category_theory.subobject.mono_over | 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

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

ce38d86c

bump to nightly-2024-04-29-08

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

6607d135

Diff

@@ -335,13 +335,13 @@ theorem map_obj_arrow (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g).
 #align category_theory.mono_over.map_obj_arrow CategoryTheory.MonoOver.map_obj_arrow
 -/
 
-#print CategoryTheory.MonoOver.fullMap /-
-instance fullMap (f : X ⟶ Y) [Mono f] : CategoryTheory.Functor.Full (map f)
+#print CategoryTheory.MonoOver.full_map /-
+instance full_map (f : X ⟶ Y) [Mono f] : CategoryTheory.Functor.Full (map f)
     where preimage g h e := by
     refine' hom_mk e.left _
     rw [← cancel_mono f, assoc]
     apply w e
-#align category_theory.mono_over.full_map CategoryTheory.MonoOver.fullMap
+#align category_theory.mono_over.full_map CategoryTheory.MonoOver.full_map
 -/
 
 #print CategoryTheory.MonoOver.faithful_map /-

ce38d86c

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -117,10 +117,10 @@ theorem forget_obj_hom {f} : ((forget X).obj f).Hom = f.arrow :=
 #align category_theory.mono_over.forget_obj_hom CategoryTheory.MonoOver.forget_obj_hom
 -/
 
-instance : Full (forget X) :=
+instance : CategoryTheory.Functor.Full (forget X) :=
   FullSubcategory.full _
 
-instance : Faithful (forget X) :=
+instance : CategoryTheory.Functor.Faithful (forget X) :=
   FullSubcategory.faithful _
 
 #print CategoryTheory.MonoOver.mono /-
@@ -190,7 +190,8 @@ def lift {Y : D} (F : Over Y ⥤ Over X)
 /-- Isomorphic functors `over Y ⥤ over X` lift to isomorphic functors `mono_over Y ⥤ mono_over X`.
 -/
 def liftIso {Y : D} {F₁ F₂ : Over Y ⥤ Over X} (h₁ h₂) (i : F₁ ≅ F₂) : lift F₁ h₁ ≅ lift F₂ h₂ :=
-  fullyFaithfulCancelRight (MonoOver.forget X) (isoWhiskerLeft (MonoOver.forget Y) i)
+  CategoryTheory.Functor.fullyFaithfulCancelRight (MonoOver.forget X)
+    (isoWhiskerLeft (MonoOver.forget Y) i)
 #align category_theory.mono_over.lift_iso CategoryTheory.MonoOver.liftIso
 -/
 
@@ -198,14 +199,14 @@ def liftIso {Y : D} {F₁ F₂ : Over Y ⥤ Over X} (h₁ h₂) (i : F₁ ≅ F
 /-- `mono_over.lift` commutes with composition of functors. -/
 def liftComp {X Z : C} {Y : D} (F : Over X ⥤ Over Y) (G : Over Y ⥤ Over Z) (h₁ h₂) :
     lift F h₁ ⋙ lift G h₂ ≅ lift (F ⋙ G) fun f => h₂ ⟨_, h₁ f⟩ :=
-  fullyFaithfulCancelRight (MonoOver.forget _) (Iso.refl _)
+  CategoryTheory.Functor.fullyFaithfulCancelRight (MonoOver.forget _) (Iso.refl _)
 #align category_theory.mono_over.lift_comp CategoryTheory.MonoOver.liftComp
 -/
 
 #print CategoryTheory.MonoOver.liftId /-
 /-- `mono_over.lift` preserves the identity functor. -/
 def liftId : (lift (𝟭 (Over X)) fun f => f.2) ≅ 𝟭 _ :=
-  fullyFaithfulCancelRight (MonoOver.forget _) (Iso.refl _)
+  CategoryTheory.Functor.fullyFaithfulCancelRight (MonoOver.forget _) (Iso.refl _)
 #align category_theory.mono_over.lift_id CategoryTheory.MonoOver.liftId
 -/
 
@@ -335,7 +336,7 @@ theorem map_obj_arrow (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g).
 -/
 
 #print CategoryTheory.MonoOver.fullMap /-
-instance fullMap (f : X ⟶ Y) [Mono f] : Full (map f)
+instance fullMap (f : X ⟶ Y) [Mono f] : CategoryTheory.Functor.Full (map f)
     where preimage g h e := by
     refine' hom_mk e.left _
     rw [← cancel_mono f, assoc]
@@ -344,7 +345,7 @@ instance fullMap (f : X ⟶ Y) [Mono f] : Full (map f)
 -/
 
 #print CategoryTheory.MonoOver.faithful_map /-
-instance faithful_map (f : X ⟶ Y) [Mono f] : Faithful (map f) where
+instance faithful_map (f : X ⟶ Y) [Mono f] : CategoryTheory.Functor.Faithful (map f) where
 #align category_theory.mono_over.faithful_map CategoryTheory.MonoOver.faithful_map
 -/
 
@@ -514,7 +515,7 @@ def exists (f : X ⟶ Y) : MonoOver X ⥤ MonoOver Y :=
 -/
 
 #print CategoryTheory.MonoOver.faithful_exists /-
-instance faithful_exists (f : X ⟶ Y) : Faithful (exists f) where
+instance faithful_exists (f : X ⟶ Y) : CategoryTheory.Functor.Faithful (exists f) where
 #align category_theory.mono_over.faithful_exists CategoryTheory.MonoOver.faithful_exists
 -/

ce38d86c

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Scott Morrison
 -/
-import Mathbin.CategoryTheory.Limits.Over
-import Mathbin.CategoryTheory.Limits.Shapes.Images
-import Mathbin.CategoryTheory.Adjunction.Reflective
+import CategoryTheory.Limits.Over
+import CategoryTheory.Limits.Shapes.Images
+import CategoryTheory.Adjunction.Reflective
 
 #align_import category_theory.subobject.mono_over from "leanprover-community/mathlib"@"ce38d86c0b2d427ce208c3cee3159cb421d2b3c4"

ce38d86c

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.subobject.mono_over
-! leanprover-community/mathlib commit ce38d86c0b2d427ce208c3cee3159cb421d2b3c4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Limits.Over
 import Mathbin.CategoryTheory.Limits.Shapes.Images
 import Mathbin.CategoryTheory.Adjunction.Reflective
 
+#align_import category_theory.subobject.mono_over from "leanprover-community/mathlib"@"ce38d86c0b2d427ce208c3cee3159cb421d2b3c4"
+
 /-!
 # Monomorphisms over a fixed object

ce38d86c

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -76,37 +76,49 @@ def mk' {X A : C} (f : A ⟶ X) [hf : Mono f] : MonoOver X
 #align category_theory.mono_over.mk' CategoryTheory.MonoOver.mk'
 -/
 
+#print CategoryTheory.MonoOver.forget /-
 /-- The inclusion from monomorphisms over X to morphisms over X. -/
 def forget (X : C) : MonoOver X ⥤ Over X :=
   fullSubcategoryInclusion _
 #align category_theory.mono_over.forget CategoryTheory.MonoOver.forget
+-/
 
 instance : Coe (MonoOver X) C where coe Y := Y.obj.left
 
+#print CategoryTheory.MonoOver.forget_obj_left /-
 @[simp]
 theorem forget_obj_left {f} : ((forget X).obj f).left = (f : C) :=
   rfl
 #align category_theory.mono_over.forget_obj_left CategoryTheory.MonoOver.forget_obj_left
+-/
 
+#print CategoryTheory.MonoOver.mk'_coe' /-
 @[simp]
 theorem mk'_coe' {X A : C} (f : A ⟶ X) [hf : Mono f] : (mk' f : C) = A :=
   rfl
 #align category_theory.mono_over.mk'_coe' CategoryTheory.MonoOver.mk'_coe'
+-/
 
+#print CategoryTheory.MonoOver.arrow /-
 /-- Convenience notation for the underlying arrow of a monomorphism over X. -/
 abbrev arrow (f : MonoOver X) : (f : C) ⟶ X :=
   ((forget X).obj f).Hom
 #align category_theory.mono_over.arrow CategoryTheory.MonoOver.arrow
+-/
 
+#print CategoryTheory.MonoOver.mk'_arrow /-
 @[simp]
 theorem mk'_arrow {X A : C} (f : A ⟶ X) [hf : Mono f] : (mk' f).arrow = f :=
   rfl
 #align category_theory.mono_over.mk'_arrow CategoryTheory.MonoOver.mk'_arrow
+-/
 
+#print CategoryTheory.MonoOver.forget_obj_hom /-
 @[simp]
 theorem forget_obj_hom {f} : ((forget X).obj f).Hom = f.arrow :=
   rfl
 #align category_theory.mono_over.forget_obj_hom CategoryTheory.MonoOver.forget_obj_hom
+-/
 
 instance : Full (forget X) :=
   FullSubcategory.full _
@@ -114,9 +126,11 @@ instance : Full (forget X) :=
 instance : Faithful (forget X) :=
   FullSubcategory.faithful _
 
+#print CategoryTheory.MonoOver.mono /-
 instance mono (f : MonoOver X) : Mono f.arrow :=
   f.property
 #align category_theory.mono_over.mono CategoryTheory.MonoOver.mono
+-/
 
 #print CategoryTheory.MonoOver.isThin /-
 /-- The category of monomorphisms over X is a thin category,
@@ -153,13 +167,16 @@ def isoMk {f g : MonoOver X} (h : f.obj.left ≅ g.obj.left) (w : h.Hom ≫ g.ar
 #align category_theory.mono_over.iso_mk CategoryTheory.MonoOver.isoMk
 -/
 
+#print CategoryTheory.MonoOver.mk'ArrowIso /-
 /-- If `f : mono_over X`, then `mk' f.arrow` is of course just `f`, but not definitionally, so we
     package it as an isomorphism. -/
 @[simp]
 def mk'ArrowIso {X : C} (f : MonoOver X) : mk' f.arrow ≅ f :=
   isoMk (Iso.refl _) (by simp)
 #align category_theory.mono_over.mk'_arrow_iso CategoryTheory.MonoOver.mk'ArrowIso
+-/
 
