ _ _ _ := Or.inl
@@ -902,10 +892,7 @@ theorem functorPullback_arrows (R : Sieve (F.obj X)) :
 
 #print CategoryTheory.Sieve.functorPullback_id /-
 @[simp]
-theorem functorPullback_id (R : Sieve X) : R.functorPullback (𝟭 _) = R :=
-  by
-  ext
-  rfl
+theorem functorPullback_id (R : Sieve X) : R.functorPullback (𝟭 _) = R := by ext; rfl
 #align category_theory.sieve.functor_pullback_id CategoryTheory.Sieve.functorPullback_id
 -/
 
@@ -916,10 +903,7 @@ but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pullback_comp CategoryTheory.Sieve.functorPullback_compₓ'. -/
 theorem functorPullback_comp (R : Sieve ((F ⋙ G).obj X)) :
-    R.functorPullback (F ⋙ G) = (R.functorPullback G).functorPullback F :=
-  by
-  ext
-  rfl
+    R.functorPullback (F ⋙ G) = (R.functorPullback G).functorPullback F := by ext; rfl
 #align category_theory.sieve.functor_pullback_comp CategoryTheory.Sieve.functorPullback_comp
 
 /- warning: category_theory.sieve.functor_pushforward_extend_eq -> CategoryTheory.Sieve.functorPushforward_extend_eq is a dubious translation:
@@ -934,8 +918,7 @@ theorem functorPushforward_extend_eq {R : Presieve X} :
   ext (Y f); constructor
   · rintro ⟨X', g, f', ⟨X'', g', f'', h₁, rfl⟩, rfl⟩
     exact ⟨X'', f'', f' ≫ F.map g', h₁, by simp⟩
-  · rintro ⟨X', g, f', h₁, h₂⟩
-    exact ⟨X', g, f', le_generate R _ h₁, h₂⟩
+  · rintro ⟨X', g, f', h₁, h₂⟩; exact ⟨X', g, f', le_generate R _ h₁, h₂⟩
 #align category_theory.sieve.functor_pushforward_extend_eq CategoryTheory.Sieve.functorPushforward_extend_eq
 
 /- warning: category_theory.sieve.functor_pushforward -> CategoryTheory.Sieve.functorPushforward is a dubious translation:
@@ -979,9 +962,7 @@ but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pushforward_comp CategoryTheory.Sieve.functorPushforward_compₓ'. -/
 theorem functorPushforward_comp (R : Sieve X) :
-    R.functorPushforward (F ⋙ G) = (R.functorPushforward F).functorPushforward G :=
-  by
-  ext
+    R.functorPushforward (F ⋙ G) = (R.functorPushforward F).functorPushforward G := by ext;
   simpa [R.arrows.functor_pushforward_comp F G]
 #align category_theory.sieve.functor_pushforward_comp CategoryTheory.Sieve.functorPushforward_comp
 
@@ -1231,9 +1212,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_inclusion_is_mono CategoryTheory.Sieve.functorInclusion_is_monoₓ'. -/
 /-- The presheaf induced by a sieve is a subobject of the yoneda embedding. -/
 instance functorInclusion_is_mono : Mono S.functorInclusion :=
-  ⟨fun Z f g h => by
-    ext (Y y)
-    apply congr_fun (nat_trans.congr_app h Y) y⟩
+  ⟨fun Z f g h => by ext (Y y); apply congr_fun (nat_trans.congr_app h Y) y⟩
 #align category_theory.sieve.functor_inclusion_is_mono CategoryTheory.Sieve.functorInclusion_is_mono
 
 /- warning: category_theory.sieve.sieve_of_subfunctor -> CategoryTheory.Sieve.sieveOfSubfunctor is a dubious translation:

f4758115

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -201,10 +201,7 @@ theorem ofArrows_pullback [HasPullbacks C] {ι : Type _} (Z : ι → C) (g : ∀
 #align category_theory.presieve.of_arrows_pullback CategoryTheory.Presieve.ofArrows_pullback
 
 /- warning: category_theory.presieve.of_arrows_bind -> CategoryTheory.Presieve.ofArrows_bind is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.presieve.of_arrows_bind CategoryTheory.Presieve.ofArrows_bindₓ'. -/
 theorem ofArrows_bind {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
     (j : ∀ ⦃Y⦄ (f : Y ⟶ X), ofArrows Z g f → Type _) (W : ∀ ⦃Y⦄ (f : Y ⟶ X) (H), j f H → C)

f4758115

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -550,7 +550,7 @@ open Order Lattice
 
 /- warning: category_theory.sieve.sets_iff_generate -> CategoryTheory.Sieve.sets_iff_generate 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.sieve.sets_iff_generate CategoryTheory.Sieve.sets_iff_generateₓ'. -/
@@ -578,7 +578,7 @@ def giGenerate : GaloisInsertion (generate : Presieve X → Sieve X) arrows
 
 /- warning: category_theory.sieve.le_generate -> CategoryTheory.Sieve.le_generate is a dubious translation:
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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} (R : CategoryTheory.Presieve.{u1, u2} C _inst_1 X), LE.le.{max u2 u1} (CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (Preorder.toHasLe.{max u2 u1} (CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (CategoryTheory.Presieve.completeLattice.{u2, u1} C _inst_1 X))))) R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (fun (_x : CategoryTheory.Sieve.{u1, u2} C _inst_1 X) => CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.hasCoeToFun.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.generate.{u1, u2} C _inst_1 X R))
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} (R : CategoryTheory.Presieve.{u1, u2} C _inst_1 X), LE.le.{max u2 u1} (CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (Preorder.toLE.{max u2 u1} (CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (CategoryTheory.instCompleteLatticePresieve.{u1, u2} C _inst_1 X))))) R (CategoryTheory.Sieve.arrows.{u1, u2} C _inst_1 X (CategoryTheory.Sieve.generate.{u1, u2} C _inst_1 X R))
 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.le_generate CategoryTheory.Sieve.le_generateₓ'. -/
@@ -766,7 +766,7 @@ theorem pushforward_monotone (f : Y ⟶ X) : Monotone (Sieve.pushforward f) :=
 
 /- warning: category_theory.sieve.le_pushforward_pullback -> CategoryTheory.Sieve.le_pushforward_pullback is a dubious translation:
 lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (R : CategoryTheory.Sieve.{u1, u2} C _inst_1 Y), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 Y))))) R (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f R))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (R : CategoryTheory.Sieve.{u1, u2} C _inst_1 Y), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (Preorder.toHasLe.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 Y))))) R (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f R))
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (R : CategoryTheory.Sieve.{u1, u2} C _inst_1 Y), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 Y))))) R (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f R))
 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.le_pushforward_pullback CategoryTheory.Sieve.le_pushforward_pullbackₓ'. -/
@@ -776,7 +776,7 @@ theorem le_pushforward_pullback (f : Y ⟶ X) (R : Sieve Y) : R ≤ (R.pushforwa
 
 /- warning: category_theory.sieve.pullback_pushforward_le -> CategoryTheory.Sieve.pullback_pushforward_le is a dubious translation:
 lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (R : CategoryTheory.Sieve.{u1, u2} C _inst_1 X), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f R)) R
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (R : CategoryTheory.Sieve.{u1, u2} C _inst_1 X), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toHasLe.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f R)) R
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (R : CategoryTheory.Sieve.{u1, u2} C _inst_1 X), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X))))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f R)) R
 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.pullback_pushforward_le CategoryTheory.Sieve.pullback_pushforward_leₓ'. -/
@@ -797,7 +797,7 @@ theorem pushforward_union {f : Y ⟶ X} (S R : Sieve Y) :
 
 /- warning: category_theory.sieve.pushforward_le_bind_of_mem -> CategoryTheory.Sieve.pushforward_le_bind_of_mem is a dubious translation:
 lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (R : forall {{Y : C}} {{f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X}}, (S Y f) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y)) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (h : S Y f), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f (R Y f h)) (CategoryTheory.Sieve.bind.{u1, u2} C _inst_1 X S R)
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (R : forall {{Y : C}} {{f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X}}, (S Y f) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y)) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (h : S Y f), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toHasLe.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f (R Y f h)) (CategoryTheory.Sieve.bind.{u1, u2} C _inst_1 X S R)
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (R : forall {{Y : C}} {{f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X}}, (S Y f) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y)) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (h : S Y f), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X))))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f (R Y f h)) (CategoryTheory.Sieve.bind.{u1, u2} C _inst_1 X S R)
 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.pushforward_le_bind_of_mem CategoryTheory.Sieve.pushforward_le_bind_of_memₓ'. -/
@@ -810,7 +810,7 @@ theorem pushforward_le_bind_of_mem (S : Presieve X) (R : ∀ ⦃Y : C⦄ ⦃f :
 
 /- warning: category_theory.sieve.le_pullback_bind -> CategoryTheory.Sieve.le_pullback_bind is a dubious translation:
 lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (R : forall {{Y : C}} {{f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X}}, (S Y f) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y)) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (h : S Y f), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 Y))))) (R Y f h) (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f (CategoryTheory.Sieve.bind.{u1, u2} C _inst_1 X S R))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (R : forall {{Y : C}} {{f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X}}, (S Y f) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y)) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (h : S Y f), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (Preorder.toHasLe.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 Y))))) (R Y f h) (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f (CategoryTheory.Sieve.bind.{u1, u2} C _inst_1 X S R))
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (R : forall {{Y : C}} {{f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X}}, (S Y f) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y)) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (h : S Y f), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 Y))))) (R Y f h) (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f (CategoryTheory.Sieve.bind.{u1, u2} C _inst_1 X S R))
 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.le_pullback_bind CategoryTheory.Sieve.le_pullback_bindₓ'. -/
@@ -1033,7 +1033,7 @@ theorem functorPushforward_monotone (X : C) :
 
 /- warning: category_theory.sieve.le_functor_pushforward_pullback -> CategoryTheory.Sieve.le_functorPushforward_pullback is a dubious translation:
 lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} (R : CategoryTheory.Sieve.{u1, u3} C _inst_1 X), LE.le.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (Preorder.toLE.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u3} C _inst_1 X))))) R (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X R))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} (R : CategoryTheory.Sieve.{u1, u3} C _inst_1 X), LE.le.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (Preorder.toHasLe.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u3} C _inst_1 X))))) R (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X R))
 but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} (R : CategoryTheory.Sieve.{u1, u3} C _inst_1 X), LE.le.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (Preorder.toLE.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u3} C _inst_1 X))))) R (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X R))
 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.le_functor_pushforward_pullback CategoryTheory.Sieve.le_functorPushforward_pullbackₓ'. -/
@@ -1044,7 +1044,7 @@ theorem le_functorPushforward_pullback (R : Sieve X) :
 
 /- warning: category_theory.sieve.functor_pullback_pushforward_le -> CategoryTheory.Sieve.functorPullback_pushforward_le is a dubious translation:
 lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} (R : CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)), LE.le.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (Preorder.toLE.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (PartialOrder.toPreorder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CompleteSemilatticeInf.toPartialOrder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CompleteLattice.toCompleteSemilatticeInf.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CategoryTheory.Sieve.completeLattice.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)))))) (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X R)) R
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} (R : CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)), LE.le.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (Preorder.toHasLe.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (PartialOrder.toPreorder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CompleteSemilatticeInf.toPartialOrder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CompleteLattice.toCompleteSemilatticeInf.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CategoryTheory.Sieve.completeLattice.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)))))) (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X R)) R
 but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} (R : CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)), LE.le.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (Preorder.toLE.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (PartialOrder.toPreorder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CompleteSemilatticeInf.toPartialOrder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CompleteLattice.toCompleteSemilatticeInf.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)))))) (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X R)) R
 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pullback_pushforward_le CategoryTheory.Sieve.functorPullback_pushforward_leₓ'. -/
@@ -1193,7 +1193,7 @@ def functor (S : Sieve X) : Cᵒᵖ ⥤ Type v₁
 
 /- warning: category_theory.sieve.nat_trans_of_le -> CategoryTheory.Sieve.natTransOfLe is a dubious translation:
 lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X} {T : CategoryTheory.Sieve.{u1, u2} C _inst_1 X}, (LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))))) S T) -> (Quiver.Hom.{succ (max u2 u1), max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X S) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X T))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X} {T : CategoryTheory.Sieve.{u1, u2} C _inst_1 X}, (LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toHasLe.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))))) S T) -> (Quiver.Hom.{succ (max u2 u1), max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X S) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X T))
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X} {T : CategoryTheory.Sieve.{u1, u2} C _inst_1 X}, (LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X))))) S T) -> (Quiver.Hom.{max (succ u2) (succ u1), max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X S) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X T))
 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.nat_trans_of_le CategoryTheory.Sieve.natTransOfLeₓ'. -/
@@ -1217,7 +1217,7 @@ def functorInclusion (S : Sieve X) : S.Functor ⟶ yoneda.obj X where app Y f :=
 
 /- warning: category_theory.sieve.nat_trans_of_le_comm -> CategoryTheory.Sieve.natTransOfLe_comm is a dubious translation:
 lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X} {T : CategoryTheory.Sieve.{u1, u2} C _inst_1 X} (h : LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))))) S T), Eq.{succ (max u2 u1)} (Quiver.Hom.{succ (max u2 u1), max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X S) (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1) X)) (CategoryTheory.CategoryStruct.comp.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X S) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X T) (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1) X) (CategoryTheory.Sieve.natTransOfLe.{u1, u2} C _inst_1 X S T h) (CategoryTheory.Sieve.functorInclusion.{u1, u2} C _inst_1 X T)) (CategoryTheory.Sieve.functorInclusion.{u1, u2} C _inst_1 X S)
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X} {T : CategoryTheory.Sieve.{u1, u2} C _inst_1 X} (h : LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toHasLe.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))))) S T), Eq.{succ (max u2 u1)} (Quiver.Hom.{succ (max u2 u1), max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X S) (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1) X)) (CategoryTheory.CategoryStruct.comp.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X S) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X T) (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1) X) (CategoryTheory.Sieve.natTransOfLe.{u1, u2} C _inst_1 X S T h) (CategoryTheory.Sieve.functorInclusion.{u1, u2} C _inst_1 X T)) (CategoryTheory.Sieve.functorInclusion.{u1, u2} C _inst_1 X S)
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X} {T : CategoryTheory.Sieve.{u1, u2} C _inst_1 X} (h : LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X))))) S T), Eq.{max (succ u2) (succ u1)} (Quiver.Hom.{succ (max u2 u1), max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X S) (Prefunctor.obj.{succ u1, max (succ u1) (succ u2), u2, max (succ u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1)) X)) (CategoryTheory.CategoryStruct.comp.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X S) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X T) (Prefunctor.obj.{succ u1, max (succ u1) (succ u2), u2, max (succ u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1)) X) (CategoryTheory.Sieve.natTransOfLe.{u1, u2} C _inst_1 X S T h) (CategoryTheory.Sieve.functorInclusion.{u1, u2} C _inst_1 X T)) (CategoryTheory.Sieve.functorInclusion.{u1, u2} C _inst_1 X S)
 Case conversion may be inaccurate. Consider using '#align category_theory.sieve.nat_trans_of_le_comm CategoryTheory.Sieve.natTransOfLe_commₓ'. -/

f4758115

bump to nightly-2023-05-14-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

d31da313

Diff

@@ -439,8 +439,8 @@ instance : CompleteLattice (Sieve X)
       downward_closed' := fun _ _ _ p _ => False.elim p }
   sup := Sieve.union
   inf := Sieve.inter
-  supₛ := Sieve.sup
-  infₛ := Sieve.inf
+  sSup := Sieve.sup
+  sInf := Sieve.inf
   le_sup 𝒮 S hS Y f hf := ⟨S, hS, hf⟩
   sup_le ℰ S hS Y f := by
     rintro ⟨R, hR, hf⟩
@@ -463,29 +463,29 @@ instance sieveInhabited : Inhabited (Sieve X) :=
 #align category_theory.sieve.sieve_inhabited CategoryTheory.Sieve.sieveInhabited
 -/
 