+#print CategoryTheory.MonoOver.lift /-
 /-- Lift a functor between over categories to a functor between `mono_over` categories,
 given suitable evidence that morphisms are taken to monomorphisms.
 -/
@@ -170,18 +187,23 @@ def lift {Y : D} (F : Over Y ⥤ Over X)
   obj f := ⟨_, h f⟩
   map _ _ k := (MonoOver.forget X).preimage ((MonoOver.forget Y ⋙ F).map k)
 #align category_theory.mono_over.lift CategoryTheory.MonoOver.lift
+-/
 
+#print CategoryTheory.MonoOver.liftIso /-
 /-- Isomorphic functors `over Y ⥤ over X` lift to isomorphic functors `mono_over Y ⥤ mono_over X`.
 -/
 def liftIso {Y : D} {F₁ F₂ : Over Y ⥤ Over X} (h₁ h₂) (i : F₁ ≅ F₂) : lift F₁ h₁ ≅ lift F₂ h₂ :=
   fullyFaithfulCancelRight (MonoOver.forget X) (isoWhiskerLeft (MonoOver.forget Y) i)
 #align category_theory.mono_over.lift_iso CategoryTheory.MonoOver.liftIso
+-/
 
+#print CategoryTheory.MonoOver.liftComp /-
 /-- `mono_over.lift` commutes with composition of functors. -/
 def liftComp {X Z : C} {Y : D} (F : Over X ⥤ Over Y) (G : Over Y ⥤ Over Z) (h₁ h₂) :
     lift F h₁ ⋙ lift G h₂ ≅ lift (F ⋙ G) fun f => h₂ ⟨_, h₁ f⟩ :=
   fullyFaithfulCancelRight (MonoOver.forget _) (Iso.refl _)
 #align category_theory.mono_over.lift_comp CategoryTheory.MonoOver.liftComp
+-/
 
 #print CategoryTheory.MonoOver.liftId /-
 /-- `mono_over.lift` preserves the identity functor. -/
@@ -190,20 +212,25 @@ def liftId : (lift (𝟭 (Over X)) fun f => f.2) ≅ 𝟭 _ :=
 #align category_theory.mono_over.lift_id CategoryTheory.MonoOver.liftId
 -/
 
+#print CategoryTheory.MonoOver.lift_comm /-
 @[simp]
 theorem lift_comm (F : Over Y ⥤ Over X)
     (h : ∀ f : MonoOver Y, Mono (F.obj ((MonoOver.forget Y).obj f)).Hom) :
     lift F h ⋙ MonoOver.forget X = MonoOver.forget Y ⋙ F :=
   rfl
 #align category_theory.mono_over.lift_comm CategoryTheory.MonoOver.lift_comm
+-/
 
+#print CategoryTheory.MonoOver.lift_obj_arrow /-
 @[simp]
 theorem lift_obj_arrow {Y : D} (F : Over Y ⥤ Over X)
     (h : ∀ f : MonoOver Y, Mono (F.obj ((MonoOver.forget Y).obj f)).Hom) (f : MonoOver Y) :
     ((lift F h).obj f).arrow = (F.obj ((forget Y).obj f)).Hom :=
   rfl
 #align category_theory.mono_over.lift_obj_arrow CategoryTheory.MonoOver.lift_obj_arrow
+-/
 
+#print CategoryTheory.MonoOver.slice /-
 /-- Monomorphisms over an object `f : over A` in an over category
 are equivalent to monomorphisms over the source of `f`.
 -/
@@ -218,6 +245,7 @@ def slice {A : C} {f : Over A} (h₁ h₂) : MonoOver f ≌ MonoOver f.left
     MonoOver.liftComp _ _ _ _ ≪≫
       MonoOver.liftIso _ _ f.iteratedSliceEquiv.counitIso ≪≫ MonoOver.liftId
 #align category_theory.mono_over.slice CategoryTheory.MonoOver.slice
+-/
 
 section Pullback
 
@@ -250,17 +278,21 @@ def pullbackId : pullback (𝟙 X) ≅ 𝟭 _ :=
 #align category_theory.mono_over.pullback_id CategoryTheory.MonoOver.pullbackId
 -/
 
+#print CategoryTheory.MonoOver.pullback_obj_left /-
 @[simp]
 theorem pullback_obj_left (f : X ⟶ Y) (g : MonoOver Y) :
     ((pullback f).obj g : C) = Limits.pullback g.arrow f :=
   rfl
 #align category_theory.mono_over.pullback_obj_left CategoryTheory.MonoOver.pullback_obj_left
+-/
 
+#print CategoryTheory.MonoOver.pullback_obj_arrow /-
 @[simp]
 theorem pullback_obj_arrow (f : X ⟶ Y) (g : MonoOver Y) :
     ((pullback f).obj g).arrow = pullback.snd :=
   rfl
 #align category_theory.mono_over.pullback_obj_arrow CategoryTheory.MonoOver.pullback_obj_arrow
+-/
 
 end Pullback
 
@@ -291,15 +323,19 @@ def mapId : map (𝟙 X) ≅ 𝟭 _ :=
 #align category_theory.mono_over.map_id CategoryTheory.MonoOver.mapId
 -/
 
+#print CategoryTheory.MonoOver.map_obj_left /-
 @[simp]
 theorem map_obj_left (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g : C) = g.obj.left :=
   rfl
 #align category_theory.mono_over.map_obj_left CategoryTheory.MonoOver.map_obj_left
+-/
 
+#print CategoryTheory.MonoOver.map_obj_arrow /-
 @[simp]
 theorem map_obj_arrow (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g).arrow = g.arrow ≫ f :=
   rfl
 #align category_theory.mono_over.map_obj_arrow CategoryTheory.MonoOver.map_obj_arrow
+-/
 
 #print CategoryTheory.MonoOver.fullMap /-
 instance fullMap (f : X ⟶ Y) [Mono f] : Full (map f)
@@ -315,6 +351,7 @@ instance faithful_map (f : X ⟶ Y) [Mono f] : Faithful (map f) where
 #align category_theory.mono_over.faithful_map CategoryTheory.MonoOver.faithful_map
 -/
 
+#print CategoryTheory.MonoOver.mapIso /-
 /-- Isomorphic objects have equivalent `mono_over` categories.
 -/
 @[simps]
@@ -325,11 +362,13 @@ def mapIso {A B : C} (e : A ≅ B) : MonoOver A ≌ MonoOver B
   unitIso := ((mapComp _ _).symm ≪≫ eqToIso (by simp) ≪≫ mapId).symm
   counitIso := (mapComp _ _).symm ≪≫ eqToIso (by simp) ≪≫ mapId
 #align category_theory.mono_over.map_iso CategoryTheory.MonoOver.mapIso
+-/
 
 section
 
 variable (X)
 
+#print CategoryTheory.MonoOver.congr /-
 /-- An equivalence of categories `e` between `C` and `D` induces an equivalence between
     `mono_over X` and `mono_over (e.functor.obj X)` whenever `X` is an object of `C`. -/
 @[simps]
@@ -342,6 +381,7 @@ def congr (e : C ≌ D) : MonoOver X ≌ MonoOver (e.Functor.obj X)
   unitIso := NatIso.ofComponents (fun Y => isoMk (e.unitIso.app Y) (by tidy)) (by tidy)
   counitIso := NatIso.ofComponents (fun Y => isoMk (e.counitIso.app Y) (by tidy)) (by tidy)
 #align category_theory.mono_over.congr CategoryTheory.MonoOver.congr
+-/
 
 end
 
@@ -380,10 +420,12 @@ def imageMonoOver (f : X ⟶ Y) [HasImage f] : MonoOver Y :=
 #align category_theory.mono_over.image_mono_over CategoryTheory.MonoOver.imageMonoOver
 -/
 
+#print CategoryTheory.MonoOver.imageMonoOver_arrow /-
 @[simp]
 theorem imageMonoOver_arrow (f : X ⟶ Y) [HasImage f] : (imageMonoOver f).arrow = image.ι f :=
   rfl
 #align category_theory.mono_over.image_mono_over_arrow CategoryTheory.MonoOver.imageMonoOver_arrow
+-/
 
 end Image
 
@@ -445,15 +487,19 @@ instance : IsRightAdjoint (forget X) where
   left := image
   adj := imageForgetAdj
 
+#print CategoryTheory.MonoOver.reflective /-
 instance reflective : Reflective (forget X) where
 #align category_theory.mono_over.reflective CategoryTheory.MonoOver.reflective
+-/
 
+#print CategoryTheory.MonoOver.forgetImage /-
 /-- Forgetting that a monomorphism over `X` is a monomorphism, then taking its image,
 is the identity functor.
 -/
 def forgetImage : forget X ⋙ image ≅ 𝟭 (MonoOver X) :=
   asIso (Adjunction.counit imageForgetAdj)
 #align category_theory.mono_over.forget_image CategoryTheory.MonoOver.forgetImage
+-/
 
 end Image
 
@@ -461,16 +507,21 @@ section Exists
 
 variable [HasImages C]
 
+#print CategoryTheory.MonoOver.exists /-
 /-- In the case where `f` is not a monomorphism but `C` has images,
 we can still take the "forward map" under it, which agrees with `mono_over.map f`.
 -/
 def exists (f : X ⟶ Y) : MonoOver X ⥤ MonoOver Y :=
   forget _ ⋙ Over.map f ⋙ image
 #align category_theory.mono_over.exists CategoryTheory.MonoOver.exists
+-/
 
+#print CategoryTheory.MonoOver.faithful_exists /-
 instance faithful_exists (f : X ⟶ Y) : Faithful (exists f) where
 #align category_theory.mono_over.faithful_exists CategoryTheory.MonoOver.faithful_exists
+-/
 
+#print CategoryTheory.MonoOver.existsIsoMap /-
 /-- When `f : X ⟶ Y` is a monomorphism, `exists f` agrees with `map f`.
 -/
 def existsIsoMap (f : X ⟶ Y) [Mono f] : exists f ≅ map f :=
@@ -492,12 +543,15 @@ def existsIsoMap (f : X ⟶ Y) [Mono f] : exists f ≅ map f :=
         image_mono_iso_source_hom_self]
       apply image.lift_fac)
 #align category_theory.mono_over.exists_iso_map CategoryTheory.MonoOver.existsIsoMap
+-/
 
+#print CategoryTheory.MonoOver.existsPullbackAdj /-
 /-- `exists` is adjoint to `pullback` when images exist -/
 def existsPullbackAdj (f : X ⟶ Y) [HasPullbacks C] : exists f ⊣ pullback f :=
   Adjunction.restrictFullyFaithful (forget X) (𝟭 _) ((Over.mapPullbackAdj f).comp imageForgetAdj)
     (Iso.refl _) (Iso.refl _)
 #align category_theory.mono_over.exists_pullback_adj CategoryTheory.MonoOver.existsPullbackAdj
+-/
 
 end Exists

ce38d86c

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -59,7 +59,8 @@ This isn't skeletal, so it's not a partial order.
 Later we define `subobject X` as the quotient of this by isomorphisms.
 -/
 def MonoOver (X : C) :=
-  FullSubcategory fun f : Over X => Mono f.Hom deriving Category
+  FullSubcategory fun f : Over X => Mono f.Hom
+deriving Category
 #align category_theory.mono_over CategoryTheory.MonoOver
 -/

ce38d86c

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -75,12 +75,6 @@ def mk' {X A : C} (f : A ⟶ X) [hf : Mono f] : MonoOver X
 #align category_theory.mono_over.mk' CategoryTheory.MonoOver.mk'
 -/
 
-/- warning: category_theory.mono_over.forget -> CategoryTheory.MonoOver.forget is a dubious translation:
-lean 3 declaration is
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 /-- The inclusion from monomorphisms over X to morphisms over X. -/
 def forget (X : C) : MonoOver X ⥤ Over X :=
   fullSubcategoryInclusion _
@@ -88,50 +82,26 @@ def forget (X : C) : MonoOver X ⥤ Over X :=
 
 instance : Coe (MonoOver X) C where coe Y := Y.obj.left
 
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 @[simp]
 theorem forget_obj_left {f} : ((forget X).obj f).left = (f : C) :=
   rfl
 #align category_theory.mono_over.forget_obj_left CategoryTheory.MonoOver.forget_obj_left
 
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 @[simp]
 theorem mk'_coe' {X A : C} (f : A ⟶ X) [hf : Mono f] : (mk' f : C) = A :=
   rfl
 #align category_theory.mono_over.mk'_coe' CategoryTheory.MonoOver.mk'_coe'
 
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 /-- Convenience notation for the underlying arrow of a monomorphism over X. -/
 abbrev arrow (f : MonoOver X) : (f : C) ⟶ X :=
   ((forget X).obj f).Hom
 #align category_theory.mono_over.arrow CategoryTheory.MonoOver.arrow
 
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 @[simp]
 theorem mk'_arrow {X A : C} (f : A ⟶ X) [hf : Mono f] : (mk' f).arrow = f :=
   rfl
 #align category_theory.mono_over.mk'_arrow CategoryTheory.MonoOver.mk'_arrow
 
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 @[simp]
 theorem forget_obj_hom {f} : ((forget X).obj f).Hom = f.arrow :=
   rfl
@@ -143,12 +113,6 @@ instance : Full (forget X) :=
 instance : Faithful (forget X) :=
   FullSubcategory.faithful _
 
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 instance mono (f : MonoOver X) : Mono f.arrow :=
   f.property
 #align category_theory.mono_over.mono CategoryTheory.MonoOver.mono
@@ -188,12 +152,6 @@ def isoMk {f g : MonoOver X} (h : f.obj.left ≅ g.obj.left) (w : h.Hom ≫ g.ar
 #align category_theory.mono_over.iso_mk CategoryTheory.MonoOver.isoMk
 -/
 
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 /-- If `f : mono_over X`, then `mk' f.arrow` is of course just `f`, but not definitionally, so we
     package it as an isomorphism. -/
 @[simp]
@@ -201,9 +159,6 @@ def mk'ArrowIso {X : C} (f : MonoOver X) : mk' f.arrow ≅ f :=
   isoMk (Iso.refl _) (by simp)
 #align category_theory.mono_over.mk'_arrow_iso CategoryTheory.MonoOver.mk'ArrowIso
 
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 /-- Lift a functor between over categories to a functor between `mono_over` categories,
 given suitable evidence that morphisms are taken to monomorphisms.
 -/
@@ -215,18 +170,12 @@ def lift {Y : D} (F : Over Y ⥤ Over X)
   map _ _ k := (MonoOver.forget X).preimage ((MonoOver.forget Y ⋙ F).map k)
 #align category_theory.mono_over.lift CategoryTheory.MonoOver.lift
 
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 /-- Isomorphic functors `over Y ⥤ over X` lift to isomorphic functors `mono_over Y ⥤ mono_over X`.
 -/
 def liftIso {Y : D} {F₁ F₂ : Over Y ⥤ Over X} (h₁ h₂) (i : F₁ ≅ F₂) : lift F₁ h₁ ≅ lift F₂ h₂ :=
   fullyFaithfulCancelRight (MonoOver.forget X) (isoWhiskerLeft (MonoOver.forget Y) i)
 #align category_theory.mono_over.lift_iso CategoryTheory.MonoOver.liftIso
 
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 /-- `mono_over.lift` commutes with composition of functors. -/
 def liftComp {X Z : C} {Y : D} (F : Over X ⥤ Over Y) (G : Over Y ⥤ Over Z) (h₁ h₂) :
     lift F h₁ ⋙ lift G h₂ ≅ lift (F ⋙ G) fun f => h₂ ⟨_, h₁ f⟩ :=
@@ -240,9 +189,6 @@ def liftId : (lift (𝟭 (Over X)) fun f => f.2) ≅ 𝟭 _ :=
 #align category_theory.mono_over.lift_id CategoryTheory.MonoOver.liftId
 -/
 
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 @[simp]
 theorem lift_comm (F : Over Y ⥤ Over X)
     (h : ∀ f : MonoOver Y, Mono (F.obj ((MonoOver.forget Y).obj f)).Hom) :
@@ -250,9 +196,6 @@ theorem lift_comm (F : Over Y ⥤ Over X)
   rfl
 #align category_theory.mono_over.lift_comm CategoryTheory.MonoOver.lift_comm
 
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 @[simp]
 theorem lift_obj_arrow {Y : D} (F : Over Y ⥤ Over X)
     (h : ∀ f : MonoOver Y, Mono (F.obj ((MonoOver.forget Y).obj f)).Hom) (f : MonoOver Y) :
@@ -260,9 +203,6 @@ theorem lift_obj_arrow {Y : D} (F : Over Y ⥤ Over X)
   rfl
 #align category_theory.mono_over.lift_obj_arrow CategoryTheory.MonoOver.lift_obj_arrow
 
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 /-- Monomorphisms over an object `f : over A` in an over category
 are equivalent to monomorphisms over the source of `f`.
 -/
@@ -309,18 +249,12 @@ def pullbackId : pullback (𝟙 X) ≅ 𝟭 _ :=
 #align category_theory.mono_over.pullback_id CategoryTheory.MonoOver.pullbackId
 -/
 
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 @[simp]
 theorem pullback_obj_left (f : X ⟶ Y) (g : MonoOver Y) :
     ((pullback f).obj g : C) = Limits.pullback g.arrow f :=
   rfl
 #align category_theory.mono_over.pullback_obj_left CategoryTheory.MonoOver.pullback_obj_left
 
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 @[simp]
 theorem pullback_obj_arrow (f : X ⟶ Y) (g : MonoOver Y) :
     ((pullback f).obj g).arrow = pullback.snd :=
@@ -356,20 +290,11 @@ def mapId : map (𝟙 X) ≅ 𝟭 _ :=
 #align category_theory.mono_over.map_id CategoryTheory.MonoOver.mapId
 -/
 
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 @[simp]
 theorem map_obj_left (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g : C) = g.obj.left :=
   rfl
 #align category_theory.mono_over.map_obj_left CategoryTheory.MonoOver.map_obj_left
 
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 @[simp]
 theorem map_obj_arrow (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g).arrow = g.arrow ≫ f :=
   rfl
@@ -389,12 +314,6 @@ instance faithful_map (f : X ⟶ Y) [Mono f] : Faithful (map f) where
 #align category_theory.mono_over.faithful_map CategoryTheory.MonoOver.faithful_map
 -/
 
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 /-- Isomorphic objects have equivalent `mono_over` categories.
 -/
 @[simps]
@@ -410,12 +329,6 @@ section
 
 variable (X)
 
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 /-- An equivalence of categories `e` between `C` and `D` induces an equivalence between
     `mono_over X` and `mono_over (e.functor.obj X)` whenever `X` is an object of `C`. -/
 @[simps]
@@ -466,12 +379,6 @@ def imageMonoOver (f : X ⟶ Y) [HasImage f] : MonoOver Y :=
 #align category_theory.mono_over.image_mono_over CategoryTheory.MonoOver.imageMonoOver
 -/
 
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 @[simp]
 theorem imageMonoOver_arrow (f : X ⟶ Y) [HasImage f] : (imageMonoOver f).arrow = image.ι f :=
   rfl
@@ -537,18 +444,9 @@ instance : IsRightAdjoint (forget X) where
   left := image
   adj := imageForgetAdj
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.reflective CategoryTheory.MonoOver.reflectiveₓ'. -/
 instance reflective : Reflective (forget X) where
 #align category_theory.mono_over.reflective CategoryTheory.MonoOver.reflective
 