-/- warning: category_theory.sieve.Inf_apply -> CategoryTheory.Sieve.infₛ_apply is a dubious translation:
+/- warning: category_theory.sieve.Inf_apply -> CategoryTheory.Sieve.sInf_apply is a dubious translation:
 lean 3 declaration is
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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Ss : Set.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X), Iff (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (fun (_x : CategoryTheory.Sieve.{u1, u2} C _inst_1 X) => CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.hasCoeToFun.{u1, u2} C _inst_1 X) (InfSet.sInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toHasInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))) Ss) Y f) (forall (S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X), (Membership.Mem.{max u2 u1, max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Set.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) (Set.hasMem.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) S Ss) -> (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (fun (_x : CategoryTheory.Sieve.{u1, u2} C _inst_1 X) => CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.hasCoeToFun.{u1, u2} C _inst_1 X) S Y f))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align category_theory.sieve.Inf_apply CategoryTheory.Sieve.infₛ_applyₓ'. -/
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Ss : Set.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X), Iff (CategoryTheory.Sieve.arrows.{u1, u2} C _inst_1 X (InfSet.sInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toInfSet.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X)) Ss) Y f) (forall (S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X), (Membership.mem.{max u2 u1, max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Set.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) (Set.instMembershipSet.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) S Ss) -> (CategoryTheory.Sieve.arrows.{u1, u2} C _inst_1 X S Y f))
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.Inf_apply CategoryTheory.Sieve.sInf_applyₓ'. -/
 @[simp]
-theorem infₛ_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
-    infₛ Ss f ↔ ∀ (S : Sieve X) (H : S ∈ Ss), S f :=
+theorem sInf_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
+    sInf Ss f ↔ ∀ (S : Sieve X) (H : S ∈ Ss), S f :=
   Iff.rfl
-#align category_theory.sieve.Inf_apply CategoryTheory.Sieve.infₛ_apply
+#align category_theory.sieve.Inf_apply CategoryTheory.Sieve.sInf_apply
 
-/- warning: category_theory.sieve.Sup_apply -> CategoryTheory.Sieve.supₛ_apply is a dubious translation:
+/- warning: category_theory.sieve.Sup_apply -> CategoryTheory.Sieve.sSup_apply is a dubious translation:
 lean 3 declaration is
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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Ss : Set.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X), Iff (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (fun (_x : CategoryTheory.Sieve.{u1, u2} C _inst_1 X) => CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.hasCoeToFun.{u1, u2} C _inst_1 X) (SupSet.sSup.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeSup.toHasSup.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeSup.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))) Ss) Y f) (Exists.{max (succ u2) (succ u1)} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (fun (S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X) => Exists.{0} (Membership.Mem.{max u2 u1, max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Set.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) (Set.hasMem.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) S Ss) (fun (H : Membership.Mem.{max u2 u1, max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Set.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) (Set.hasMem.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) S Ss) => coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (fun (_x : CategoryTheory.Sieve.{u1, u2} C _inst_1 X) => CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.hasCoeToFun.{u1, u2} C _inst_1 X) S Y f)))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align category_theory.sieve.Sup_apply CategoryTheory.Sieve.supₛ_applyₓ'. -/
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Ss : Set.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X), Iff (CategoryTheory.Sieve.arrows.{u1, u2} C _inst_1 X (SupSet.sSup.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toSupSet.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X)) Ss) Y f) (Exists.{max (succ u2) (succ u1)} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (fun (S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X) => Exists.{0} (Membership.mem.{max u2 u1, max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Set.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) (Set.instMembershipSet.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) S Ss) (fun (H : Membership.mem.{max u2 u1, max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Set.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) (Set.instMembershipSet.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)) S Ss) => CategoryTheory.Sieve.arrows.{u1, u2} C _inst_1 X S Y f)))
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.Sup_apply CategoryTheory.Sieve.sSup_applyₓ'. -/
 @[simp]
-theorem supₛ_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
-    supₛ Ss f ↔ ∃ (S : Sieve X)(H : S ∈ Ss), S f :=
+theorem sSup_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
+    sSup Ss f ↔ ∃ (S : Sieve X)(H : S ∈ Ss), S f :=
   Iff.rfl
-#align category_theory.sieve.Sup_apply CategoryTheory.Sieve.supₛ_apply
+#align category_theory.sieve.Sup_apply CategoryTheory.Sieve.sSup_apply
 
 /- warning: category_theory.sieve.inter_apply -> CategoryTheory.Sieve.inter_apply is a dubious translation:
 lean 3 declaration is

f4758115

bump to nightly-2023-03-09-03

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

061741a1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, E. W. Ayers
 
 ! This file was ported from Lean 3 source module category_theory.sites.sieves
-! leanprover-community/mathlib commit 239d882c4fb58361ee8b3b39fb2091320edef10a
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Data.Set.Lattice
 /-!
 # Theory of sieves
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 - For an object `X` of a category `C`, a `sieve X` is a set of morphisms to `X`
   which is closed under left-composition.
 - The complete lattice structure on sieves is given, as well as the Galois insertion

239d882c

bump to nightly-2023-03-07-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25

a8442c3c

Diff

@@ -40,16 +40,24 @@ variable {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₂} D]
 
 variable {X Y Z : C} (f : Y ⟶ X)
 
+#print CategoryTheory.Presieve /-
 /-- A set of arrows all with codomain `X`. -/
 def Presieve (X : C) :=
   ∀ ⦃Y⦄, Set (Y ⟶ X)deriving CompleteLattice
 #align category_theory.presieve CategoryTheory.Presieve
+-/
 
 namespace Presieve
 
 instance : Inhabited (Presieve X) :=
   ⟨⊤⟩
 
+/- warning: category_theory.presieve.diagram -> CategoryTheory.Presieve.diagram is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X), CategoryTheory.Functor.{u1, u1, max u2 u1, u2} (CategoryTheory.FullSubcategoryₓ.{u1, max u2 u1} (CategoryTheory.Over.{u1, u2} C _inst_1 X) (CategoryTheory.Over.category.{u2, u1} C _inst_1 X) (fun (f : CategoryTheory.Over.{u1, u2} C _inst_1 X) => S (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f))) (CategoryTheory.FullSubcategory.category.{u1, max u2 u1} (CategoryTheory.Over.{u1, u2} C _inst_1 X) (CategoryTheory.Over.category.{u2, u1} C _inst_1 X) (fun (f : CategoryTheory.Over.{u1, u2} C _inst_1 X) => S (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f))) C _inst_1
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X), CategoryTheory.Functor.{u1, u1, max u2 u1, u2} (CategoryTheory.FullSubcategory.{max u2 u1} (CategoryTheory.Over.{u1, u2} C _inst_1 X) (fun (f : CategoryTheory.Over.{u1, u2} C _inst_1 X) => S (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f))) (CategoryTheory.FullSubcategory.category.{u1, max u2 u1} (CategoryTheory.Over.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryOver.{u1, u2} C _inst_1 X) (fun (f : CategoryTheory.Over.{u1, u2} C _inst_1 X) => S (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f))) C _inst_1
+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.diagram CategoryTheory.Presieve.diagramₓ'. -/
 /-- Given a sieve `S` on `X : C`, its associated diagram `S.diagram` is defined to be
     the natural functor from the full subcategory of the over category `C/X` consisting
     of arrows in `S` to `C`. -/
@@ -57,12 +65,19 @@ abbrev diagram (S : Presieve X) : (FullSubcategory fun f : Over X => S f.Hom) 
   fullSubcategoryInclusion _ ⋙ Over.forget X
 #align category_theory.presieve.diagram CategoryTheory.Presieve.diagram
 
+/- warning: category_theory.presieve.cocone -> CategoryTheory.Presieve.cocone is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X), CategoryTheory.Limits.Cocone.{u1, u1, max u2 u1, u2} (CategoryTheory.FullSubcategoryₓ.{u1, max u2 u1} (CategoryTheory.Over.{u1, u2} C _inst_1 X) (CategoryTheory.Over.category.{u2, u1} C _inst_1 X) (fun (f : CategoryTheory.Over.{u1, u2} C _inst_1 X) => S (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f))) (CategoryTheory.FullSubcategory.category.{u1, max u2 u1} (CategoryTheory.Over.{u1, u2} C _inst_1 X) (CategoryTheory.Over.category.{u2, u1} C _inst_1 X) (fun (f : CategoryTheory.Over.{u1, u2} C _inst_1 X) => S (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f))) C _inst_1 (CategoryTheory.Presieve.diagram.{u1, u2} C _inst_1 X S)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X), CategoryTheory.Limits.Cocone.{u1, u1, max u2 u1, u2} (CategoryTheory.FullSubcategory.{max u2 u1} (CategoryTheory.Over.{u1, u2} C _inst_1 X) (fun (f : CategoryTheory.Over.{u1, u2} C _inst_1 X) => S (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f))) (CategoryTheory.FullSubcategory.category.{u1, max u2 u1} (CategoryTheory.Over.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryOver.{u1, u2} C _inst_1 X) (fun (f : CategoryTheory.Over.{u1, u2} C _inst_1 X) => S (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u1, u2} C _inst_1 (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) f))) C _inst_1 (CategoryTheory.Presieve.diagram.{u1, u2} C _inst_1 X S)
+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.cocone CategoryTheory.Presieve.coconeₓ'. -/
 /-- Given a sieve `S` on `X : C`, its associated cocone `S.cocone` is defined to be
     the natural cocone over the diagram defined above with cocone point `X`. -/
 abbrev cocone (S : Presieve X) : Cocone S.diagram :=
   (Over.forgetCocone X).whisker (fullSubcategoryInclusion _)
 #align category_theory.presieve.cocone CategoryTheory.Presieve.cocone
 
+#print CategoryTheory.Presieve.bind /-
 /-- Given a set of arrows `S` all with codomain `X`, and a set of arrows with codomain `Y` for each
 `f : Y ⟶ X` in `S`, produce a set of arrows with codomain `X`:
 `{ g ≫ f | (f : Y ⟶ X) ∈ S, (g : Z ⟶ Y) ∈ R f }`.
@@ -70,19 +85,28 @@ abbrev cocone (S : Presieve X) : Cocone S.diagram :=
 def bind (S : Presieve X) (R : ∀ ⦃Y⦄ ⦃f : Y ⟶ X⦄, S f → Presieve Y) : Presieve X := fun Z h =>
   ∃ (Y : C)(g : Z ⟶ Y)(f : Y ⟶ X)(H : S f), R H g ∧ g ≫ f = h
 #align category_theory.presieve.bind CategoryTheory.Presieve.bind
+-/
 
+#print CategoryTheory.Presieve.bind_comp /-
 @[simp]
 theorem bind_comp {S : Presieve X} {R : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄, S f → Presieve Y} {g : Z ⟶ Y}
     (h₁ : S f) (h₂ : R h₁ g) : bind S R (g ≫ f) :=
   ⟨_, _, _, h₁, h₂, rfl⟩
 #align category_theory.presieve.bind_comp CategoryTheory.Presieve.bind_comp
+-/
 
 -- Note we can't make this into `has_singleton` because of the out-param.
 /-- The singleton presieve.  -/
 inductive singleton : Presieve X
   | mk : singleton f
-#align category_theory.presieve.singleton CategoryTheory.Presieve.singleton
-
+#align category_theory.presieve.singleton CategoryTheory.Presieve.singletonₓ
+
+/- warning: category_theory.presieve.singleton_eq_iff_domain -> CategoryTheory.Presieve.singleton_eq_iff_domain is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X), Iff (CategoryTheory.Presieve.singletonₓ.{u1, u2} C _inst_1 X Y f Y g) (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) f g)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X), Iff (CategoryTheory.Presieve.singleton.{u1, u2} C _inst_1 X Y f Y g) (Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) f g)
+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.singleton_eq_iff_domain CategoryTheory.Presieve.singleton_eq_iff_domainₓ'. -/
 @[simp]
 theorem singleton_eq_iff_domain (f g : Y ⟶ X) : singleton f g ↔ f = g :=
   by
@@ -93,10 +117,17 @@ theorem singleton_eq_iff_domain (f g : Y ⟶ X) : singleton f g ↔ f = g :=
     apply singleton.mk
 #align category_theory.presieve.singleton_eq_iff_domain CategoryTheory.Presieve.singleton_eq_iff_domain
 
+/- warning: category_theory.presieve.singleton_self -> CategoryTheory.Presieve.singleton_self is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X), CategoryTheory.Presieve.singletonₓ.{u1, u2} C _inst_1 X Y f Y f
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X), CategoryTheory.Presieve.singleton.{u1, u2} C _inst_1 X Y f Y f
+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.singleton_self CategoryTheory.Presieve.singleton_selfₓ'. -/
 theorem singleton_self : singleton f f :=
   singleton.mk
 #align category_theory.presieve.singleton_self CategoryTheory.Presieve.singleton_self
 
+#print CategoryTheory.Presieve.pullbackArrows /-
 /-- Pullback a set of arrows with given codomain along a fixed map, by taking the pullback in the
 category.
 This is not the same as the arrow set of `sieve.pullback`, but there is a relation between them
@@ -105,7 +136,14 @@ in `pullback_arrows_comm`.
 inductive pullbackArrows [HasPullbacks C] (R : Presieve X) : Presieve Y
   | mk (Z : C) (h : Z ⟶ X) : R h → pullback_arrows (pullback.snd : pullback h f ⟶ Y)
 #align category_theory.presieve.pullback_arrows CategoryTheory.Presieve.pullbackArrows
+-/
 