-/- warning: category_theory.mono_over.forget_image -> CategoryTheory.MonoOver.forgetImage is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.forget_image CategoryTheory.MonoOver.forgetImageₓ'. -/
 /-- Forgetting that a monomorphism over `X` is a monomorphism, then taking its image,
 is the identity functor.
 -/
@@ -562,12 +460,6 @@ section Exists
 
 variable [HasImages C]
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists CategoryTheory.MonoOver.existsₓ'. -/
 /-- In the case where `f` is not a monomorphism but `C` has images,
 we can still take the "forward map" under it, which agrees with `mono_over.map f`.
 -/
@@ -575,18 +467,9 @@ def exists (f : X ⟶ Y) : MonoOver X ⥤ MonoOver Y :=
   forget _ ⋙ Over.map f ⋙ image
 #align category_theory.mono_over.exists CategoryTheory.MonoOver.exists
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.faithful_exists CategoryTheory.MonoOver.faithful_existsₓ'. -/
 instance faithful_exists (f : X ⟶ Y) : Faithful (exists f) where
 #align category_theory.mono_over.faithful_exists CategoryTheory.MonoOver.faithful_exists
 
-/- warning: category_theory.mono_over.exists_iso_map -> CategoryTheory.MonoOver.existsIsoMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists_iso_map CategoryTheory.MonoOver.existsIsoMapₓ'. -/
 /-- When `f : X ⟶ Y` is a monomorphism, `exists f` agrees with `map f`.
 -/
 def existsIsoMap (f : X ⟶ Y) [Mono f] : exists f ≅ map f :=
@@ -609,9 +492,6 @@ def existsIsoMap (f : X ⟶ Y) [Mono f] : exists f ≅ map f :=
       apply image.lift_fac)
 #align category_theory.mono_over.exists_iso_map CategoryTheory.MonoOver.existsIsoMap
 
-/- warning: category_theory.mono_over.exists_pullback_adj -> CategoryTheory.MonoOver.existsPullbackAdj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists_pullback_adj CategoryTheory.MonoOver.existsPullbackAdjₓ'. -/
 /-- `exists` is adjoint to `pullback` when images exist -/
 def existsPullbackAdj (f : X ⟶ Y) [HasPullbacks C] : exists f ⊣ pullback f :=
   Adjunction.restrictFullyFaithful (forget X) (𝟭 _) ((Over.mapPullbackAdj f).comp imageForgetAdj)

ce38d86c

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -421,14 +421,9 @@ Case conversion may be inaccurate. Consider using '#align category_theory.mono_o
 @[simps]
 def congr (e : C ≌ D) : MonoOver X ≌ MonoOver (e.Functor.obj X)
     where
-  Functor :=
-    lift (Over.post e.Functor) fun f => by
-      dsimp
-      infer_instance
+  Functor := lift (Over.post e.Functor) fun f => by dsimp; infer_instance
   inverse :=
-    (lift (Over.post e.inverse) fun f => by
-        dsimp
-        infer_instance) ⋙
+    (lift (Over.post e.inverse) fun f => by dsimp; infer_instance) ⋙
       (mapIso (e.unitIso.symm.app X)).Functor
   unitIso := NatIso.ofComponents (fun Y => isoMk (e.unitIso.app Y) (by tidy)) (by tidy)
   counitIso := NatIso.ofComponents (fun Y => isoMk (e.counitIso.app Y) (by tidy)) (by tidy)

ce38d86c

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -89,10 +89,7 @@ def forget (X : C) : MonoOver X ⥤ Over X :=
 instance : Coe (MonoOver X) C where coe Y := Y.obj.left
 
 /- warning: category_theory.mono_over.forget_obj_left -> CategoryTheory.MonoOver.forget_obj_left is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.forget_obj_left CategoryTheory.MonoOver.forget_obj_leftₓ'. -/
 @[simp]
 theorem forget_obj_left {f} : ((forget X).obj f).left = (f : C) :=
@@ -133,10 +130,7 @@ theorem mk'_arrow {X A : C} (f : A ⟶ X) [hf : Mono f] : (mk' f).arrow = f :=
 #align category_theory.mono_over.mk'_arrow CategoryTheory.MonoOver.mk'_arrow
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.forget_obj_hom CategoryTheory.MonoOver.forget_obj_homₓ'. -/
 @[simp]
 theorem forget_obj_hom {f} : ((forget X).obj f).Hom = f.arrow :=
@@ -208,10 +202,7 @@ def mk'ArrowIso {X : C} (f : MonoOver X) : mk' f.arrow ≅ f :=
 #align category_theory.mono_over.mk'_arrow_iso CategoryTheory.MonoOver.mk'ArrowIso
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.lift CategoryTheory.MonoOver.liftₓ'. -/
 /-- Lift a functor between over categories to a functor between `mono_over` categories,
 given suitable evidence that morphisms are taken to monomorphisms.
@@ -225,10 +216,7 @@ def lift {Y : D} (F : Over Y ⥤ Over X)
 #align category_theory.mono_over.lift CategoryTheory.MonoOver.lift
 
 /- warning: category_theory.mono_over.lift_iso -> CategoryTheory.MonoOver.liftIso is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.lift_iso CategoryTheory.MonoOver.liftIsoₓ'. -/
 /-- Isomorphic functors `over Y ⥤ over X` lift to isomorphic functors `mono_over Y ⥤ mono_over X`.
 -/
@@ -237,10 +225,7 @@ def liftIso {Y : D} {F₁ F₂ : Over Y ⥤ Over X} (h₁ h₂) (i : F₁ ≅ F
 #align category_theory.mono_over.lift_iso CategoryTheory.MonoOver.liftIso
 
 /- warning: category_theory.mono_over.lift_comp -> CategoryTheory.MonoOver.liftComp is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.lift_comp CategoryTheory.MonoOver.liftCompₓ'. -/
 /-- `mono_over.lift` commutes with composition of functors. -/
 def liftComp {X Z : C} {Y : D} (F : Over X ⥤ Over Y) (G : Over Y ⥤ Over Z) (h₁ h₂) :
@@ -256,10 +241,7 @@ def liftId : (lift (𝟭 (Over X)) fun f => f.2) ≅ 𝟭 _ :=
 -/
 
 /- warning: category_theory.mono_over.lift_comm -> CategoryTheory.MonoOver.lift_comm is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.lift_comm CategoryTheory.MonoOver.lift_commₓ'. -/
 @[simp]
 theorem lift_comm (F : Over Y ⥤ Over X)
@@ -269,10 +251,7 @@ theorem lift_comm (F : Over Y ⥤ Over X)
 #align category_theory.mono_over.lift_comm CategoryTheory.MonoOver.lift_comm
 
 /- warning: category_theory.mono_over.lift_obj_arrow -> CategoryTheory.MonoOver.lift_obj_arrow is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.lift_obj_arrow CategoryTheory.MonoOver.lift_obj_arrowₓ'. -/
 @[simp]
 theorem lift_obj_arrow {Y : D} (F : Over Y ⥤ Over X)
@@ -282,10 +261,7 @@ theorem lift_obj_arrow {Y : D} (F : Over Y ⥤ Over X)
 #align category_theory.mono_over.lift_obj_arrow CategoryTheory.MonoOver.lift_obj_arrow
 
 /- warning: category_theory.mono_over.slice -> CategoryTheory.MonoOver.slice is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.slice CategoryTheory.MonoOver.sliceₓ'. -/
 /-- Monomorphisms over an object `f : over A` in an over category
 are equivalent to monomorphisms over the source of `f`.
@@ -334,10 +310,7 @@ def pullbackId : pullback (𝟙 X) ≅ 𝟭 _ :=
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.pullback_obj_left CategoryTheory.MonoOver.pullback_obj_leftₓ'. -/
 @[simp]
 theorem pullback_obj_left (f : X ⟶ Y) (g : MonoOver Y) :
@@ -346,10 +319,7 @@ theorem pullback_obj_left (f : X ⟶ Y) (g : MonoOver Y) :
 #align category_theory.mono_over.pullback_obj_left CategoryTheory.MonoOver.pullback_obj_left
 
 /- warning: category_theory.mono_over.pullback_obj_arrow -> CategoryTheory.MonoOver.pullback_obj_arrow is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.pullback_obj_arrow CategoryTheory.MonoOver.pullback_obj_arrowₓ'. -/
 @[simp]
 theorem pullback_obj_arrow (f : X ⟶ Y) (g : MonoOver Y) :
@@ -398,10 +368,7 @@ theorem map_obj_left (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g :
 #align category_theory.mono_over.map_obj_left CategoryTheory.MonoOver.map_obj_left
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.map_obj_arrow CategoryTheory.MonoOver.map_obj_arrowₓ'. -/
 @[simp]
 theorem map_obj_arrow (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g).arrow = g.arrow ≫ f :=
@@ -585,10 +552,7 @@ instance reflective : Reflective (forget X) where
 #align category_theory.mono_over.reflective CategoryTheory.MonoOver.reflective
 
 /- warning: category_theory.mono_over.forget_image -> CategoryTheory.MonoOver.forgetImage is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.forget_image CategoryTheory.MonoOver.forgetImageₓ'. -/
 /-- Forgetting that a monomorphism over `X` is a monomorphism, then taking its image,
 is the identity functor.
@@ -626,10 +590,7 @@ instance faithful_exists (f : X ⟶ Y) : Faithful (exists f) where
 #align category_theory.mono_over.faithful_exists CategoryTheory.MonoOver.faithful_exists
 
 /- warning: category_theory.mono_over.exists_iso_map -> CategoryTheory.MonoOver.existsIsoMap is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists_iso_map CategoryTheory.MonoOver.existsIsoMapₓ'. -/
 /-- When `f : X ⟶ Y` is a monomorphism, `exists f` agrees with `map f`.
 -/
@@ -654,10 +615,7 @@ def existsIsoMap (f : X ⟶ Y) [Mono f] : exists f ≅ map f :=
 #align category_theory.mono_over.exists_iso_map CategoryTheory.MonoOver.existsIsoMap
 
 /- warning: category_theory.mono_over.exists_pullback_adj -> CategoryTheory.MonoOver.existsPullbackAdj is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists_pullback_adj CategoryTheory.MonoOver.existsPullbackAdjₓ'. -/
 /-- `exists` is adjoint to `pullback` when images exist -/
 def existsPullbackAdj (f : X ⟶ Y) [HasPullbacks C] : exists f ⊣ pullback f :=

ce38d86c

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -171,7 +171,7 @@ instance isThin {X : C} : Quiver.IsThin (MonoOver X) := fun f g =>
 -/
 