+/- warning: category_theory.presieve.pullback_singleton -> CategoryTheory.Presieve.pullback_singleton is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.pullback_singleton CategoryTheory.Presieve.pullback_singletonₓ'. -/
 theorem pullback_singleton [HasPullbacks C] (g : Z ⟶ X) :
     pullbackArrows f (singleton g) = singleton (pullback.snd : pullback g f ⟶ _) :=
   by
@@ -117,11 +155,19 @@ theorem pullback_singleton [HasPullbacks C] (g : Z ⟶ X) :
     exact pullback_arrows.mk Z g singleton.mk
 #align category_theory.presieve.pullback_singleton CategoryTheory.Presieve.pullback_singleton
 
+#print CategoryTheory.Presieve.ofArrows /-
 /-- Construct the presieve given by the family of arrows indexed by `ι`. -/
 inductive ofArrows {ι : Type _} (Y : ι → C) (f : ∀ i, Y i ⟶ X) : Presieve X
   | mk (i : ι) : of_arrows (f i)
 #align category_theory.presieve.of_arrows CategoryTheory.Presieve.ofArrows
+-/
 
+/- warning: category_theory.presieve.of_arrows_punit -> CategoryTheory.Presieve.ofArrows_pUnit is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.of_arrows_punit CategoryTheory.Presieve.ofArrows_pUnitₓ'. -/
 theorem ofArrows_pUnit : (ofArrows _ fun _ : PUnit => f) = singleton f :=
   by
   ext (Y g)
@@ -132,6 +178,12 @@ theorem ofArrows_pUnit : (ofArrows _ fun _ : PUnit => f) = singleton f :=
     exact of_arrows.mk PUnit.unit
 #align category_theory.presieve.of_arrows_punit CategoryTheory.Presieve.ofArrows_pUnit
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.of_arrows_pullback CategoryTheory.Presieve.ofArrows_pullbackₓ'. -/
 theorem ofArrows_pullback [HasPullbacks C] {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X) :
     (ofArrows (fun i => pullback (g i) f) fun i => pullback.snd) =
       pullbackArrows f (ofArrows Z g) :=
@@ -145,6 +197,12 @@ theorem ofArrows_pullback [HasPullbacks C] {ι : Type _} (Z : ι → C) (g : ∀
     apply of_arrows.mk
 #align category_theory.presieve.of_arrows_pullback CategoryTheory.Presieve.ofArrows_pullback
 
+/- warning: category_theory.presieve.of_arrows_bind -> CategoryTheory.Presieve.ofArrows_bind is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.of_arrows_bind CategoryTheory.Presieve.ofArrows_bindₓ'. -/
 theorem ofArrows_bind {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
     (j : ∀ ⦃Y⦄ (f : Y ⟶ X), ofArrows Z g f → Type _) (W : ∀ ⦃Y⦄ (f : Y ⟶ X) (H), j f H → C)
     (k : ∀ ⦃Y⦄ (f : Y ⟶ X) (H i), W f H i ⟶ Y) :
@@ -160,25 +218,45 @@ theorem ofArrows_bind {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
     exact bind_comp _ (of_arrows.mk _) (of_arrows.mk _)
 #align category_theory.presieve.of_arrows_bind CategoryTheory.Presieve.ofArrows_bind
 
+/- warning: category_theory.presieve.functor_pullback -> CategoryTheory.Presieve.functorPullback is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C}, (CategoryTheory.Presieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) -> (CategoryTheory.Presieve.{u1, u3} C _inst_1 X)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C}, (CategoryTheory.Presieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) -> (CategoryTheory.Presieve.{u1, u3} C _inst_1 X)
+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.functor_pullback CategoryTheory.Presieve.functorPullbackₓ'. -/
 /-- Given a presieve on `F(X)`, we can define a presieve on `X` by taking the preimage via `F`. -/
 def functorPullback (R : Presieve (F.obj X)) : Presieve X := fun _ f => R (F.map f)
 #align category_theory.presieve.functor_pullback CategoryTheory.Presieve.functorPullback
 
+/- warning: category_theory.presieve.functor_pullback_mem -> CategoryTheory.Presieve.functorPullback_mem is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} (R : CategoryTheory.Presieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y X), Iff (CategoryTheory.Presieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X R Y f) (R (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y X f))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} (R : CategoryTheory.Presieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y X), Iff (CategoryTheory.Presieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X R Y f) (R (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y X f))
+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.functor_pullback_mem CategoryTheory.Presieve.functorPullback_memₓ'. -/
 @[simp]
 theorem functorPullback_mem (R : Presieve (F.obj X)) {Y} (f : Y ⟶ X) :
     R.functorPullback F f ↔ R (F.map f) :=
   Iff.rfl
 #align category_theory.presieve.functor_pullback_mem CategoryTheory.Presieve.functorPullback_mem
 
+#print CategoryTheory.Presieve.functorPullback_id /-
 @[simp]
 theorem functorPullback_id (R : Presieve X) : R.functorPullback (𝟭 _) = R :=
   rfl
 #align category_theory.presieve.functor_pullback_id CategoryTheory.Presieve.functorPullback_id
+-/
 
 section FunctorPushforward
 
 variable {E : Type u₃} [Category.{v₃} E] (G : D ⥤ E)
 
+/- warning: category_theory.presieve.functor_pushforward -> CategoryTheory.Presieve.functorPushforward is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C}, (CategoryTheory.Presieve.{u1, u3} C _inst_1 X) -> (CategoryTheory.Presieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C}, (CategoryTheory.Presieve.{u1, u3} C _inst_1 X) -> (CategoryTheory.Presieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X))
+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.functor_pushforward CategoryTheory.Presieve.functorPushforwardₓ'. -/
 /-- Given a presieve on `X`, we can define a presieve on `F(X)` (which is actually a sieve)
 by taking the sieve generated by the image via `F`.
 -/
@@ -186,6 +264,12 @@ def functorPushforward (S : Presieve X) : Presieve (F.obj X) := fun Y f =>
   ∃ (Z : C)(g : Z ⟶ X)(h : Y ⟶ F.obj Z), S g ∧ f = h ≫ F.map g
 #align category_theory.presieve.functor_pushforward CategoryTheory.Presieve.functorPushforward
 
+/- warning: category_theory.presieve.functor_pushforward_structure -> CategoryTheory.Presieve.FunctorPushforwardStructure 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.presieve.functor_pushforward_structure CategoryTheory.Presieve.FunctorPushforwardStructureₓ'. -/
 /-- An auxillary definition in order to fix the choice of the preimages between various definitions.
 -/
 @[nolint has_nonempty_instance]
@@ -197,6 +281,12 @@ structure FunctorPushforwardStructure (S : Presieve X) {Y} (f : Y ⟶ F.obj X) w
   fac : f = lift ≫ F.map premap
 #align category_theory.presieve.functor_pushforward_structure CategoryTheory.Presieve.FunctorPushforwardStructure
 
+/- warning: category_theory.presieve.get_functor_pushforward_structure -> CategoryTheory.Presieve.getFunctorPushforwardStructure is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.get_functor_pushforward_structure CategoryTheory.Presieve.getFunctorPushforwardStructureₓ'. -/
 /-- The fixed choice of a preimage. -/
 noncomputable def getFunctorPushforwardStructure {F : C ⥤ D} {S : Presieve X} {Y : D}
     {f : Y ⟶ F.obj X} (h : S.functorPushforward F f) : FunctorPushforwardStructure F S f :=
@@ -205,6 +295,12 @@ noncomputable def getFunctorPushforwardStructure {F : C ⥤ D} {S : Presieve X}
   exact ⟨Z, f', g, h₁, h⟩
 #align category_theory.presieve.get_functor_pushforward_structure CategoryTheory.Presieve.getFunctorPushforwardStructure
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.functor_pushforward_comp CategoryTheory.Presieve.functorPushforward_compₓ'. -/
 theorem functorPushforward_comp (R : Presieve X) :
     R.functorPushforward (F ⋙ G) = (R.functorPushforward F).functorPushforward G :=
   by
@@ -216,6 +312,12 @@ theorem functorPushforward_comp (R : Presieve X) :
     use ⟨X', f₂, g₁ ≫ G.map g₂, h₁, by simp⟩
 #align category_theory.presieve.functor_pushforward_comp CategoryTheory.Presieve.functorPushforward_comp
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.presieve.image_mem_functor_pushforward CategoryTheory.Presieve.image_mem_functorPushforwardₓ'. -/
 theorem image_mem_functorPushforward (R : Presieve X) {f : Y ⟶ X} (h : R f) :
     R.functorPushforward F (F.map f) :=
   ⟨Y, f, 𝟙 _, h, by simp⟩
@@ -225,6 +327,7 @@ end FunctorPushforward
 
 end Presieve
 
+#print CategoryTheory.Sieve /-
 /--
 For an object `X` of a category `C`, a `sieve X` is a set of morphisms to `X` which is closed under
 left-composition.
@@ -233,6 +336,7 @@ structure Sieve {C : Type u₁} [Category.{v₁} C] (X : C) where
   arrows : Presieve X
   downward_closed' : ∀ {Y Z f} (hf : arrows f) (g : Z ⟶ Y), arrows (g ≫ f)
 #align category_theory.sieve CategoryTheory.Sieve
+-/
 
 namespace Sieve
 
@@ -243,26 +347,39 @@ initialize_simps_projections Sieve (arrows → apply)
 
 variable {S R : Sieve X}
 
+/- warning: category_theory.sieve.downward_closed -> CategoryTheory.Sieve.downward_closed is a dubious translation:
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 @[simp]
 theorem downward_closed (S : Sieve X) {f : Y ⟶ X} (hf : S f) (g : Z ⟶ Y) : S (g ≫ f) :=
   S.downward_closed' hf g
 #align category_theory.sieve.downward_closed CategoryTheory.Sieve.downward_closed
 
+#print CategoryTheory.Sieve.arrows_ext /-
 theorem arrows_ext : ∀ {R S : Sieve X}, R.arrows = S.arrows → R = S
   | ⟨Ra, _⟩, ⟨Sa, _⟩, rfl => rfl
 #align category_theory.sieve.arrows_ext CategoryTheory.Sieve.arrows_ext
+-/
 
+#print CategoryTheory.Sieve.ext /-
 @[ext]
 protected theorem ext {R S : Sieve X} (h : ∀ ⦃Y⦄ (f : Y ⟶ X), R f ↔ S f) : R = S :=
   arrows_ext <| funext fun x => funext fun f => propext <| h f
 #align category_theory.sieve.ext CategoryTheory.Sieve.ext
+-/
 
+#print CategoryTheory.Sieve.ext_iff /-
 protected theorem ext_iff {R S : Sieve X} : R = S ↔ ∀ ⦃Y⦄ (f : Y ⟶ X), R f ↔ S f :=
   ⟨fun h Y f => h ▸ Iff.rfl, Sieve.ext⟩
 #align category_theory.sieve.ext_iff CategoryTheory.Sieve.ext_iff
+-/
 
 open Lattice
 
+#print CategoryTheory.Sieve.sup /-
 /-- The supremum of a collection of sieves: the union of them all. -/
 protected def sup (𝒮 : Set (Sieve X)) : Sieve X
     where
@@ -271,21 +388,27 @@ protected def sup (𝒮 : Set (Sieve X)) : Sieve X
     rintro ⟨S, hS, hf⟩ g
     exact ⟨S, hS, S.downward_closed hf _⟩
 #align category_theory.sieve.Sup CategoryTheory.Sieve.sup
+-/
 
+#print CategoryTheory.Sieve.inf /-
 /-- The infimum of a collection of sieves: the intersection of them all. -/
 protected def inf (𝒮 : Set (Sieve X)) : Sieve X
     where
   arrows Y := { f | ∀ S ∈ 𝒮, Sieve.arrows S f }
   downward_closed' Y Z f hf g S H := S.downward_closed (hf S H) g
 #align category_theory.sieve.Inf CategoryTheory.Sieve.inf
+-/
 
+#print CategoryTheory.Sieve.union /-
 /-- The union of two sieves is a sieve. -/
 protected def union (S R : Sieve X) : Sieve X
     where
   arrows Y f := S f ∨ R f
   downward_closed' := by rintro Y Z f (h | h) g <;> simp [h]
 #align category_theory.sieve.union CategoryTheory.Sieve.union
+-/
 
+#print CategoryTheory.Sieve.inter /-
 /-- The intersection of two sieves is a sieve. -/
 protected def inter (S R : Sieve X) : Sieve X
     where
@@ -294,6 +417,7 @@ protected def inter (S R : Sieve X) : Sieve X
     rintro Y Z f ⟨h₁, h₂⟩ g
     simp [h₁, h₂]
 #align category_theory.sieve.inter CategoryTheory.Sieve.inter
+-/
 
 /-- Sieves on an object `X` form a complete lattice.
 We generate this directly rather than using the galois insertion for nicer definitional properties.
@@ -329,38 +453,71 @@ instance : CompleteLattice (Sieve X)
   le_top _ _ _ _ := trivial
   bot_le _ _ _ := False.elim
 
+#print CategoryTheory.Sieve.sieveInhabited /-
 /-- The maximal sieve always exists. -/
 instance sieveInhabited : Inhabited (Sieve X) :=
   ⟨⊤⟩
 #align category_theory.sieve.sieve_inhabited CategoryTheory.Sieve.sieveInhabited
+-/
 
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 @[simp]
 theorem infₛ_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
     infₛ Ss f ↔ ∀ (S : Sieve X) (H : S ∈ Ss), S f :=
   Iff.rfl
 #align category_theory.sieve.Inf_apply CategoryTheory.Sieve.infₛ_apply
 
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 @[simp]
 theorem supₛ_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
     supₛ Ss f ↔ ∃ (S : Sieve X)(H : S ∈ Ss), S f :=
   Iff.rfl
 #align category_theory.sieve.Sup_apply CategoryTheory.Sieve.supₛ_apply
 
+/- warning: category_theory.sieve.inter_apply -> CategoryTheory.Sieve.inter_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.inter_apply CategoryTheory.Sieve.inter_applyₓ'. -/
 @[simp]
 theorem inter_apply {R S : Sieve X} {Y} (f : Y ⟶ X) : (R ⊓ S) f ↔ R f ∧ S f :=
   Iff.rfl
 #align category_theory.sieve.inter_apply CategoryTheory.Sieve.inter_apply
 
+/- warning: category_theory.sieve.union_apply -> CategoryTheory.Sieve.union_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.union_apply CategoryTheory.Sieve.union_applyₓ'. -/
 @[simp]
 theorem union_apply {R S : Sieve X} {Y} (f : Y ⟶ X) : (R ⊔ S) f ↔ R f ∨ S f :=
   Iff.rfl
 #align category_theory.sieve.union_apply CategoryTheory.Sieve.union_apply
 
+/- warning: category_theory.sieve.top_apply -> CategoryTheory.Sieve.top_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.top_apply CategoryTheory.Sieve.top_applyₓ'. -/
 @[simp]
 theorem top_apply (f : Y ⟶ X) : (⊤ : Sieve X) f :=
   trivial
 #align category_theory.sieve.top_apply CategoryTheory.Sieve.top_apply
 
+#print CategoryTheory.Sieve.generate /-
 /-- Generate the smallest sieve containing the given set of arrows. -/
 @[simps]
 def generate (R : Presieve X) : Sieve X
@@ -370,7 +527,9 @@ def generate (R : Presieve X) : Sieve X
     rintro Y Z _ ⟨W, g, f, hf, rfl⟩ h
     exact ⟨_, h ≫ g, _, hf, by simp⟩
 #align category_theory.sieve.generate CategoryTheory.Sieve.generate
+-/
 
+#print CategoryTheory.Sieve.bind /-
 /-- Given a presieve on `X`, and a sieve on each domain of an arrow in the presieve, we can bind to
 produce a sieve on `X`.
 -/
@@ -382,9 +541,16 @@ def bind (S : Presieve X) (R : ∀ ⦃Y⦄ ⦃f : Y ⟶ X⦄, S f → Sieve Y) :
     rintro Y Z f ⟨W, f, h, hh, hf, rfl⟩ g
     exact ⟨_, g ≫ f, _, hh, by simp [hf]⟩
 #align category_theory.sieve.bind CategoryTheory.Sieve.bind
+-/
 
 open Order Lattice
 
+/- warning: category_theory.sieve.sets_iff_generate -> CategoryTheory.Sieve.sets_iff_generate 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.sieve.sets_iff_generate CategoryTheory.Sieve.sets_iff_generateₓ'. -/
 theorem sets_iff_generate (R : Presieve X) (S : Sieve X) : generate R ≤ S ↔ R ≤ S :=
   ⟨fun H Y g hg => H _ ⟨_, 𝟙 _, _, hg, id_comp _⟩, fun ss Y f =>
     by
@@ -392,6 +558,12 @@ theorem sets_iff_generate (R : Presieve X) (S : Sieve X) : generate R ≤ S ↔
     exact S.downward_closed (ss Z hg) f⟩
 #align category_theory.sieve.sets_iff_generate CategoryTheory.Sieve.sets_iff_generate
 
+/- warning: category_theory.sieve.gi_generate -> CategoryTheory.Sieve.giGenerate 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.sieve.gi_generate CategoryTheory.Sieve.giGenerateₓ'. -/
 /-- Show that there is a galois insertion (generate, set_over). -/
 def giGenerate : GaloisInsertion (generate : Presieve X → Sieve X) arrows
     where
@@ -401,20 +573,40 @@ def giGenerate : GaloisInsertion (generate : Presieve X → Sieve X) arrows
   le_l_u S Y f hf := ⟨_, 𝟙 _, _, hf, id_comp _⟩
 #align category_theory.sieve.gi_generate CategoryTheory.Sieve.giGenerate
 
+/- warning: category_theory.sieve.le_generate -> CategoryTheory.Sieve.le_generate 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.sieve.le_generate CategoryTheory.Sieve.le_generateₓ'. -/
 theorem le_generate (R : Presieve X) : R ≤ generate R :=
   giGenerate.gc.le_u_l R
 #align category_theory.sieve.le_generate CategoryTheory.Sieve.le_generate
 
+#print CategoryTheory.Sieve.generate_sieve /-
 @[simp]
 theorem generate_sieve (S : Sieve X) : generate S = S :=
   giGenerate.l_u_eq S
 #align category_theory.sieve.generate_sieve CategoryTheory.Sieve.generate_sieve
+-/
 
+/- warning: category_theory.sieve.id_mem_iff_eq_top -> CategoryTheory.Sieve.id_mem_iff_eq_top 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.sieve.id_mem_iff_eq_top CategoryTheory.Sieve.id_mem_iff_eq_topₓ'. -/
 /-- If the identity arrow is in a sieve, the sieve is maximal. -/
 theorem id_mem_iff_eq_top : S (𝟙 X) ↔ S = ⊤ :=
   ⟨fun h => top_unique fun Y f _ => by simpa using downward_closed _ h f, fun h => h.symm ▸ trivial⟩
 #align category_theory.sieve.id_mem_iff_eq_top CategoryTheory.Sieve.id_mem_iff_eq_top
 
+/- warning: category_theory.sieve.generate_of_contains_is_split_epi -> CategoryTheory.Sieve.generate_of_contains_isSplitEpi is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.generate_of_contains_is_split_epi CategoryTheory.Sieve.generate_of_contains_isSplitEpiₓ'. -/
 /-- If an arrow set contains a split epi, it generates the maximal sieve. -/
 theorem generate_of_contains_isSplitEpi {R : Presieve X} (f : Y ⟶ X) [IsSplitEpi f] (hf : R f) :
     generate R = ⊤ := by
@@ -422,17 +614,30 @@ theorem generate_of_contains_isSplitEpi {R : Presieve X} (f : Y ⟶ X) [IsSplitE
   exact ⟨_, section_ f, f, hf, by simp⟩
 #align category_theory.sieve.generate_of_contains_is_split_epi CategoryTheory.Sieve.generate_of_contains_isSplitEpi
 
+/- warning: category_theory.sieve.generate_of_singleton_is_split_epi -> CategoryTheory.Sieve.generate_of_singleton_isSplitEpi is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.generate_of_singleton_is_split_epi CategoryTheory.Sieve.generate_of_singleton_isSplitEpiₓ'. -/
 @[simp]
 theorem generate_of_singleton_isSplitEpi (f : Y ⟶ X) [IsSplitEpi f] :
     generate (Presieve.singleton f) = ⊤ :=
   generate_of_contains_isSplitEpi f (Presieve.singleton_self _)
 #align category_theory.sieve.generate_of_singleton_is_split_epi CategoryTheory.Sieve.generate_of_singleton_isSplitEpi
 
+/- warning: category_theory.sieve.generate_top -> CategoryTheory.Sieve.generate_top is a dubious translation:
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 @[simp]
 theorem generate_top : generate (⊤ : Presieve X) = ⊤ :=
   generate_of_contains_isSplitEpi (𝟙 _) ⟨⟩
 #align category_theory.sieve.generate_top CategoryTheory.Sieve.generate_top
 
+#print CategoryTheory.Sieve.pullback /-
 /-- Given a morphism `h : Y ⟶ X`, send a sieve S on X to a sieve on Y
     as the inverse image of S with `_ ≫ h`.
     That is, `sieve.pullback S h := (≫ h) '⁻¹ S`. -/
@@ -442,33 +647,63 @@ def pullback (h : Y ⟶ X) (S : Sieve X) : Sieve Y
   arrows Y sl := S (sl ≫ h)
   downward_closed' Z W f g h := by simp [g]
 #align category_theory.sieve.pullback CategoryTheory.Sieve.pullback
+-/
 
+#print CategoryTheory.Sieve.pullback_id /-
 @[simp]
 theorem pullback_id : S.pullback (𝟙 _) = S := by simp [sieve.ext_iff]
 #align category_theory.sieve.pullback_id CategoryTheory.Sieve.pullback_id
+-/
 
+/- warning: category_theory.sieve.pullback_top -> CategoryTheory.Sieve.pullback_top is a dubious translation:
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 @[simp]
 theorem pullback_top {f : Y ⟶ X} : (⊤ : Sieve X).pullback f = ⊤ :=
   top_unique fun _ g => id
 #align category_theory.sieve.pullback_top CategoryTheory.Sieve.pullback_top
 
+#print CategoryTheory.Sieve.pullback_comp /-
 theorem pullback_comp {f : Y ⟶ X} {g : Z ⟶ Y} (S : Sieve X) :
     S.pullback (g ≫ f) = (S.pullback f).pullback g := by simp [sieve.ext_iff]
 #align category_theory.sieve.pullback_comp CategoryTheory.Sieve.pullback_comp
+-/
 
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 @[simp]
 theorem pullback_inter {f : Y ⟶ X} (S R : Sieve X) :
     (S ⊓ R).pullback f = S.pullback f ⊓ R.pullback f := by simp [sieve.ext_iff]
 #align category_theory.sieve.pullback_inter CategoryTheory.Sieve.pullback_inter
 
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 theorem pullback_eq_top_iff_mem (f : Y ⟶ X) : S f ↔ S.pullback f = ⊤ := by
   rw [← id_mem_iff_eq_top, pullback_apply, id_comp]
 #align category_theory.sieve.pullback_eq_top_iff_mem CategoryTheory.Sieve.pullback_eq_top_iff_mem
 
+/- warning: category_theory.sieve.pullback_eq_top_of_mem -> CategoryTheory.Sieve.pullback_eq_top_of_mem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.pullback_eq_top_of_mem CategoryTheory.Sieve.pullback_eq_top_of_memₓ'. -/
 theorem pullback_eq_top_of_mem (S : Sieve X) {f : Y ⟶ X} : S f → S.pullback f = ⊤ :=
   (pullback_eq_top_iff_mem f).1
 #align category_theory.sieve.pullback_eq_top_of_mem CategoryTheory.Sieve.pullback_eq_top_of_mem
 
+#print CategoryTheory.Sieve.pushforward /-
 /-- Push a sieve `R` on `Y` forward along an arrow `f : Y ⟶ X`: `gf : Z ⟶ X` is in the sieve if `gf`
 factors through some `g : Z ⟶ Y` which is in `R`.
 -/
@@ -478,44 +713,91 @@ def pushforward (f : Y ⟶ X) (R : Sieve Y) : Sieve X
   arrows Z gf := ∃ g, g ≫ f = gf ∧ R g
   downward_closed' := fun Z₁ Z₂ g ⟨j, k, z⟩ h => ⟨h ≫ j, by simp [k], by simp [z]⟩
 #align category_theory.sieve.pushforward CategoryTheory.Sieve.pushforward
+-/
 
+#print CategoryTheory.Sieve.pushforward_apply_comp /-
 theorem pushforward_apply_comp {R : Sieve Y} {Z : C} {g : Z ⟶ Y} (hg : R g) (f : Y ⟶ X) :
     R.pushforward f (g ≫ f) :=
   ⟨g, rfl, hg⟩
 #align category_theory.sieve.pushforward_apply_comp CategoryTheory.Sieve.pushforward_apply_comp
+-/
 
+#print CategoryTheory.Sieve.pushforward_comp /-
 theorem pushforward_comp {f : Y ⟶ X} {g : Z ⟶ Y} (R : Sieve Z) :
     R.pushforward (g ≫ f) = (R.pushforward g).pushforward f :=
   Sieve.ext fun W h =>
     ⟨fun ⟨f₁, hq, hf₁⟩ => ⟨f₁ ≫ g, by simpa, f₁, rfl, hf₁⟩, fun ⟨y, hy, z, hR, hz⟩ =>
       ⟨z, by rwa [reassoc_of hR], hz⟩⟩
 #align category_theory.sieve.pushforward_comp CategoryTheory.Sieve.pushforward_comp
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.galois_connection CategoryTheory.Sieve.galoisConnectionₓ'. -/
 theorem galoisConnection (f : Y ⟶ X) : GaloisConnection (Sieve.pushforward f) (Sieve.pullback f) :=
   fun S R => ⟨fun hR Z g hg => hR _ ⟨g, rfl, hg⟩, fun hS Z g ⟨h, hg, hh⟩ => hg ▸ hS h hh⟩
 #align category_theory.sieve.galois_connection CategoryTheory.Sieve.galoisConnection
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.pullback_monotone CategoryTheory.Sieve.pullback_monotoneₓ'. -/
 theorem pullback_monotone (f : Y ⟶ X) : Monotone (Sieve.pullback f) :=
   (galoisConnection f).monotone_u
 #align category_theory.sieve.pullback_monotone CategoryTheory.Sieve.pullback_monotone
 
+/- warning: category_theory.sieve.pushforward_monotone -> CategoryTheory.Sieve.pushforward_monotone is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.pushforward_monotone CategoryTheory.Sieve.pushforward_monotoneₓ'. -/
 theorem pushforward_monotone (f : Y ⟶ X) : Monotone (Sieve.pushforward f) :=
   (galoisConnection f).monotone_l
 #align category_theory.sieve.pushforward_monotone CategoryTheory.Sieve.pushforward_monotone
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.le_pushforward_pullback CategoryTheory.Sieve.le_pushforward_pullbackₓ'. -/
 theorem le_pushforward_pullback (f : Y ⟶ X) (R : Sieve Y) : R ≤ (R.pushforward f).pullback f :=
   (galoisConnection f).le_u_l _
 #align category_theory.sieve.le_pushforward_pullback CategoryTheory.Sieve.le_pushforward_pullback
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.pullback_pushforward_le CategoryTheory.Sieve.pullback_pushforward_leₓ'. -/
 theorem pullback_pushforward_le (f : Y ⟶ X) (R : Sieve X) : (R.pullback f).pushforward f ≤ R :=
   (galoisConnection f).l_u_le _
 #align category_theory.sieve.pullback_pushforward_le CategoryTheory.Sieve.pullback_pushforward_le
 
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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} {f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X} (S : CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (R : CategoryTheory.Sieve.{u1, u2} C _inst_1 Y), Eq.{max (succ u2) (succ u1)} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f (Sup.sup.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (SemilatticeSup.toSup.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (Lattice.toSemilatticeSup.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toLattice.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 Y)))) S R)) (Sup.sup.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (SemilatticeSup.toSup.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Lattice.toSemilatticeSup.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toLattice.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X)))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f S) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f R))
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.pushforward_union CategoryTheory.Sieve.pushforward_unionₓ'. -/
 theorem pushforward_union {f : Y ⟶ X} (S R : Sieve Y) :
     (S ⊔ R).pushforward f = S.pushforward f ⊔ R.pushforward f :=
   (galoisConnection f).l_sup
 #align category_theory.sieve.pushforward_union CategoryTheory.Sieve.pushforward_union
 