 #print CategoryTheory.MonoOver.w /-
-@[reassoc.1]
+@[reassoc]
 theorem w {f g : MonoOver X} (k : f ⟶ g) : k.left ≫ g.arrow = f.arrow :=
   Over.w _
 #align category_theory.mono_over.w CategoryTheory.MonoOver.w

ce38d86c

bump to nightly-2023-05-09-13

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

6ff25244

Diff

@@ -603,37 +603,37 @@ section Exists
 
 variable [HasImages C]
 
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+/- warning: category_theory.mono_over.exists -> CategoryTheory.MonoOver.exists is a dubious translation:
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   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1], (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) -> (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 Y))
-Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists CategoryTheory.MonoOver.exists_ₓ'. -/
+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists CategoryTheory.MonoOver.existsₓ'. -/
 /-- In the case where `f` is not a monomorphism but `C` has images,
 we can still take the "forward map" under it, which agrees with `mono_over.map f`.
 -/
-def exists_ (f : X ⟶ Y) : MonoOver X ⥤ MonoOver Y :=
+def exists (f : X ⟶ Y) : MonoOver X ⥤ MonoOver Y :=
   forget _ ⋙ Over.map f ⋙ image
-#align category_theory.mono_over.exists CategoryTheory.MonoOver.exists_
+#align category_theory.mono_over.exists CategoryTheory.MonoOver.exists
 
 /- warning: category_theory.mono_over.faithful_exists -> CategoryTheory.MonoOver.faithful_exists 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} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y), CategoryTheory.Faithful.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.InducedCategory.category.{u1, max u2 u1, max u2 u1} (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) => CategoryTheory.Mono.{u1, u2} C _inst_1 (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.Functor.obj.{u1, u1, u1, u2} (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) (CategoryTheory.Comma.right.{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.Over.{u1, u2} C _inst_1 X) (CategoryTheory.Over.category.{u2, u1} C _inst_1 X) (CategoryTheory.FullSubcategoryₓ.obj.{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) => CategoryTheory.Mono.{u1, u2} C _inst_1 (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.Functor.obj.{u1, u1, u1, u2} (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) (CategoryTheory.Comma.right.{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.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.MonoOver.category.{u2, u1} C _inst_1 Y) (CategoryTheory.MonoOver.exists.{u1, u2} C _inst_1 X Y _inst_3 f)
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y), CategoryTheory.Faithful.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.MonoOver.exists_.{u1, u2} C _inst_1 X Y _inst_3 f)
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y), CategoryTheory.Faithful.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.MonoOver.exists.{u1, u2} C _inst_1 X Y _inst_3 f)
 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.faithful_exists CategoryTheory.MonoOver.faithful_existsₓ'. -/
-instance faithful_exists (f : X ⟶ Y) : Faithful (exists_ f) where
+instance faithful_exists (f : X ⟶ Y) : Faithful (exists f) where
 #align category_theory.mono_over.faithful_exists CategoryTheory.MonoOver.faithful_exists
 
 /- warning: category_theory.mono_over.exists_iso_map -> CategoryTheory.MonoOver.existsIsoMap 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} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Mono.{u1, u2} C _inst_1 X Y f], CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.InducedCategory.category.{u1, max u2 u1, max u2 u1} (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) => CategoryTheory.Mono.{u1, u2} C _inst_1 (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 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 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Mono.{u1, u2} C _inst_1 X Y f], CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 Y)) (CategoryTheory.Functor.category.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 Y)) (CategoryTheory.MonoOver.exists_.{u1, u2} C _inst_1 X Y _inst_3 f) (CategoryTheory.MonoOver.map.{u1, u2} C _inst_1 X Y f _inst_4)
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Mono.{u1, u2} C _inst_1 X Y f], CategoryTheory.Iso.{max u2 u1, max u2 u1} (CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 Y)) (CategoryTheory.Functor.category.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 Y)) (CategoryTheory.MonoOver.exists.{u1, u2} C _inst_1 X Y _inst_3 f) (CategoryTheory.MonoOver.map.{u1, u2} C _inst_1 X Y f _inst_4)
 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists_iso_map CategoryTheory.MonoOver.existsIsoMapₓ'. -/
 /-- When `f : X ⟶ Y` is a monomorphism, `exists f` agrees with `map f`.
 -/
-def existsIsoMap (f : X ⟶ Y) [Mono f] : exists_ f ≅ map f :=
+def existsIsoMap (f : X ⟶ Y) [Mono f] : exists f ≅ map f :=
   NatIso.ofComponents
     (by
       intro Z
@@ -655,12 +655,12 @@ def existsIsoMap (f : X ⟶ Y) [Mono f] : exists_ f ≅ map f :=
 
 /- warning: category_theory.mono_over.exists_pullback_adj -> CategoryTheory.MonoOver.existsPullbackAdj is a dubious translation:
 lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Limits.HasPullbacks.{u1, u2} C _inst_1], CategoryTheory.Adjunction.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.InducedCategory.category.{u1, max u2 u1, max u2 u1} (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) => CategoryTheory.Mono.{u1, u2} C _inst_1 (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.Functor.obj.{u1, u1, u1, u2} (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) (CategoryTheory.Comma.right.{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.Over.{u1, u2} C _inst_1 X) (CategoryTheory.Over.category.{u2, u1} C _inst_1 X) (CategoryTheory.FullSubcategoryₓ.obj.{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) => CategoryTheory.Mono.{u1, u2} C _inst_1 (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.Functor.obj.{u1, u1, u1, u2} (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) (CategoryTheory.Comma.right.{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.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.MonoOver.category.{u2, u1} C _inst_1 Y) (CategoryTheory.MonoOver.exists_.{u1, u2} C _inst_1 X Y _inst_3 f) (CategoryTheory.MonoOver.pullback.{u1, u2} C _inst_1 X Y _inst_4 f)
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Limits.HasPullbacks.{u1, u2} C _inst_1], CategoryTheory.Adjunction.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.InducedCategory.category.{u1, max u2 u1, max u2 u1} (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) => CategoryTheory.Mono.{u1, u2} C _inst_1 (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.Functor.obj.{u1, u1, u1, u2} (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) (CategoryTheory.Comma.right.{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.Over.{u1, u2} C _inst_1 X) (CategoryTheory.Over.category.{u2, u1} C _inst_1 X) (CategoryTheory.FullSubcategoryₓ.obj.{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) => CategoryTheory.Mono.{u1, u2} C _inst_1 (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.Functor.obj.{u1, u1, u1, u2} (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) (CategoryTheory.Comma.right.{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.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.MonoOver.category.{u2, u1} C _inst_1 Y) (CategoryTheory.MonoOver.exists.{u1, u2} C _inst_1 X Y _inst_3 f) (CategoryTheory.MonoOver.pullback.{u1, u2} C _inst_1 X Y _inst_4 f)
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Limits.HasPullbacks.{u1, u2} C _inst_1], CategoryTheory.Adjunction.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.MonoOver.exists_.{u1, u2} C _inst_1 X Y _inst_3 f) (CategoryTheory.MonoOver.pullback.{u1, u2} C _inst_1 X Y _inst_4 f)
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Limits.HasPullbacks.{u1, u2} C _inst_1], CategoryTheory.Adjunction.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.MonoOver.exists.{u1, u2} C _inst_1 X Y _inst_3 f) (CategoryTheory.MonoOver.pullback.{u1, u2} C _inst_1 X Y _inst_4 f)
 Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists_pullback_adj CategoryTheory.MonoOver.existsPullbackAdjₓ'. -/
 /-- `exists` is adjoint to `pullback` when images exist -/
-def existsPullbackAdj (f : X ⟶ Y) [HasPullbacks C] : exists_ f ⊣ pullback f :=
+def existsPullbackAdj (f : X ⟶ Y) [HasPullbacks C] : exists f ⊣ pullback f :=
   Adjunction.restrictFullyFaithful (forget X) (𝟭 _) ((Over.mapPullbackAdj f).comp imageForgetAdj)
     (Iso.refl _) (Iso.refl _)
 #align category_theory.mono_over.exists_pullback_adj CategoryTheory.MonoOver.existsPullbackAdj

ce38d86c

bump to nightly-2023-04-20-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af

d6678ca6

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Scott Morrison
 
 ! This file was ported from Lean 3 source module category_theory.subobject.mono_over
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit ce38d86c0b2d427ce208c3cee3159cb421d2b3c4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Adjunction.Reflective
 /-!
 # Monomorphisms over a fixed object
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 As preparation for defining `subobject X`, we set up the theory for
 `mono_over X := {f : over X // mono f.hom}`.

70fd9563

bump to nightly-2023-04-15-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/0e2aab2b0d521f060f62a14d2cf2e2c54e8491d6

bf39278e

Diff

@@ -49,6 +49,7 @@ variable {C : Type u₁} [Category.{v₁} C] {X Y Z : C}
 
 variable {D : Type u₂} [Category.{v₂} D]
 
+#print CategoryTheory.MonoOver /-
 /-- The category of monomorphisms into `X` as a full subcategory of the over category.
 This isn't skeletal, so it's not a partial order.
 