+/- warning: category_theory.sieve.pushforward_le_bind_of_mem -> CategoryTheory.Sieve.pushforward_le_bind_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (R : forall {{Y : C}} {{f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X}}, (S Y f) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y)) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (h : S Y f), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f (R Y f h)) (CategoryTheory.Sieve.bind.{u1, u2} C _inst_1 X S R)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (R : forall {{Y : C}} {{f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X}}, (S Y f) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y)) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (h : S Y f), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X))))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f (R Y f h)) (CategoryTheory.Sieve.bind.{u1, u2} C _inst_1 X S R)
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.pushforward_le_bind_of_mem CategoryTheory.Sieve.pushforward_le_bind_of_memₓ'. -/
 theorem pushforward_le_bind_of_mem (S : Presieve X) (R : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄, S f → Sieve Y)
     (f : Y ⟶ X) (h : S f) : (R h).pushforward f ≤ bind S R :=
   by
@@ -523,6 +805,12 @@ theorem pushforward_le_bind_of_mem (S : Presieve X) (R : ∀ ⦃Y : C⦄ ⦃f :
   exact ⟨_, g, f, h, hg, rfl⟩
 #align category_theory.sieve.pushforward_le_bind_of_mem CategoryTheory.Sieve.pushforward_le_bind_of_mem
 
+/- warning: category_theory.sieve.le_pullback_bind -> CategoryTheory.Sieve.le_pullback_bind is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (R : forall {{Y : C}} {{f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X}}, (S Y f) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y)) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (h : S Y f), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 Y))))) (R Y f h) (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f (CategoryTheory.Sieve.bind.{u1, u2} C _inst_1 X S R))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (S : CategoryTheory.Presieve.{u1, u2} C _inst_1 X) (R : forall {{Y : C}} {{f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X}}, (S Y f) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y)) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) (h : S Y f), LE.le.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (Preorder.toLE.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 Y))))) (R Y f h) (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f (CategoryTheory.Sieve.bind.{u1, u2} C _inst_1 X S R))
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.le_pullback_bind CategoryTheory.Sieve.le_pullback_bindₓ'. -/
 theorem le_pullback_bind (S : Presieve X) (R : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄, S f → Sieve Y) (f : Y ⟶ X)
     (h : S f) : R h ≤ (bind S R).pullback f :=
   by
@@ -530,6 +818,12 @@ theorem le_pullback_bind (S : Presieve X) (R : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄
   apply pushforward_le_bind_of_mem
 #align category_theory.sieve.le_pullback_bind CategoryTheory.Sieve.le_pullback_bind
 
+/- warning: category_theory.sieve.galois_coinsertion_of_mono -> CategoryTheory.Sieve.galoisCoinsertionOfMono is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) [_inst_3 : CategoryTheory.Mono.{u1, u2} C _inst_1 Y X f], GaloisCoinsertion.{max u2 u1, max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 Y)))) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X)))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f) (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) [_inst_3 : CategoryTheory.Mono.{u1, u2} C _inst_1 Y X f], GaloisCoinsertion.{max u2 u1, max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 Y)))) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X)))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f) (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f)
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.galois_coinsertion_of_mono CategoryTheory.Sieve.galoisCoinsertionOfMonoₓ'. -/
 /-- If `f` is a monomorphism, the pushforward-pullback adjunction on sieves is coreflective. -/
 def galoisCoinsertionOfMono (f : Y ⟶ X) [Mono f] :
     GaloisCoinsertion (Sieve.pushforward f) (Sieve.pullback f) :=
@@ -540,6 +834,12 @@ def galoisCoinsertionOfMono (f : Y ⟶ X) [Mono f] :
   rwa [← hf]
 #align category_theory.sieve.galois_coinsertion_of_mono CategoryTheory.Sieve.galoisCoinsertionOfMono
 
+/- warning: category_theory.sieve.galois_insertion_of_is_split_epi -> CategoryTheory.Sieve.galoisInsertionOfIsSplitEpi is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) [_inst_3 : CategoryTheory.IsSplitEpi.{u1, u2} C _inst_1 Y X f], GaloisInsertion.{max u2 u1, max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 Y)))) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X)))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f) (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) [_inst_3 : CategoryTheory.IsSplitEpi.{u1, u2} C _inst_1 Y X f], GaloisInsertion.{max u2 u1, max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 Y) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 Y)))) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X)))) (CategoryTheory.Sieve.pushforward.{u1, u2} C _inst_1 X Y f) (CategoryTheory.Sieve.pullback.{u1, u2} C _inst_1 X Y f)
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.galois_insertion_of_is_split_epi CategoryTheory.Sieve.galoisInsertionOfIsSplitEpiₓ'. -/
 /-- If `f` is a split epi, the pushforward-pullback adjunction on sieves is reflective. -/
 def galoisInsertionOfIsSplitEpi (f : Y ⟶ X) [IsSplitEpi f] :
     GaloisInsertion (Sieve.pushforward f) (Sieve.pullback f) :=
@@ -549,6 +849,7 @@ def galoisInsertionOfIsSplitEpi (f : Y ⟶ X) [IsSplitEpi f] :
   refine' ⟨g ≫ section_ f, by simpa⟩
 #align category_theory.sieve.galois_insertion_of_is_split_epi CategoryTheory.Sieve.galoisInsertionOfIsSplitEpi
 
+#print CategoryTheory.Sieve.pullbackArrows_comm /-
 theorem pullbackArrows_comm [HasPullbacks C] {X Y : C} (f : Y ⟶ X) (R : Presieve X) :
     Sieve.generate (R.pullbackArrows f) = (Sieve.generate R).pullback f :=
   by
@@ -562,11 +863,18 @@ theorem pullbackArrows_comm [HasPullbacks C] {X Y : C} (f : Y ⟶ X) (R : Presie
   · rintro ⟨W, h, k, hk, comm⟩
     exact ⟨_, _, _, presieve.pullback_arrows.mk _ _ hk, pullback.lift_snd _ _ comm⟩
 #align category_theory.sieve.pullback_arrows_comm CategoryTheory.Sieve.pullbackArrows_comm
+-/
 
 section Functor
 
 variable {E : Type u₃} [Category.{v₃} E] (G : D ⥤ E)
 
+/- warning: category_theory.sieve.functor_pullback -> CategoryTheory.Sieve.functorPullback is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C}, (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) -> (CategoryTheory.Sieve.{u1, u3} C _inst_1 X)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C}, (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) -> (CategoryTheory.Sieve.{u1, u3} C _inst_1 X)
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pullback CategoryTheory.Sieve.functorPullbackₓ'. -/
 /--
 If `R` is a sieve, then the `category_theory.presieve.functor_pullback` of `R` is actually a sieve.
 -/
@@ -580,19 +888,33 @@ def functorPullback (R : Sieve (F.obj X)) : Sieve X
     exact R.downward_closed hf (F.map g)
 #align category_theory.sieve.functor_pullback CategoryTheory.Sieve.functorPullback
 
+/- warning: category_theory.sieve.functor_pullback_arrows -> CategoryTheory.Sieve.functorPullback_arrows is a dubious translation:
+lean 3 declaration is
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 @[simp]
 theorem functorPullback_arrows (R : Sieve (F.obj X)) :
     (R.functorPullback F).arrows = R.arrows.functorPullback F :=
   rfl
 #align category_theory.sieve.functor_pullback_arrows CategoryTheory.Sieve.functorPullback_arrows
 
+#print CategoryTheory.Sieve.functorPullback_id /-
 @[simp]
 theorem functorPullback_id (R : Sieve X) : R.functorPullback (𝟭 _) = R :=
   by
   ext
   rfl
 #align category_theory.sieve.functor_pullback_id CategoryTheory.Sieve.functorPullback_id
+-/
 
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 theorem functorPullback_comp (R : Sieve ((F ⋙ G).obj X)) :
     R.functorPullback (F ⋙ G) = (R.functorPullback G).functorPullback F :=
   by
@@ -600,6 +922,12 @@ theorem functorPullback_comp (R : Sieve ((F ⋙ G).obj X)) :
   rfl
 #align category_theory.sieve.functor_pullback_comp CategoryTheory.Sieve.functorPullback_comp
 
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 theorem functorPushforward_extend_eq {R : Presieve X} :
     (generate R).arrows.functorPushforward F = R.functorPushforward F :=
   by
@@ -610,6 +938,12 @@ theorem functorPushforward_extend_eq {R : Presieve X} :
     exact ⟨X', g, f', le_generate R _ h₁, h₂⟩
 #align category_theory.sieve.functor_pushforward_extend_eq CategoryTheory.Sieve.functorPushforward_extend_eq
 
+/- warning: category_theory.sieve.functor_pushforward -> CategoryTheory.Sieve.functorPushforward is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pushforward CategoryTheory.Sieve.functorPushforwardₓ'. -/
 /-- The sieve generated by the image of `R` under `F`. -/
 @[simps]
 def functorPushforward (R : Sieve X) : Sieve (F.obj X)
@@ -620,6 +954,12 @@ def functorPushforward (R : Sieve X) : Sieve (F.obj X)
     exact ⟨X, α, g ≫ β, hα, by simp⟩
 #align category_theory.sieve.functor_pushforward CategoryTheory.Sieve.functorPushforward
 
+/- warning: category_theory.sieve.functor_pushforward_id -> CategoryTheory.Sieve.functorPushforward_id is a dubious translation:
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 @[simp]
 theorem functorPushforward_id (R : Sieve X) : R.functorPushforward (𝟭 _) = R :=
   by
@@ -632,6 +972,12 @@ theorem functorPushforward_id (R : Sieve X) : R.functorPushforward (𝟭 _) = R
     exact ⟨X, f, 𝟙 _, hf, by simp⟩
 #align category_theory.sieve.functor_pushforward_id CategoryTheory.Sieve.functorPushforward_id
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pushforward_comp CategoryTheory.Sieve.functorPushforward_compₓ'. -/
 theorem functorPushforward_comp (R : Sieve X) :
     R.functorPushforward (F ⋙ G) = (R.functorPushforward F).functorPushforward G :=
   by
@@ -639,6 +985,12 @@ theorem functorPushforward_comp (R : Sieve X) :
   simpa [R.arrows.functor_pushforward_comp F G]
 #align category_theory.sieve.functor_pushforward_comp CategoryTheory.Sieve.functorPushforward_comp
 
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+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (X : C), GaloisConnection.{max u3 u1, max u4 u2} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u3} C _inst_1 X)))) (PartialOrder.toPreorder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CompleteSemilatticeInf.toPartialOrder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CompleteLattice.toCompleteSemilatticeInf.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CategoryTheory.Sieve.completeLattice.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X))))) (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (X : C), GaloisConnection.{max u3 u1, max u4 u2} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u3} C _inst_1 X)))) (PartialOrder.toPreorder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CompleteSemilatticeInf.toPartialOrder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CompleteLattice.toCompleteSemilatticeInf.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X))))) (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_galois_connection CategoryTheory.Sieve.functor_galoisConnectionₓ'. -/
 theorem functor_galoisConnection (X : C) :
     GaloisConnection (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
       (Sieve.functorPullback F) :=
@@ -654,46 +1006,100 @@ theorem functor_galoisConnection (X : C) :
     exact hle g hg
 #align category_theory.sieve.functor_galois_connection CategoryTheory.Sieve.functor_galoisConnection
 
+/- warning: category_theory.sieve.functor_pullback_monotone -> CategoryTheory.Sieve.functorPullback_monotone is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (X : C), Monotone.{max u4 u2, max u3 u1} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (PartialOrder.toPreorder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CompleteSemilatticeInf.toPartialOrder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CompleteLattice.toCompleteSemilatticeInf.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CategoryTheory.Sieve.completeLattice.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X))))) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u3} C _inst_1 X)))) (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (X : C), Monotone.{max u4 u2, max u3 u1} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (PartialOrder.toPreorder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CompleteSemilatticeInf.toPartialOrder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CompleteLattice.toCompleteSemilatticeInf.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X))))) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u3} C _inst_1 X)))) (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pullback_monotone CategoryTheory.Sieve.functorPullback_monotoneₓ'. -/
 theorem functorPullback_monotone (X : C) :
     Monotone (Sieve.functorPullback F : Sieve (F.obj X) → Sieve X) :=
   (functor_galoisConnection F X).monotone_u
 #align category_theory.sieve.functor_pullback_monotone CategoryTheory.Sieve.functorPullback_monotone
 
+/- warning: category_theory.sieve.functor_pushforward_monotone -> CategoryTheory.Sieve.functorPushforward_monotone is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (X : C), Monotone.{max u3 u1, max u4 u2} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u3} C _inst_1 X)))) (PartialOrder.toPreorder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CompleteSemilatticeInf.toPartialOrder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CompleteLattice.toCompleteSemilatticeInf.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)) (CategoryTheory.Sieve.completeLattice.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X))))) (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (X : C), Monotone.{max u3 u1, max u4 u2} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u3} C _inst_1 X)))) (PartialOrder.toPreorder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CompleteSemilatticeInf.toPartialOrder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CompleteLattice.toCompleteSemilatticeInf.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X))))) (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pushforward_monotone CategoryTheory.Sieve.functorPushforward_monotoneₓ'. -/
 theorem functorPushforward_monotone (X : C) :
     Monotone (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X)) :=
   (functor_galoisConnection F X).monotone_l
 #align category_theory.sieve.functor_pushforward_monotone CategoryTheory.Sieve.functorPushforward_monotone
 
+/- warning: category_theory.sieve.le_functor_pushforward_pullback -> CategoryTheory.Sieve.le_functorPushforward_pullback is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} (R : CategoryTheory.Sieve.{u1, u3} C _inst_1 X), LE.le.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (Preorder.toLE.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u3} C _inst_1 X))))) R (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X R))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} (R : CategoryTheory.Sieve.{u1, u3} C _inst_1 X), LE.le.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (Preorder.toLE.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u3} C _inst_1 X))))) R (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X R))
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.le_functor_pushforward_pullback CategoryTheory.Sieve.le_functorPushforward_pullbackₓ'. -/
 theorem le_functorPushforward_pullback (R : Sieve X) :
     R ≤ (R.functorPushforward F).functorPullback F :=
   (functor_galoisConnection F X).le_u_l _
 #align category_theory.sieve.le_functor_pushforward_pullback CategoryTheory.Sieve.le_functorPushforward_pullback
 
+/- warning: category_theory.sieve.functor_pullback_pushforward_le -> CategoryTheory.Sieve.functorPullback_pushforward_le 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.sieve.functor_pullback_pushforward_le CategoryTheory.Sieve.functorPullback_pushforward_leₓ'. -/
 theorem functorPullback_pushforward_le (R : Sieve (F.obj X)) :
     (R.functorPullback F).functorPushforward F ≤ R :=
   (functor_galoisConnection F X).l_u_le _
 #align category_theory.sieve.functor_pullback_pushforward_le CategoryTheory.Sieve.functorPullback_pushforward_le
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pushforward_union CategoryTheory.Sieve.functorPushforward_unionₓ'. -/
 theorem functorPushforward_union (S R : Sieve X) :
     (S ⊔ R).functorPushforward F = S.functorPushforward F ⊔ R.functorPushforward F :=
   (functor_galoisConnection F X).l_sup
 #align category_theory.sieve.functor_pushforward_union CategoryTheory.Sieve.functorPushforward_union
 
+/- warning: category_theory.sieve.functor_pullback_union -> CategoryTheory.Sieve.functorPullback_union is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pullback_union CategoryTheory.Sieve.functorPullback_unionₓ'. -/
 theorem functorPullback_union (S R : Sieve (F.obj X)) :
     (S ⊔ R).functorPullback F = S.functorPullback F ⊔ R.functorPullback F :=
   rfl
 #align category_theory.sieve.functor_pullback_union CategoryTheory.Sieve.functorPullback_union
 
+/- warning: category_theory.sieve.functor_pullback_inter -> CategoryTheory.Sieve.functorPullback_inter is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pullback_inter CategoryTheory.Sieve.functorPullback_interₓ'. -/
 theorem functorPullback_inter (S R : Sieve (F.obj X)) :
     (S ⊓ R).functorPullback F = S.functorPullback F ⊓ R.functorPullback F :=
   rfl
 #align category_theory.sieve.functor_pullback_inter CategoryTheory.Sieve.functorPullback_inter
 
+/- warning: category_theory.sieve.functor_pushforward_bot -> CategoryTheory.Sieve.functorPushforward_bot is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pushforward_bot CategoryTheory.Sieve.functorPushforward_botₓ'. -/
 @[simp]
 theorem functorPushforward_bot (F : C ⥤ D) (X : C) : (⊥ : Sieve X).functorPushforward F = ⊥ :=
   (functor_galoisConnection F X).l_bot
 #align category_theory.sieve.functor_pushforward_bot CategoryTheory.Sieve.functorPushforward_bot
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pushforward_top CategoryTheory.Sieve.functorPushforward_topₓ'. -/
 @[simp]
 theorem functorPushforward_top (F : C ⥤ D) (X : C) : (⊤ : Sieve X).functorPushforward F = ⊤ :=
   by
@@ -702,21 +1108,45 @@ theorem functorPushforward_top (F : C ⥤ D) (X : C) : (⊤ : Sieve X).functorPu
   refine' ⟨X, 𝟙 _, 𝟙 _, trivial, by simp⟩
 #align category_theory.sieve.functor_pushforward_top CategoryTheory.Sieve.functorPushforward_top
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pullback_bot CategoryTheory.Sieve.functorPullback_botₓ'. -/
 @[simp]
 theorem functorPullback_bot (F : C ⥤ D) (X : C) : (⊥ : Sieve (F.obj X)).functorPullback F = ⊥ :=
   rfl
 #align category_theory.sieve.functor_pullback_bot CategoryTheory.Sieve.functorPullback_bot
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_pullback_top CategoryTheory.Sieve.functorPullback_topₓ'. -/
 @[simp]
 theorem functorPullback_top (F : C ⥤ D) (X : C) : (⊤ : Sieve (F.obj X)).functorPullback F = ⊤ :=
   rfl
 #align category_theory.sieve.functor_pullback_top CategoryTheory.Sieve.functorPullback_top
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.image_mem_functor_pushforward CategoryTheory.Sieve.image_mem_functorPushforwardₓ'. -/
 theorem image_mem_functorPushforward (R : Sieve X) {V} {f : V ⟶ X} (h : R f) :
     R.functorPushforward F (F.map f) :=
   ⟨V, f, 𝟙 _, h, by simp⟩
 #align category_theory.sieve.image_mem_functor_pushforward CategoryTheory.Sieve.image_mem_functorPushforward
 
+/- warning: category_theory.sieve.ess_surj_full_functor_galois_insertion -> CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion 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.sieve.ess_surj_full_functor_galois_insertion CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertionₓ'. -/
 /-- When `F` is essentially surjective and full, the galois connection is a galois insertion. -/
 def essSurjFullFunctorGaloisInsertion [EssSurj F] [Full F] (X : C) :
     GaloisInsertion (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
@@ -728,6 +1158,12 @@ def essSurjFullFunctorGaloisInsertion [EssSurj F] [Full F] (X : C) :
   simpa using S.downward_closed hf _
 #align category_theory.sieve.ess_surj_full_functor_galois_insertion CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion
 
+/- warning: category_theory.sieve.fully_faithful_functor_galois_coinsertion -> CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertion is a dubious translation:
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) [_inst_4 : CategoryTheory.Full.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [_inst_5 : CategoryTheory.Faithful.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] (X : C), GaloisCoinsertion.{max u3 u1, max u4 u2} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (PartialOrder.toPreorder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteSemilatticeInf.toPartialOrder.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CompleteLattice.toCompleteSemilatticeInf.{max u3 u1} (CategoryTheory.Sieve.{u1, u3} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u3} C _inst_1 X)))) (PartialOrder.toPreorder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CompleteSemilatticeInf.toPartialOrder.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CompleteLattice.toCompleteSemilatticeInf.{max u4 u2} (CategoryTheory.Sieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X)) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X))))) (CategoryTheory.Sieve.functorPushforward.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Sieve.functorPullback.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X)
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.fully_faithful_functor_galois_coinsertion CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertionₓ'. -/
 /-- When `F` is fully faithful, the galois connection is a galois coinsertion. -/
 def fullyFaithfulFunctorGaloisCoinsertion [Full F] [Faithful F] (X : C) :
     GaloisCoinsertion (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
@@ -742,6 +1178,7 @@ def fullyFaithfulFunctorGaloisCoinsertion [Full F] [Faithful F] (X : C) :
 
 end Functor
 
+#print CategoryTheory.Sieve.functor /-
 /-- A sieve induces a presheaf. -/
 @[simps]
 def functor (S : Sieve X) : Cᵒᵖ ⥤ Type v₁
@@ -749,7 +1186,14 @@ def functor (S : Sieve X) : Cᵒᵖ ⥤ Type v₁
   obj Y := { g : Y.unop ⟶ X // S g }
   map Y Z f g := ⟨f.unop ≫ g.1, downward_closed _ g.2 _⟩
 #align category_theory.sieve.functor CategoryTheory.Sieve.functor
+-/
 
+/- warning: category_theory.sieve.nat_trans_of_le -> CategoryTheory.Sieve.natTransOfLe is a dubious translation:
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 /-- If a sieve S is contained in a sieve T, then we have a morphism of presheaves on their induced
 presheaves.
 -/
@@ -757,16 +1201,34 @@ presheaves.
 def natTransOfLe {S T : Sieve X} (h : S ≤ T) : S.Functor ⟶ T.Functor where app Y f := ⟨f.1, h _ f.2⟩
 #align category_theory.sieve.nat_trans_of_le CategoryTheory.Sieve.natTransOfLe
 
+/- warning: category_theory.sieve.functor_inclusion -> CategoryTheory.Sieve.functorInclusion is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_inclusion CategoryTheory.Sieve.functorInclusionₓ'. -/
 /-- The natural inclusion from the functor induced by a sieve to the yoneda embedding. -/
 @[simps]
 def functorInclusion (S : Sieve X) : S.Functor ⟶ yoneda.obj X where app Y f := f.1
 #align category_theory.sieve.functor_inclusion CategoryTheory.Sieve.functorInclusion
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.nat_trans_of_le_comm CategoryTheory.Sieve.natTransOfLe_commₓ'. -/
 theorem natTransOfLe_comm {S T : Sieve X} (h : S ≤ T) :
     natTransOfLe h ≫ functorInclusion _ = functorInclusion _ :=
   rfl
 #align category_theory.sieve.nat_trans_of_le_comm CategoryTheory.Sieve.natTransOfLe_comm
 
+/- warning: category_theory.sieve.functor_inclusion_is_mono -> CategoryTheory.Sieve.functorInclusion_is_mono is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X}, CategoryTheory.Mono.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X S) (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1) X) (CategoryTheory.Sieve.functorInclusion.{u1, u2} C _inst_1 X S)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {S : CategoryTheory.Sieve.{u1, u2} C _inst_1 X}, CategoryTheory.Mono.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X S) (Prefunctor.obj.{succ u1, max (succ u1) (succ u2), u2, max (succ u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1)) X) (CategoryTheory.Sieve.functorInclusion.{u1, u2} C _inst_1 X S)
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_inclusion_is_mono CategoryTheory.Sieve.functorInclusion_is_monoₓ'. -/
 /-- The presheaf induced by a sieve is a subobject of the yoneda embedding. -/
 instance functorInclusion_is_mono : Mono S.functorInclusion :=
   ⟨fun Z f g h => by
@@ -774,6 +1236,12 @@ instance functorInclusion_is_mono : Mono S.functorInclusion :=
     apply congr_fun (nat_trans.congr_app h Y) y⟩
 #align category_theory.sieve.functor_inclusion_is_mono CategoryTheory.Sieve.functorInclusion_is_mono
 
+/- warning: category_theory.sieve.sieve_of_subfunctor -> CategoryTheory.Sieve.sieveOfSubfunctor is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {R : CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}}, (Quiver.Hom.{succ (max u2 u1), max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) R (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1) X)) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {R : CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}}, (Quiver.Hom.{max (succ u2) (succ u1), max (succ u1) u2} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) R (Prefunctor.obj.{succ u1, max (succ u1) (succ u2), u2, max (succ u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1)) X)) -> (CategoryTheory.Sieve.{u1, u2} C _inst_1 X)
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.sieve_of_subfunctor CategoryTheory.Sieve.sieveOfSubfunctorₓ'. -/
 -- TODO: Show that when `f` is mono, this is right inverse to `functor_inclusion` up to isomorphism.
 /-- A natural transformation to a representable functor induces a sieve. This is the left inverse of
 `functor_inclusion`, shown in `sieve_of_functor_inclusion`.
@@ -789,6 +1257,7 @@ def sieveOfSubfunctor {R} (f : R ⟶ yoneda.obj X) : Sieve X
     simp
 #align category_theory.sieve.sieve_of_subfunctor CategoryTheory.Sieve.sieveOfSubfunctor
 
+#print CategoryTheory.Sieve.sieveOfSubfunctor_functorInclusion /-
 theorem sieveOfSubfunctor_functorInclusion : sieveOfSubfunctor S.functorInclusion = S :=
   by
   ext
@@ -799,7 +1268,14 @@ theorem sieveOfSubfunctor_functorInclusion : sieveOfSubfunctor S.functorInclusio
   · intro hf
     exact ⟨⟨_, hf⟩, rfl⟩
 #align category_theory.sieve.sieve_of_subfunctor_functor_inclusion CategoryTheory.Sieve.sieveOfSubfunctor_functorInclusion
+-/
 
+/- warning: category_theory.sieve.functor_inclusion_top_is_iso -> CategoryTheory.Sieve.functorInclusion_top_isIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C}, CategoryTheory.IsIso.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X (Top.top.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toHasTop.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X)))) (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1) X) (CategoryTheory.Sieve.functorInclusion.{u1, u2} C _inst_1 X (Top.top.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toHasTop.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.completeLattice.{u1, u2} C _inst_1 X))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C}, CategoryTheory.IsIso.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Sieve.functor.{u1, u2} C _inst_1 X (Top.top.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toTop.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X)))) (Prefunctor.obj.{succ u1, max (succ u1) (succ u2), u2, max (succ u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1)) X) (CategoryTheory.Sieve.functorInclusion.{u1, u2} C _inst_1 X (Top.top.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CompleteLattice.toTop.{max u2 u1} (CategoryTheory.Sieve.{u1, u2} C _inst_1 X) (CategoryTheory.Sieve.instCompleteLatticeSieve.{u1, u2} C _inst_1 X))))
+Case conversion may be inaccurate. Consider using '#align category_theory.sieve.functor_inclusion_top_is_iso CategoryTheory.Sieve.functorInclusion_top_isIsoₓ'. -/
 instance functorInclusion_top_isIso : IsIso (⊤ : Sieve X).functorInclusion :=
   ⟨⟨{ app := fun Y a => ⟨a, ⟨⟩⟩ }, by tidy⟩⟩
 #align category_theory.sieve.functor_inclusion_top_is_iso CategoryTheory.Sieve.functorInclusion_top_isIso

239d882c

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

239d882c

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

@@ -817,7 +817,7 @@ def fullyFaithfulFunctorGaloisCoinsertion [F.Full] [F.Faithful] (X : C) :
       (Sieve.functorPullback F) := by
   apply (functor_galoisConnection F X).toGaloisCoinsertion
   rintro S Y f ⟨Z, g, h, h₁, h₂⟩
-  rw [← F.image_preimage h, ← F.map_comp] at h₂
+  rw [← F.map_preimage h, ← F.map_comp] at h₂
   rw [F.map_injective h₂]
   exact S.downward_closed h₁ _
 #align category_theory.sieve.fully_faithful_functor_galois_coinsertion CategoryTheory.Sieve.fullyFaithfulFunctorGaloisCoinsertion

239d882c

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

@@ -802,7 +802,7 @@ theorem image_mem_functorPushforward (R : Sieve X) {V} {f : V ⟶ X} (h : R f) :
 #align category_theory.sieve.image_mem_functor_pushforward CategoryTheory.Sieve.image_mem_functorPushforward
 
 /-- When `F` is essentially surjective and full, the galois connection is a galois insertion. -/
-def essSurjFullFunctorGaloisInsertion [EssSurj F] [Full F] (X : C) :
+def essSurjFullFunctorGaloisInsertion [F.EssSurj] [F.Full] (X : C) :
     GaloisInsertion (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
       (Sieve.functorPullback F) := by
   apply (functor_galoisConnection F X).toGaloisInsertion
@@ -812,7 +812,7 @@ def essSurjFullFunctorGaloisInsertion [EssSurj F] [Full F] (X : C) :
 #align category_theory.sieve.ess_surj_full_functor_galois_insertion CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion
 
 /-- When `F` is fully faithful, the galois connection is a galois coinsertion. -/
-def fullyFaithfulFunctorGaloisCoinsertion [Full F] [Faithful F] (X : C) :
+def fullyFaithfulFunctorGaloisCoinsertion [F.Full] [F.Faithful] (X : C) :
     GaloisCoinsertion (Sieve.functorPushforward F : Sieve X → Sieve (F.obj X))
       (Sieve.functorPullback F) := by
   apply (functor_galoisConnection F X).toGaloisCoinsertion

239d882c

feat(CategoryTheory/Sites): add some API for regular sheaves and the equalizer condition (#10420)

This PR gives an equivalent condition to regularTopology.EqualizerCondition (previously called regularCoverage.EqualizerCondition), phrased in more categorical language. We use this new condition to show that EqualizerCondition respects natural isomorphisms.