@@ -57,9 +58,11 @@ Later we define `subobject X` as the quotient of this by isomorphisms.
 def MonoOver (X : C) :=
   FullSubcategory fun f : Over X => Mono f.Hom deriving Category
 #align category_theory.mono_over CategoryTheory.MonoOver
+-/
 
 namespace MonoOver
 
+#print CategoryTheory.MonoOver.mk' /-
 /-- Construct a `mono_over X`. -/
 @[simps]
 def mk' {X A : C} (f : A ⟶ X) [hf : Mono f] : MonoOver X
@@ -67,7 +70,14 @@ def mk' {X A : C} (f : A ⟶ X) [hf : Mono f] : MonoOver X
   obj := Over.mk f
   property := hf
 #align category_theory.mono_over.mk' CategoryTheory.MonoOver.mk'
+-/
 
+/- warning: category_theory.mono_over.forget -> CategoryTheory.MonoOver.forget is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : C), CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.InducedCategory.category.{u1, max u2 u1, max u2 u1} (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) => CategoryTheory.Mono.{u1, u2} C _inst_1 (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.Functor.obj.{u1, u1, u1, u2} (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) (CategoryTheory.Comma.right.{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.Over.{u1, u2} C _inst_1 X) (CategoryTheory.Over.category.{u2, u1} C _inst_1 X) (CategoryTheory.FullSubcategoryₓ.obj.{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) => CategoryTheory.Mono.{u1, u2} C _inst_1 (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.Functor.obj.{u1, u1, u1, u2} (CategoryTheory.Discrete.{u1} PUnit.{succ u1}) (CategoryTheory.discreteCategory.{u1} PUnit.{succ u1}) C _inst_1 (CategoryTheory.Functor.fromPUnit.{u1, u2} C _inst_1 X) (CategoryTheory.Comma.right.{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.Over.{u1, u2} C _inst_1 X) (CategoryTheory.Over.category.{u2, u1} C _inst_1 X)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : C), CategoryTheory.Functor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.Over.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryOver.{u1, u2} C _inst_1 X)
+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.forget CategoryTheory.MonoOver.forgetₓ'. -/
 /-- The inclusion from monomorphisms over X to morphisms over X. -/
 def forget (X : C) : MonoOver X ⥤ Over X :=
   fullSubcategoryInclusion _
@@ -75,26 +85,56 @@ def forget (X : C) : MonoOver X ⥤ Over X :=
 
 instance : Coe (MonoOver X) C where coe Y := Y.obj.left
 
+/- warning: category_theory.mono_over.forget_obj_left -> CategoryTheory.MonoOver.forget_obj_left is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.forget_obj_left CategoryTheory.MonoOver.forget_obj_leftₓ'. -/
 @[simp]
 theorem forget_obj_left {f} : ((forget X).obj f).left = (f : C) :=
   rfl
 #align category_theory.mono_over.forget_obj_left CategoryTheory.MonoOver.forget_obj_left
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.mk'_coe' CategoryTheory.MonoOver.mk'_coe'ₓ'. -/
 @[simp]
 theorem mk'_coe' {X A : C} (f : A ⟶ X) [hf : Mono f] : (mk' f : C) = A :=
   rfl
 #align category_theory.mono_over.mk'_coe' CategoryTheory.MonoOver.mk'_coe'
 
+/- warning: category_theory.mono_over.arrow -> CategoryTheory.MonoOver.arrow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.arrow CategoryTheory.MonoOver.arrowₓ'. -/
 /-- Convenience notation for the underlying arrow of a monomorphism over X. -/
 abbrev arrow (f : MonoOver X) : (f : C) ⟶ X :=
   ((forget X).obj f).Hom
 #align category_theory.mono_over.arrow CategoryTheory.MonoOver.arrow
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.mk'_arrow CategoryTheory.MonoOver.mk'_arrowₓ'. -/
 @[simp]
 theorem mk'_arrow {X A : C} (f : A ⟶ X) [hf : Mono f] : (mk' f).arrow = f :=
   rfl
 #align category_theory.mono_over.mk'_arrow CategoryTheory.MonoOver.mk'_arrow
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.forget_obj_hom CategoryTheory.MonoOver.forget_obj_homₓ'. -/
 @[simp]
 theorem forget_obj_hom {f} : ((forget X).obj f).Hom = f.arrow :=
   rfl
@@ -106,10 +146,17 @@ instance : Full (forget X) :=
 instance : Faithful (forget X) :=
   FullSubcategory.faithful _
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.mono CategoryTheory.MonoOver.monoₓ'. -/
 instance mono (f : MonoOver X) : Mono f.arrow :=
   f.property
 #align category_theory.mono_over.mono CategoryTheory.MonoOver.mono
 
+#print CategoryTheory.MonoOver.isThin /-
 /-- The category of monomorphisms over X is a thin category,
 which makes defining its skeleton easy. -/
 instance isThin {X : C} : Quiver.IsThin (MonoOver X) := fun f g =>
@@ -118,17 +165,23 @@ instance isThin {X : C} : Quiver.IsThin (MonoOver X) := fun f g =>
     ext1
     erw [← cancel_mono g.arrow, over.w h₁, over.w h₂]⟩
 #align category_theory.mono_over.is_thin CategoryTheory.MonoOver.isThin
+-/
 
+#print CategoryTheory.MonoOver.w /-
 @[reassoc.1]
 theorem w {f g : MonoOver X} (k : f ⟶ g) : k.left ≫ g.arrow = f.arrow :=
   Over.w _
 #align category_theory.mono_over.w CategoryTheory.MonoOver.w
+-/
 
+#print CategoryTheory.MonoOver.homMk /-
 /-- Convenience constructor for a morphism in monomorphisms over `X`. -/
 abbrev homMk {f g : MonoOver X} (h : f.obj.left ⟶ g.obj.left) (w : h ≫ g.arrow = f.arrow) : f ⟶ g :=
   Over.homMk h w
 #align category_theory.mono_over.hom_mk CategoryTheory.MonoOver.homMk
+-/
 
+#print CategoryTheory.MonoOver.isoMk /-
 /-- Convenience constructor for an isomorphism in monomorphisms over `X`. -/
 @[simps]
 def isoMk {f g : MonoOver X} (h : f.obj.left ≅ g.obj.left) (w : h.Hom ≫ g.arrow = f.arrow) : f ≅ g
@@ -136,7 +189,14 @@ def isoMk {f g : MonoOver X} (h : f.obj.left ≅ g.obj.left) (w : h.Hom ≫ g.ar
   Hom := homMk h.Hom w
   inv := homMk h.inv (by rw [h.inv_comp_eq, w])
 #align category_theory.mono_over.iso_mk CategoryTheory.MonoOver.isoMk
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.mk'_arrow_iso CategoryTheory.MonoOver.mk'ArrowIsoₓ'. -/
 /-- If `f : mono_over X`, then `mk' f.arrow` is of course just `f`, but not definitionally, so we
     package it as an isomorphism. -/
 @[simp]
@@ -144,6 +204,12 @@ def mk'ArrowIso {X : C} (f : MonoOver X) : mk' f.arrow ≅ f :=
   isoMk (Iso.refl _) (by simp)
 #align category_theory.mono_over.mk'_arrow_iso CategoryTheory.MonoOver.mk'ArrowIso
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.lift CategoryTheory.MonoOver.liftₓ'. -/
 /-- Lift a functor between over categories to a functor between `mono_over` categories,
 given suitable evidence that morphisms are taken to monomorphisms.
 -/
@@ -155,23 +221,43 @@ def lift {Y : D} (F : Over Y ⥤ Over X)
   map _ _ k := (MonoOver.forget X).preimage ((MonoOver.forget Y ⋙ F).map k)
 #align category_theory.mono_over.lift CategoryTheory.MonoOver.lift
 
+/- warning: category_theory.mono_over.lift_iso -> CategoryTheory.MonoOver.liftIso is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.lift_iso CategoryTheory.MonoOver.liftIsoₓ'. -/
 /-- Isomorphic functors `over Y ⥤ over X` lift to isomorphic functors `mono_over Y ⥤ mono_over X`.
 -/
 def liftIso {Y : D} {F₁ F₂ : Over Y ⥤ Over X} (h₁ h₂) (i : F₁ ≅ F₂) : lift F₁ h₁ ≅ lift F₂ h₂ :=
   fullyFaithfulCancelRight (MonoOver.forget X) (isoWhiskerLeft (MonoOver.forget Y) i)
 #align category_theory.mono_over.lift_iso CategoryTheory.MonoOver.liftIso
 
+/- warning: category_theory.mono_over.lift_comp -> CategoryTheory.MonoOver.liftComp is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.instCategoryOver.{u1, u3} C _inst_1 X) (CategoryTheory.MonoOver.forget.{u1, u3} C _inst_1 X)) f)) (h₁ f))))
+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.lift_comp CategoryTheory.MonoOver.liftCompₓ'. -/
 /-- `mono_over.lift` commutes with composition of functors. -/
 def liftComp {X Z : C} {Y : D} (F : Over X ⥤ Over Y) (G : Over Y ⥤ Over Z) (h₁ h₂) :
     lift F h₁ ⋙ lift G h₂ ≅ lift (F ⋙ G) fun f => h₂ ⟨_, h₁ f⟩ :=
   fullyFaithfulCancelRight (MonoOver.forget _) (Iso.refl _)
 #align category_theory.mono_over.lift_comp CategoryTheory.MonoOver.liftComp
 
+#print CategoryTheory.MonoOver.liftId /-
 /-- `mono_over.lift` preserves the identity functor. -/
 def liftId : (lift (𝟭 (Over X)) fun f => f.2) ≅ 𝟭 _ :=
   fullyFaithfulCancelRight (MonoOver.forget _) (Iso.refl _)
 #align category_theory.mono_over.lift_id CategoryTheory.MonoOver.liftId
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.lift_comm CategoryTheory.MonoOver.lift_commₓ'. -/
 @[simp]
 theorem lift_comm (F : Over Y ⥤ Over X)
     (h : ∀ f : MonoOver Y, Mono (F.obj ((MonoOver.forget Y).obj f)).Hom) :
@@ -179,6 +265,12 @@ theorem lift_comm (F : Over Y ⥤ Over X)
   rfl
 #align category_theory.mono_over.lift_comm CategoryTheory.MonoOver.lift_comm
 
+/- warning: category_theory.mono_over.lift_obj_arrow -> CategoryTheory.MonoOver.lift_obj_arrow is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.lift_obj_arrow CategoryTheory.MonoOver.lift_obj_arrowₓ'. -/
 @[simp]
 theorem lift_obj_arrow {Y : D} (F : Over Y ⥤ Over X)
     (h : ∀ f : MonoOver Y, Mono (F.obj ((MonoOver.forget Y).obj f)).Hom) (f : MonoOver Y) :
@@ -186,6 +278,12 @@ theorem lift_obj_arrow {Y : D} (F : Over Y ⥤ Over X)
   rfl
 #align category_theory.mono_over.lift_obj_arrow CategoryTheory.MonoOver.lift_obj_arrow
 