Co-authored-by: faenuccio <filippo.nuccio@univ-st-etienne.fr> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>

8d5f6cf4

Diff

@@ -50,10 +50,19 @@ namespace Presieve
 noncomputable instance : Inhabited (Presieve X) :=
   ⟨⊤⟩
 
+/-- The full subcategory of the over category `C/X` consisting of arrows which belong to a
+    presieve on `X`. -/
+abbrev category {X : C} (P : Presieve X) :=
+  FullSubcategory fun f : Over X => P f.hom
+
+/-- Construct an object of `P.category`. -/
+abbrev categoryMk {X : C} (P : Presieve X) {Y : C} (f : Y ⟶ X) (hf : P f) : P.category :=
+  ⟨Over.mk f, hf⟩
+
 /-- Given a sieve `S` on `X : C`, its associated diagram `S.diagram` is defined to be
     the natural functor from the full subcategory of the over category `C/X` consisting
     of arrows in `S` to `C`. -/
-abbrev diagram (S : Presieve X) : (FullSubcategory fun f : Over X => S f.hom) ⥤ C :=
+abbrev diagram (S : Presieve X) : S.category ⥤ C :=
   fullSubcategoryInclusion _ ⋙ Over.forget X
 #align category_theory.presieve.diagram CategoryTheory.Presieve.diagram

239d882c

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

@@ -34,7 +34,6 @@ namespace CategoryTheory
 open Category Limits
 
 variable {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₂} D] (F : C ⥤ D)
-
 variable {X Y Z : C} (f : Y ⟶ X)
 
 /-- A set of arrows all with codomain `X`. -/

239d882c

chore: remove unnecessary pp_dots (#11166)

Release 4.7.0-rc1 makes it unnecessary to add pp_dot to structure fields. It used to be that function fields wouldn't pretty print using dot notation when the function was applied unless pp_dot was added.

d8c7b27e

Diff

@@ -266,8 +266,6 @@ structure Sieve {C : Type u₁} [Category.{v₁} C] (X : C) where
   downward_closed : ∀ {Y Z f} (_ : arrows f) (g : Z ⟶ Y), arrows (g ≫ f)
 #align category_theory.sieve CategoryTheory.Sieve
 
-attribute [pp_dot] Sieve.arrows
-
 namespace Sieve
 
 instance : CoeFun (Sieve X) fun _ => Presieve X :=

239d882c

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

@@ -78,7 +78,7 @@ theorem bind_comp {S : Presieve X} {R : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄, S f 
   ⟨_, _, _, h₁, h₂, rfl⟩
 #align category_theory.presieve.bind_comp CategoryTheory.Presieve.bind_comp
 
--- porting note: it seems the definition of `Presieve` must be unfolded in order to define
+-- Porting note: it seems the definition of `Presieve` must be unfolded in order to define
 --   this inductive type, it was thus renamed `singleton'`
 -- Note we can't make this into `HasSingleton` because of the out-param.
 /-- The singleton presieve.  -/
@@ -212,7 +212,7 @@ def functorPushforward (S : Presieve X) : Presieve (F.obj X) := fun Y f =>
   ∃ (Z : C) (g : Z ⟶ X) (h : Y ⟶ F.obj Z), S g ∧ f = h ≫ F.map g
 #align category_theory.presieve.functor_pushforward CategoryTheory.Presieve.functorPushforward
 
---porting note: removed @[nolint hasNonemptyInstance]
+-- Porting note: removed @[nolint hasNonemptyInstance]
 /-- An auxiliary definition in order to fix the choice of the preimages between various definitions.
 -/
 structure FunctorPushforwardStructure (S : Presieve X) {Y} (f : Y ⟶ F.obj X) where

239d882c

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

@@ -628,7 +628,7 @@ def galoisInsertionOfIsSplitEpi (f : Y ⟶ X) [IsSplitEpi f] :
     GaloisInsertion (Sieve.pushforward f) (Sieve.pullback f) := by
   apply (galoisConnection f).toGaloisInsertion
   intro S Z g hg
-  refine' ⟨g ≫ section_ f, by simpa⟩
+  exact ⟨g ≫ section_ f, by simpa⟩
 #align category_theory.sieve.galois_insertion_of_is_split_epi CategoryTheory.Sieve.galoisInsertionOfIsSplitEpi
 
 theorem pullbackArrows_comm [HasPullbacks C] {X Y : C} (f : Y ⟶ X) (R : Presieve X) :
@@ -777,7 +777,7 @@ theorem functorPushforward_bot (F : C ⥤ D) (X : C) : (⊥ : Sieve X).functorPu
 theorem functorPushforward_top (F : C ⥤ D) (X : C) : (⊤ : Sieve X).functorPushforward F = ⊤ := by
   refine' (generate_sieve _).symm.trans _
   apply generate_of_contains_isSplitEpi (𝟙 (F.obj X))
-  refine' ⟨X, 𝟙 _, 𝟙 _, trivial, by simp⟩
+  exact ⟨X, 𝟙 _, 𝟙 _, trivial, by simp⟩
 #align category_theory.sieve.functor_pushforward_top CategoryTheory.Sieve.functorPushforward_top
 
 @[simp]

239d882c

refactor: create folder CategoryTheory/Comma (#10108)

38cd7278

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, E. W. Ayers
 -/
-import Mathlib.Order.CompleteLattice
-import Mathlib.CategoryTheory.Over
-import Mathlib.CategoryTheory.Yoneda
+import Mathlib.CategoryTheory.Comma.Over
 import Mathlib.CategoryTheory.Limits.Shapes.Pullbacks
+import Mathlib.CategoryTheory.Yoneda
 import Mathlib.Data.Set.Lattice
+import Mathlib.Order.CompleteLattice
 
 #align_import category_theory.sites.sieves from "leanprover-community/mathlib"@"239d882c4fb58361ee8b3b39fb2091320edef10a"

239d882c

feat(CategoryTheory/Sites): objects which cover the terminal object (#8632)

In this PR, given a site (C, J), we introduce the notion of a family of objects Y : I → C which "cover the final object". This notion is used in order to formulate results about global sections of sheaves. It shall also be useful in future PRs in order to formulate descent properties of sheaves.

c9e4122d

Diff

@@ -465,6 +465,52 @@ theorem generate_top : generate (⊤ : Presieve X) = ⊤ :=
   generate_of_contains_isSplitEpi (𝟙 _) ⟨⟩
 #align category_theory.sieve.generate_top CategoryTheory.Sieve.generate_top
 
+/-- The sieve of `X` generated by family of morphisms `Y i ⟶ X`. -/
+abbrev ofArrows {I : Type*} {X : C} (Y : I → C) (f : ∀ i, Y i ⟶ X) :
+    Sieve X :=
+  generate (Presieve.ofArrows Y f)
+
+lemma ofArrows_mk {I : Type*} {X : C} (Y : I → C) (f : ∀ i, Y i ⟶ X) (i : I) :
+    ofArrows Y f (f i) :=
+  ⟨_, 𝟙 _, _, ⟨i⟩, by simp⟩
+
+lemma mem_ofArrows_iff {I : Type*} {X : C} (Y : I → C) (f : ∀ i, Y i ⟶ X)
+    {W : C} (g : W ⟶ X) :
+    ofArrows Y f g ↔ ∃ (i : I) (a : W ⟶ Y i), g = a ≫ f i := by
+  constructor
+  · rintro ⟨T, a, b, ⟨i⟩, rfl⟩
+    exact ⟨i, a, rfl⟩
+  · rintro ⟨i, a, rfl⟩
+    apply downward_closed _ (ofArrows_mk Y f i)
+
+
+/-- The sieve of `X : C` that is generated by a family of objects `Y : I → C`:
+it consists of morphisms to `X` which factor through at least one of the `Y i`. -/
+def ofObjects {I : Type*} (Y : I → C) (X : C) : Sieve X where
+  arrows Z _ := ∃ (i : I), Nonempty (Z ⟶ Y i)
+  downward_closed := by
+    rintro Z₁ Z₂ p ⟨i, ⟨f⟩⟩ g
+    exact ⟨i, ⟨g ≫ f⟩⟩
+
+lemma mem_ofObjects_iff {I : Type*} (Y : I → C) {Z X : C} (g : Z ⟶ X) :
+    ofObjects Y X g ↔ ∃ (i : I), Nonempty (Z ⟶ Y i) := by rfl
+
+lemma ofArrows_le_ofObjects
+    {I : Type*} (Y : I → C) {X : C} (f : ∀ i, Y i ⟶ X) :
+    Sieve.ofArrows Y f ≤ Sieve.ofObjects Y X := by
+  intro W g hg
+  rw [mem_ofArrows_iff] at hg
+  obtain ⟨i, a, rfl⟩ := hg
+  exact ⟨i, ⟨a⟩⟩
+
+lemma ofArrows_eq_ofObjects {X : C} (hX : IsTerminal X)
+    {I : Type*} (Y : I → C) (f : ∀ i, Y i ⟶ X) :
+    ofArrows Y f = ofObjects Y X := by
+  refine' le_antisymm (ofArrows_le_ofObjects Y f) (fun W g => _)
+  rw [mem_ofArrows_iff, mem_ofObjects_iff]
+  rintro ⟨i, ⟨h⟩⟩
+  exact ⟨i, h, hX.hom_ext _ _⟩
+
 /-- Given a morphism `h : Y ⟶ X`, send a sieve S on X to a sieve on Y
     as the inverse image of S with `_ ≫ h`.
     That is, `Sieve.pullback S h := (≫ h) '⁻¹ S`. -/
@@ -501,6 +547,14 @@ theorem pullback_eq_top_of_mem (S : Sieve X) {f : Y ⟶ X} : S f → S.pullback
   (pullback_eq_top_iff_mem f).1
 #align category_theory.sieve.pullback_eq_top_of_mem CategoryTheory.Sieve.pullback_eq_top_of_mem
 
+lemma pullback_ofObjects_eq_top
+    {I : Type*} (Y : I → C) {X : C} {i : I} (g : X ⟶ Y i) :
+    ofObjects Y X = ⊤ := by
+  ext Z h
+  simp only [top_apply, iff_true]
+  rw [mem_ofObjects_iff ]
+  exact ⟨i, ⟨h ≫ g⟩⟩
+
 /-- Push a sieve `R` on `Y` forward along an arrow `f : Y ⟶ X`: `gf : Z ⟶ X` is in the sieve if `gf`
 factors through some `g : Z ⟶ Y` which is in `R`.
 -/

239d882c

feat: more explicit sheaf condition for presieves of arrows (#7855)

We give more explicit analogues for compatible families of elements for a Presieve.ofArrows and prove that if such families have unique amalgamation then the sheaf condition is satisfied.

depends on: #7854

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

0830b6a3

Diff

@@ -168,6 +168,12 @@ theorem ofArrows_bind {ι : Type*} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
     exact bind_comp _ (ofArrows.mk _) (ofArrows.mk _)
 #align category_theory.presieve.of_arrows_bind CategoryTheory.Presieve.ofArrows_bind
 
+theorem ofArrows_surj {ι : Type*} {Y : ι → C} (f : ∀ i, Y i ⟶ X) {Z : C} (g : Z ⟶ X)
+    (hg : ofArrows Y f g) : ∃ (i : ι) (h : Y i = Z),
+    g = eqToHom h.symm ≫ f i := by
+  cases' hg with i
+  exact ⟨i, rfl, by simp only [eqToHom_refl, id_comp]⟩
+
 /-- Given a presieve on `F(X)`, we can define a presieve on `X` by taking the preimage via `F`. -/
 def functorPullback (R : Presieve (F.obj X)) : Presieve X := fun _ f => R (F.map f)
 #align category_theory.presieve.functor_pullback CategoryTheory.Presieve.functorPullback
@@ -191,6 +197,10 @@ class hasPullbacks (R : Presieve X) : Prop where
 
 instance (R : Presieve X) [HasPullbacks C] : R.hasPullbacks := ⟨fun _ _ ↦ inferInstance⟩
 
+instance {α : Type v₂} {X : α → C} {B : C} (π : (a : α) → X a ⟶ B)
+    [(Presieve.ofArrows X π).hasPullbacks] (a b : α) : HasPullback (π a) (π b) :=
+  Presieve.hasPullbacks.has_pullbacks (Presieve.ofArrows.mk _) (Presieve.ofArrows.mk _)
+
 section FunctorPushforward
 
 variable {E : Type u₃} [Category.{v₃} E] (G : D ⥤ E)

239d882c

feat: generalize sheaf condition to only the relevant pullbacks existing (#6750)

We define a predicate Presieve.hasPullbacks which says that the pullback of every pair of arrows in the presieve exists. This allows to generalize Equalizer.Presieve.sheaf_condition to categories that don't necessarily have all pullbacks (such as Stonean).

Co-authored-by: Riccardo Brasca @riccardobrasca [riccardo.brasca@gmail.com](mailto:riccardo.brasca@gmail.com) Co-authored-by: Filippo A E Nuccio @faenuccio [filippo.nuccio@univ-st-etienne.fr](mailto:filippo.nuccio@univ-st-etienne.fr)

7c2f3841

Diff

@@ -183,6 +183,14 @@ theorem functorPullback_id (R : Presieve X) : R.functorPullback (𝟭 _) = R :=
   rfl
 #align category_theory.presieve.functor_pullback_id CategoryTheory.Presieve.functorPullback_id
 
+/-- Given a presieve `R` on `X`, the predicate `R.hasPullbacks` means that for all arrows `f` and
+    `g` in `R`, the pullback of `f` and `g` exists. -/
+class hasPullbacks (R : Presieve X) : Prop where
+  /-- For all arrows `f` and `g` in `R`, the pullback of `f` and `g` exists. -/
+  has_pullbacks : ∀ {Y Z} {f : Y ⟶ X} (_ : R f) {g : Z ⟶ X} (_ : R g), HasPullback f g
+
+instance (R : Presieve X) [HasPullbacks C] : R.hasPullbacks := ⟨fun _ _ ↦ inferInstance⟩
+
 section FunctorPushforward
 
 variable {E : Type u₃} [Category.{v₃} E] (G : D ⥤ E)

239d882c

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -126,7 +126,7 @@ theorem pullback_singleton [HasPullbacks C] (g : Z ⟶ X) :
 #align category_theory.presieve.pullback_singleton CategoryTheory.Presieve.pullback_singleton
 
 /-- Construct the presieve given by the family of arrows indexed by `ι`. -/
-inductive ofArrows {ι : Type _} (Y : ι → C) (f : ∀ i, Y i ⟶ X) : Presieve X
+inductive ofArrows {ι : Type*} (Y : ι → C) (f : ∀ i, Y i ⟶ X) : Presieve X
   | mk (i : ι) : ofArrows _ _ (f i)
 #align category_theory.presieve.of_arrows CategoryTheory.Presieve.ofArrows
 
@@ -140,7 +140,7 @@ theorem ofArrows_pUnit : (ofArrows _ fun _ : PUnit => f) = singleton f := by
     exact ofArrows.mk PUnit.unit
 #align category_theory.presieve.of_arrows_punit CategoryTheory.Presieve.ofArrows_pUnit
 
-theorem ofArrows_pullback [HasPullbacks C] {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X) :
+theorem ofArrows_pullback [HasPullbacks C] {ι : Type*} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X) :
     (ofArrows (fun i => pullback (g i) f) fun i => pullback.snd) =
       pullbackArrows f (ofArrows Z g) := by
   funext T
@@ -153,8 +153,8 @@ theorem ofArrows_pullback [HasPullbacks C] {ι : Type _} (Z : ι → C) (g : ∀
     apply ofArrows.mk
 #align category_theory.presieve.of_arrows_pullback CategoryTheory.Presieve.ofArrows_pullback
 
-theorem ofArrows_bind {ι : Type _} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
-    (j : ∀ ⦃Y⦄ (f : Y ⟶ X), ofArrows Z g f → Type _) (W : ∀ ⦃Y⦄ (f : Y ⟶ X) (H), j f H → C)
+theorem ofArrows_bind {ι : Type*} (Z : ι → C) (g : ∀ i : ι, Z i ⟶ X)
+    (j : ∀ ⦃Y⦄ (f : Y ⟶ X), ofArrows Z g f → Type*) (W : ∀ ⦃Y⦄ (f : Y ⟶ X) (H), j f H → C)
     (k : ∀ ⦃Y⦄ (f : Y ⟶ X) (H i), W f H i ⟶ Y) :
     ((ofArrows Z g).bind fun Y f H => ofArrows (W f H) (k f H)) =
       ofArrows (fun i : Σi, j _ (ofArrows.mk i) => W (g i.1) _ i.2) fun ij =>

239d882c

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 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, E. W. Ayers
-
-! This file was ported from Lean 3 source module category_theory.sites.sieves
-! leanprover-community/mathlib commit 239d882c4fb58361ee8b3b39fb2091320edef10a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Order.CompleteLattice
 import Mathlib.CategoryTheory.Over
@@ -14,6 +9,8 @@ import Mathlib.CategoryTheory.Yoneda
 import Mathlib.CategoryTheory.Limits.Shapes.Pullbacks
 import Mathlib.Data.Set.Lattice
 
+#align_import category_theory.sites.sieves from "leanprover-community/mathlib"@"239d882c4fb58361ee8b3b39fb2091320edef10a"
+
 /-!
 # Theory of sieves

239d882c

feat: pp_dot attribute to replace pp_extended_field_notation command (#5632)

760b24bf

Diff

@@ -251,7 +251,7 @@ structure Sieve {C : Type u₁} [Category.{v₁} C] (X : C) where
   downward_closed : ∀ {Y Z f} (_ : arrows f) (g : Z ⟶ Y), arrows (g ≫ f)
 #align category_theory.sieve CategoryTheory.Sieve
 
-pp_extended_field_notation Sieve.arrows
+attribute [pp_dot] Sieve.arrows
 
 namespace Sieve

239d882c

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -339,8 +339,8 @@ instance : CompleteLattice (Sieve X)
   le_sup_right _ _ _ _ := Or.inr
   sup_le _ _ _ h₁ h₂ _ f := by--ℰ S hS Y f := by
     rintro (hf | hf)
-    . exact h₁ _ hf
-    . exact h₂ _ hf
+    · exact h₁ _ hf
+    · exact h₂ _ hf
   inf_le_left _ _ _ _ := And.left
   inf_le_right _ _ _ _ := And.right
   le_inf _ _ _ p q _ _ z := ⟨p _ z, q _ z⟩

239d882c

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

@@ -564,8 +564,7 @@ def galoisInsertionOfIsSplitEpi (f : Y ⟶ X) [IsSplitEpi f] :
 
 theorem pullbackArrows_comm [HasPullbacks C] {X Y : C} (f : Y ⟶ X) (R : Presieve X) :
     Sieve.generate (R.pullbackArrows f) = (Sieve.generate R).pullback f := by
-  ext W
-  intro g
+  ext W g
   constructor
   · rintro ⟨_, h, k, hk, rfl⟩
     cases' hk with W g hg
@@ -636,8 +635,7 @@ def functorPushforward (R : Sieve X) : Sieve (F.obj X)
 
 @[simp]
 theorem functorPushforward_id (R : Sieve X) : R.functorPushforward (𝟭 _) = R := by
-  ext X
-  intro f
+  ext X f
   constructor
   · intro hf
     obtain ⟨X, g, h, hg, rfl⟩ := hf

239d882c

chore: formatting issues (#4947)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5068808d

Diff

@@ -72,7 +72,7 @@ abbrev cocone (S : Presieve X) : Cocone S.diagram :=
 `{ g ≫ f | (f : Y ⟶ X) ∈ S, (g : Z ⟶ Y) ∈ R f }`.
 -/
 def bind (S : Presieve X) (R : ∀ ⦃Y⦄ ⦃f : Y ⟶ X⦄, S f → Presieve Y) : Presieve X := fun Z h =>
-  ∃ (Y : C)(g : Z ⟶ Y)(f : Y ⟶ X)(H : S f), R H g ∧ g ≫ f = h
+  ∃ (Y : C) (g : Z ⟶ Y) (f : Y ⟶ X) (H : S f), R H g ∧ g ≫ f = h
 #align category_theory.presieve.bind CategoryTheory.Presieve.bind
 
 @[simp]
@@ -194,7 +194,7 @@ variable {E : Type u₃} [Category.{v₃} E] (G : D ⥤ E)
 by taking the sieve generated by the image via `F`.
 -/
 def functorPushforward (S : Presieve X) : Presieve (F.obj X) := fun Y f =>
-  ∃ (Z : C)(g : Z ⟶ X)(h : Y ⟶ F.obj Z), S g ∧ f = h ≫ F.map g
+  ∃ (Z : C) (g : Z ⟶ X) (h : Y ⟶ F.obj Z), S g ∧ f = h ≫ F.map g
 #align category_theory.presieve.functor_pushforward CategoryTheory.Presieve.functorPushforward
 
 --porting note: removed @[nolint hasNonemptyInstance]
@@ -360,7 +360,7 @@ theorem sInf_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
 
 @[simp]
 theorem sSup_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
-    sSup Ss f ↔ ∃ (S : Sieve X)(_ : S ∈ Ss), S f := by
+    sSup Ss f ↔ ∃ (S : Sieve X) (_ : S ∈ Ss), S f := by
   simp [sSup, Sieve.sup, setOf]
 #align category_theory.sieve.Sup_apply CategoryTheory.Sieve.sSup_apply
 
@@ -383,7 +383,7 @@ theorem top_apply (f : Y ⟶ X) : (⊤ : Sieve X) f :=
 @[simps]
 def generate (R : Presieve X) : Sieve X
     where
-  arrows Z f := ∃ (Y : _)(h : Z ⟶ Y)(g : Y ⟶ X), R g ∧ h ≫ g = f
+  arrows Z f := ∃ (Y : _) (h : Z ⟶ Y) (g : Y ⟶ X), R g ∧ h ≫ g = f
   downward_closed := by
     rintro Y Z _ ⟨W, g, f, hf, rfl⟩ h
     exact ⟨_, h ≫ g, _, hf, by simp⟩

239d882c

feat: port CategoryTheory.Sites.Canonical (#3936)

33b0b066

Diff

@@ -251,6 +251,8 @@ structure Sieve {C : Type u₁} [Category.{v₁} C] (X : C) where
   downward_closed : ∀ {Y Z f} (_ : arrows f) (g : Z ⟶ Y), arrows (g ≫ f)
 #align category_theory.sieve CategoryTheory.Sieve
 
+pp_extended_field_notation Sieve.arrows
+
 namespace Sieve
 
 instance : CoeFun (Sieve X) fun _ => Presieve X :=

239d882c

chore: fix typos (#4518)

I ran codespell Mathlib and got tired halfway through the suggestions.

92beef58

Diff

@@ -198,7 +198,7 @@ def functorPushforward (S : Presieve X) : Presieve (F.obj X) := fun Y f =>
 #align category_theory.presieve.functor_pushforward CategoryTheory.Presieve.functorPushforward
 
 --porting note: removed @[nolint hasNonemptyInstance]
-/-- An auxillary definition in order to fix the choice of the preimages between various definitions.
+/-- An auxiliary definition in order to fix the choice of the preimages between various definitions.
 -/
 structure FunctorPushforwardStructure (S : Presieve X) {Y} (f : Y ⟶ F.obj X) where
   /-- an object in the source category -/

239d882c

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

supₛ → sSup
infₛ → sInf
supᵢ → iSup
infᵢ → iInf
bsupₛ → bsSup
binfₛ → bsInf
bsupᵢ → biSup
binfᵢ → biInf
csupₛ → csSup
cinfₛ → csInf
csupᵢ → ciSup
cinfᵢ → ciInf
unionₛ → sUnion
interₛ → sInter
unionᵢ → iUnion
interᵢ → iInter
bunionₛ → bsUnion
binterₛ → bsInter
bunionᵢ → biUnion
binterᵢ → biInter

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

d1eb6264

Diff

@@ -327,12 +327,12 @@ instance : CompleteLattice (Sieve X)
       downward_closed := False.elim }
   sup := Sieve.union
   inf := Sieve.inter
-  supₛ := Sieve.sup
-  infₛ := Sieve.inf
-  le_supₛ 𝒮 S hS Y f hf := ⟨S, hS, hf⟩
-  supₛ_le := fun s a ha Y f ⟨b, hb, hf⟩ => (ha b hb) _ hf
-  infₛ_le _ _ hS _ _ h := h _ hS
-  le_infₛ _ _ hS _ _ hf _ hR := hS _ hR _ hf
+  sSup := Sieve.sup
+  sInf := Sieve.inf
+  le_sSup 𝒮 S hS Y f hf := ⟨S, hS, hf⟩
+  sSup_le := fun s a ha Y f ⟨b, hb, hf⟩ => (ha b hb) _ hf
+  sInf_le _ _ hS _ _ h := h _ hS
+  le_sInf _ _ hS _ _ hf _ hR := hS _ hR _ hf
   le_sup_left _ _ _ _ := Or.inl
   le_sup_right _ _ _ _ := Or.inr
   sup_le _ _ _ h₁ h₂ _ f := by--ℰ S hS Y f := by
@@ -351,16 +351,16 @@ instance sieveInhabited : Inhabited (Sieve X) :=
 #align category_theory.sieve.sieve_inhabited CategoryTheory.Sieve.sieveInhabited
 
 @[simp]
-theorem infₛ_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
-    infₛ Ss f ↔ ∀ (S : Sieve X) (_ : S ∈ Ss), S f :=
+theorem sInf_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
+    sInf Ss f ↔ ∀ (S : Sieve X) (_ : S ∈ Ss), S f :=
   Iff.rfl
-#align category_theory.sieve.Inf_apply CategoryTheory.Sieve.infₛ_apply
+#align category_theory.sieve.Inf_apply CategoryTheory.Sieve.sInf_apply
 
 @[simp]
-theorem supₛ_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
-    supₛ Ss f ↔ ∃ (S : Sieve X)(_ : S ∈ Ss), S f := by
-  simp [supₛ, Sieve.sup, setOf]
-#align category_theory.sieve.Sup_apply CategoryTheory.Sieve.supₛ_apply
+theorem sSup_apply {Ss : Set (Sieve X)} {Y} (f : Y ⟶ X) :
+    sSup Ss f ↔ ∃ (S : Sieve X)(_ : S ∈ Ss), S f := by
+  simp [sSup, Sieve.sup, setOf]
+#align category_theory.sieve.Sup_apply CategoryTheory.Sieve.sSup_apply
 
 @[simp]
 theorem inter_apply {R S : Sieve X} {Y} (f : Y ⟶ X) : (R ⊓ S) f ↔ R f ∧ S f :=

239d882c

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -402,8 +402,7 @@ def bind (S : Presieve X) (R : ∀ ⦃Y⦄ ⦃f : Y ⟶ X⦄, S f → Sieve Y) :
 open Order Lattice
 
 theorem sets_iff_generate (R : Presieve X) (S : Sieve X) : generate R ≤ S ↔ R ≤ S :=
-  ⟨fun H Y g hg => H _ ⟨_, 𝟙 _, _, hg, id_comp _⟩, fun ss Y f =>
-    by
+  ⟨fun H Y g hg => H _ ⟨_, 𝟙 _, _, hg, id_comp _⟩, fun ss Y f => by
     rintro ⟨Z, f, g, hg, rfl⟩
     exact S.downward_closed (ss Z hg) f⟩
 #align category_theory.sieve.sets_iff_generate CategoryTheory.Sieve.sets_iff_generate

239d882c

feat : add ext lemma for Type u (#3593)

This lemma, which was not needed in mathlib3, simplifies several proofs (back to the state they were in in mathlib3).

Note on what's going on here: Lean 3 ext would fall back on "try all ext lemmas" if it failed, and thus it could see through lots of definitional equalities. Lean 4 ext doesn't do this (because it's inefficient) and so we need to add more ext lemmas in order to recover Lean 3 functionality.

68f5770d

Diff

@@ -778,8 +778,7 @@ theorem natTransOfLe_comm {S T : Sieve X} (h : S ≤ T) :
 /-- The presheaf induced by a sieve is a subobject of the yoneda embedding. -/
 instance functorInclusion_is_mono : Mono S.functorInclusion :=
   ⟨fun f g h => by
-    ext Y
-    funext y
+    ext Y y
     simpa [Subtype.ext_iff_val] using congr_fun (NatTrans.congr_app h Y) y⟩
 #align category_theory.sieve.functor_inclusion_is_mono CategoryTheory.Sieve.functorInclusion_is_mono

239d882c

feat: port CategoryTheory.Sites.Sieves (#2691)

26763c5c

`category_theory.sites.sieves` ⟷ `Mathlib.CategoryTheory.Sites.Sieves`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 122

category_theory.sites.sieves ⟷ Mathlib.CategoryTheory.Sites.Sieves

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 122

`category_theory.sites.sieves` ⟷ `Mathlib.CategoryTheory.Sites.Sieves`