+/- warning: category_theory.mono_over.slice -> CategoryTheory.MonoOver.slice is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.slice CategoryTheory.MonoOver.sliceₓ'. -/
 /-- Monomorphisms over an object `f : over A` in an over category
 are equivalent to monomorphisms over the source of `f`.
 -/
@@ -205,6 +303,7 @@ section Pullback
 
 variable [HasPullbacks C]
 
+#print CategoryTheory.MonoOver.pullback /-
 /-- When `C` has pullbacks, a morphism `f : X ⟶ Y` induces a functor `mono_over Y ⥤ mono_over X`,
 by pulling back a monomorphism along `f`. -/
 def pullback (f : X ⟶ Y) : MonoOver Y ⥤ MonoOver X :=
@@ -215,23 +314,40 @@ def pullback (f : X ⟶ Y) : MonoOver Y ⥤ MonoOver X :=
       change mono g.arrow
       infer_instance)
 #align category_theory.mono_over.pullback CategoryTheory.MonoOver.pullback
+-/
 
+#print CategoryTheory.MonoOver.pullbackComp /-
 /-- pullback commutes with composition (up to a natural isomorphism) -/
 def pullbackComp (f : X ⟶ Y) (g : Y ⟶ Z) : pullback (f ≫ g) ≅ pullback g ⋙ pullback f :=
   liftIso _ _ (Over.pullbackComp _ _) ≪≫ (liftComp _ _ _ _).symm
 #align category_theory.mono_over.pullback_comp CategoryTheory.MonoOver.pullbackComp
+-/
 
+#print CategoryTheory.MonoOver.pullbackId /-
 /-- pullback preserves the identity (up to a natural isomorphism) -/
 def pullbackId : pullback (𝟙 X) ≅ 𝟭 _ :=
   liftIso _ _ Over.pullbackId ≪≫ liftId
 #align category_theory.mono_over.pullback_id CategoryTheory.MonoOver.pullbackId
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.pullback_obj_left CategoryTheory.MonoOver.pullback_obj_leftₓ'. -/
 @[simp]
 theorem pullback_obj_left (f : X ⟶ Y) (g : MonoOver Y) :
     ((pullback f).obj g : C) = Limits.pullback g.arrow f :=
   rfl
 #align category_theory.mono_over.pullback_obj_left CategoryTheory.MonoOver.pullback_obj_left
 
+/- warning: category_theory.mono_over.pullback_obj_arrow -> CategoryTheory.MonoOver.pullback_obj_arrow 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.mono_over.pullback_obj_arrow CategoryTheory.MonoOver.pullback_obj_arrowₓ'. -/
 @[simp]
 theorem pullback_obj_arrow (f : X ⟶ Y) (g : MonoOver Y) :
     ((pullback f).obj g).arrow = pullback.snd :=
@@ -244,43 +360,71 @@ section Map
 
 attribute [instance] mono_comp
 
+#print CategoryTheory.MonoOver.map /-
 /-- We can map monomorphisms over `X` to monomorphisms over `Y`
 by post-composition with a monomorphism `f : X ⟶ Y`.
 -/
 def map (f : X ⟶ Y) [Mono f] : MonoOver X ⥤ MonoOver Y :=
   lift (Over.map f) fun g => by apply mono_comp g.arrow f
 #align category_theory.mono_over.map CategoryTheory.MonoOver.map
+-/
 
+#print CategoryTheory.MonoOver.mapComp /-
 /-- `mono_over.map` commutes with composition (up to a natural isomorphism). -/
 def mapComp (f : X ⟶ Y) (g : Y ⟶ Z) [Mono f] [Mono g] : map (f ≫ g) ≅ map f ⋙ map g :=
   liftIso _ _ (Over.mapComp _ _) ≪≫ (liftComp _ _ _ _).symm
 #align category_theory.mono_over.map_comp CategoryTheory.MonoOver.mapComp
+-/
 
+#print CategoryTheory.MonoOver.mapId /-
 /-- `mono_over.map` preserves the identity (up to a natural isomorphism). -/
 def mapId : map (𝟙 X) ≅ 𝟭 _ :=
   liftIso _ _ Over.mapId ≪≫ liftId
 #align category_theory.mono_over.map_id CategoryTheory.MonoOver.mapId
+-/
 
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 @[simp]
 theorem map_obj_left (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g : C) = g.obj.left :=
   rfl
 #align category_theory.mono_over.map_obj_left CategoryTheory.MonoOver.map_obj_left
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.map_obj_arrow CategoryTheory.MonoOver.map_obj_arrowₓ'. -/
 @[simp]
 theorem map_obj_arrow (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g).arrow = g.arrow ≫ f :=
   rfl
 #align category_theory.mono_over.map_obj_arrow CategoryTheory.MonoOver.map_obj_arrow
 
+#print CategoryTheory.MonoOver.fullMap /-
 instance fullMap (f : X ⟶ Y) [Mono f] : Full (map f)
     where preimage g h e := by
     refine' hom_mk e.left _
     rw [← cancel_mono f, assoc]
     apply w e
 #align category_theory.mono_over.full_map CategoryTheory.MonoOver.fullMap
+-/
 
+#print CategoryTheory.MonoOver.faithful_map /-
 instance faithful_map (f : X ⟶ Y) [Mono f] : Faithful (map f) where
 #align category_theory.mono_over.faithful_map CategoryTheory.MonoOver.faithful_map
+-/
 
+/- warning: category_theory.mono_over.map_iso -> CategoryTheory.MonoOver.mapIso is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {A : C} {B : C}, (CategoryTheory.Iso.{u1, u2} C _inst_1 A B) -> (CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 A) (CategoryTheory.MonoOver.{u1, u2} C _inst_1 B) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 A) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 B))
+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.map_iso CategoryTheory.MonoOver.mapIsoₓ'. -/
 /-- Isomorphic objects have equivalent `mono_over` categories.
 -/
 @[simps]
@@ -296,6 +440,12 @@ section
 
 variable (X)
 
+/- warning: category_theory.mono_over.congr -> CategoryTheory.MonoOver.congr 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.mono_over.congr CategoryTheory.MonoOver.congrₓ'. -/
 /-- An equivalence of categories `e` between `C` and `D` induces an equivalence between
     `mono_over X` and `mono_over (e.functor.obj X)` whenever `X` is an object of `C`. -/
 @[simps]
@@ -320,16 +470,20 @@ section
 
 variable [HasPullbacks C]
 
+#print CategoryTheory.MonoOver.mapPullbackAdj /-
 /-- `map f` is left adjoint to `pullback f` when `f` is a monomorphism -/
 def mapPullbackAdj (f : X ⟶ Y) [Mono f] : map f ⊣ pullback f :=
   Adjunction.restrictFullyFaithful (forget X) (forget Y) (Over.mapPullbackAdj f) (Iso.refl _)
     (Iso.refl _)
 #align category_theory.mono_over.map_pullback_adj CategoryTheory.MonoOver.mapPullbackAdj
+-/
 
+#print CategoryTheory.MonoOver.pullbackMapSelf /-
 /-- `mono_over.map f` followed by `mono_over.pullback f` is the identity. -/
 def pullbackMapSelf (f : X ⟶ Y) [Mono f] : map f ⋙ pullback f ≅ 𝟭 _ :=
   (asIso (MonoOver.mapPullbackAdj f).Unit).symm
 #align category_theory.mono_over.pullback_map_self CategoryTheory.MonoOver.pullbackMapSelf
+-/
 
 end
 
@@ -339,12 +493,20 @@ section Image
 
 variable (f : X ⟶ Y) [HasImage f]
 
+#print CategoryTheory.MonoOver.imageMonoOver /-
 /-- The `mono_over Y` for the image inclusion for a morphism `f : X ⟶ Y`.
 -/
 def imageMonoOver (f : X ⟶ Y) [HasImage f] : MonoOver Y :=
   MonoOver.mk' (image.ι f)
 #align category_theory.mono_over.image_mono_over CategoryTheory.MonoOver.imageMonoOver
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.image_mono_over_arrow CategoryTheory.MonoOver.imageMonoOver_arrowₓ'. -/
 @[simp]
 theorem imageMonoOver_arrow (f : X ⟶ Y) [HasImage f] : (imageMonoOver f).arrow = image.ι f :=
   rfl
@@ -356,6 +518,7 @@ section Image
 
 variable [HasImages C]
 
+#print CategoryTheory.MonoOver.image /-
 /-- Taking the image of a morphism gives a functor `over X ⥤ mono_over X`.
 -/
 @[simps]
@@ -371,7 +534,9 @@ def image : Over X ⥤ MonoOver X where
           e := k.left ≫ factor_thru_image g.hom }
     apply image.lift_fac
 #align category_theory.mono_over.image CategoryTheory.MonoOver.image
+-/
 
+#print CategoryTheory.MonoOver.imageForgetAdj /-
 /-- `mono_over.image : over X ⥤ mono_over X` is left adjoint to
 `mono_over.forget : mono_over X ⥤ over X`
 -/
@@ -401,14 +566,27 @@ def imageForgetAdj : image ⊣ forget X :=
             rw [← cancel_mono g.arrow, assoc, image.lift_fac, image.fac f.hom]
             exact (over.w k).symm } }
 #align category_theory.mono_over.image_forget_adj CategoryTheory.MonoOver.imageForgetAdj
+-/
 
 instance : IsRightAdjoint (forget X) where
   left := image
   adj := imageForgetAdj
 
+/- warning: category_theory.mono_over.reflective -> CategoryTheory.MonoOver.reflective is a dubious translation:
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 instance reflective : Reflective (forget X) where
 #align category_theory.mono_over.reflective CategoryTheory.MonoOver.reflective
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.forget_image CategoryTheory.MonoOver.forgetImageₓ'. -/
 /-- Forgetting that a monomorphism over `X` is a monomorphism, then taking its image,
 is the identity functor.
 -/
@@ -422,19 +600,37 @@ section Exists
 
 variable [HasImages C]
 
+/- warning: category_theory.mono_over.exists -> CategoryTheory.MonoOver.exists_ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists CategoryTheory.MonoOver.exists_ₓ'. -/
 /-- In the case where `f` is not a monomorphism but `C` has images,
 we can still take the "forward map" under it, which agrees with `mono_over.map f`.
 -/
-def exists (f : X ⟶ Y) : MonoOver X ⥤ MonoOver Y :=
+def exists_ (f : X ⟶ Y) : MonoOver X ⥤ MonoOver Y :=
   forget _ ⋙ Over.map f ⋙ image
-#align category_theory.mono_over.exists CategoryTheory.MonoOver.exists
-
-instance faithful_exists (f : X ⟶ Y) : Faithful (exists f) where
+#align category_theory.mono_over.exists CategoryTheory.MonoOver.exists_
+
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.faithful_exists CategoryTheory.MonoOver.faithful_existsₓ'. -/
+instance faithful_exists (f : X ⟶ Y) : Faithful (exists_ f) where
 #align category_theory.mono_over.faithful_exists CategoryTheory.MonoOver.faithful_exists
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists_iso_map CategoryTheory.MonoOver.existsIsoMapₓ'. -/
 /-- When `f : X ⟶ Y` is a monomorphism, `exists f` agrees with `map f`.
 -/
-def existsIsoMap (f : X ⟶ Y) [Mono f] : exists f ≅ map f :=
+def existsIsoMap (f : X ⟶ Y) [Mono f] : exists_ f ≅ map f :=
   NatIso.ofComponents
     (by
       intro Z
@@ -454,8 +650,14 @@ def existsIsoMap (f : X ⟶ Y) [Mono f] : exists f ≅ map f :=
       apply image.lift_fac)
 #align category_theory.mono_over.exists_iso_map CategoryTheory.MonoOver.existsIsoMap
 
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} [_inst_3 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Limits.HasPullbacks.{u1, u2} C _inst_1], CategoryTheory.Adjunction.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.MonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 X) (CategoryTheory.MonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.instCategoryMonoOver.{u1, u2} C _inst_1 Y) (CategoryTheory.MonoOver.exists_.{u1, u2} C _inst_1 X Y _inst_3 f) (CategoryTheory.MonoOver.pullback.{u1, u2} C _inst_1 X Y _inst_4 f)
+Case conversion may be inaccurate. Consider using '#align category_theory.mono_over.exists_pullback_adj CategoryTheory.MonoOver.existsPullbackAdjₓ'. -/
 /-- `exists` is adjoint to `pullback` when images exist -/
-def existsPullbackAdj (f : X ⟶ Y) [HasPullbacks C] : exists f ⊣ pullback f :=
+def existsPullbackAdj (f : X ⟶ Y) [HasPullbacks C] : exists_ f ⊣ pullback f :=
   Adjunction.restrictFullyFaithful (forget X) (𝟭 _) ((Over.mapPullbackAdj f).comp imageForgetAdj)
     (Iso.refl _) (Iso.refl _)
 #align category_theory.mono_over.exists_pullback_adj CategoryTheory.MonoOver.existsPullbackAdj

70fd9563

bump to nightly-2023-02-27-08

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

91d8c210

Diff

@@ -392,7 +392,7 @@ def imageForgetAdj : image ⊣ forget X :=
                 { i := g.obj.left
                   m := g.arrow
                   e := k.left
-                  fac' := over.w k }
+                  fac := over.w k }
             apply image.lift_fac
           left_inv := fun k => Subsingleton.elim _ _
           right_inv := fun k => by

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

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

A PR accompanying #12339.

Zulip discussion

45f93f3f

Diff

@@ -367,12 +367,12 @@ def image : Over X ⥤ MonoOver X where
   map {f g} k := by
     apply (forget X).preimage _
     apply Over.homMk _ _
-    exact
-      image.lift
-        { I := Limits.image _
-          m := image.ι g.hom
-          e := k.left ≫ factorThruImage g.hom }
-    apply image.lift_fac
+    · exact
+        image.lift
+          { I := Limits.image _
+            m := image.ι g.hom
+            e := k.left ≫ factorThruImage g.hom }
+    · apply image.lift_fac
 #align category_theory.mono_over.image CategoryTheory.MonoOver.image
 
 /-- `MonoOver.image : Over X ⥤ MonoOver X` is left adjoint to
@@ -388,13 +388,13 @@ def imageForgetAdj : image ⊣ forget X :=
             apply image.fac
           invFun := fun k => by
             refine' Over.homMk _ _
-            exact
-              image.lift
-                { I := g.obj.left
-                  m := g.arrow
-                  e := k.left
-                  fac := Over.w k }
-            apply image.lift_fac
+            · exact
+                image.lift
+                  { I := g.obj.left
+                    m := g.arrow
+                    e := k.left
+                    fac := Over.w k }
+            · apply image.lift_fac
           left_inv := fun k => Subsingleton.elim _ _
           right_inv := fun k => by
             ext1
@@ -441,8 +441,8 @@ def existsIsoMap (f : X ⟶ Y) [Mono f] : «exists» f ≅ map f :=
     suffices (forget _).obj ((«exists» f).obj Z) ≅ (forget _).obj ((map f).obj Z) by
       apply (forget _).preimageIso this
     apply Over.isoMk _ _
-    apply imageMonoIsoSource (Z.arrow ≫ f)
-    apply imageMonoIsoSource_hom_self)
+    · apply imageMonoIsoSource (Z.arrow ≫ f)
+    · apply imageMonoIsoSource_hom_self)
 #align category_theory.mono_over.exists_iso_map CategoryTheory.MonoOver.existsIsoMap
 
 /-- `exists` is adjoint to `pullback` when images exist -/

70fd9563

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

@@ -152,7 +152,7 @@ def lift {Y : D} (F : Over Y ⥤ Over X)
     (h : ∀ f : MonoOver Y, Mono (F.obj ((MonoOver.forget Y).obj f)).hom) :
     MonoOver Y ⥤ MonoOver X where
   obj f := ⟨_, h f⟩
-  map k := (MonoOver.forget X).preimage ((MonoOver.forget Y ⋙ F).map k)
+  map k := (MonoOver.forget Y ⋙ F).map k
 #align category_theory.mono_over.lift CategoryTheory.MonoOver.lift
 
 /-- Isomorphic functors `Over Y ⥤ Over X` lift to isomorphic functors `MonoOver Y ⥤ MonoOver X`.
@@ -276,12 +276,12 @@ theorem map_obj_arrow (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g).
   rfl
 #align category_theory.mono_over.map_obj_arrow CategoryTheory.MonoOver.map_obj_arrow
 
-instance fullMap (f : X ⟶ Y) [Mono f] : Functor.Full (map f) where
-  preimage {g h} e := by
-    refine' homMk e.left _
-    rw [← cancel_mono f, assoc]
-    apply w e
-#align category_theory.mono_over.full_map CategoryTheory.MonoOver.fullMap
+instance full_map (f : X ⟶ Y) [Mono f] : Functor.Full (map f) where
+  map_surjective {g h} e := by
+    refine' ⟨homMk e.left _, rfl⟩
+    · rw [← cancel_mono f, assoc]
+      apply w e
+#align category_theory.mono_over.full_map CategoryTheory.MonoOver.full_map
 
 instance faithful_map (f : X ⟶ Y) [Mono f] : Functor.Faithful (map f) where
 #align category_theory.mono_over.faithful_map CategoryTheory.MonoOver.faithful_map

70fd9563

chore: split CategoryTheory.MorphismProperty (#12393)

The file CategoryTheory.MorphismProperty is split into five files Basic, Composition, Limits, Concrete, IsInvertedBy.

9e489ab7

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Scott Morrison
 -/
 import Mathlib.CategoryTheory.Limits.Over
+import Mathlib.CategoryTheory.Limits.Shapes.Images
 import Mathlib.CategoryTheory.Adjunction.Reflective
 import Mathlib.CategoryTheory.Adjunction.Restrict

70fd9563

chore(CategoryTheory/Adjunction): move Adjunction.restrictFullyFaithful to separate file (#12363)

Also resolves a TODO to add lemmas about Adjunction.restrictFullyFaithful

38faa1d2

Diff

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Scott Morrison
 -/
 import Mathlib.CategoryTheory.Limits.Over
-import Mathlib.CategoryTheory.Limits.Shapes.Images
 import Mathlib.CategoryTheory.Adjunction.Reflective
+import Mathlib.CategoryTheory.Adjunction.Restrict
 
 #align_import category_theory.subobject.mono_over from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"

70fd9563

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

@@ -98,10 +98,10 @@ theorem forget_obj_hom {f} : ((forget X).obj f).hom = f.arrow :=
   rfl
 #align category_theory.mono_over.forget_obj_hom CategoryTheory.MonoOver.forget_obj_hom
 
-instance : Full (forget X) :=
+instance : (forget X).Full :=
   FullSubcategory.full _
 
-instance : Faithful (forget X) :=
+instance : (forget X).Faithful :=
   FullSubcategory.faithful _
 
 instance mono (f : MonoOver X) : Mono f.arrow :=
@@ -157,18 +157,18 @@ def lift {Y : D} (F : Over Y ⥤ Over X)
 /-- Isomorphic functors `Over Y ⥤ Over X` lift to isomorphic functors `MonoOver Y ⥤ MonoOver X`.
 -/
 def liftIso {Y : D} {F₁ F₂ : Over Y ⥤ Over X} (h₁ h₂) (i : F₁ ≅ F₂) : lift F₁ h₁ ≅ lift F₂ h₂ :=
-  fullyFaithfulCancelRight (MonoOver.forget X) (isoWhiskerLeft (MonoOver.forget Y) i)
+  Functor.fullyFaithfulCancelRight (MonoOver.forget X) (isoWhiskerLeft (MonoOver.forget Y) i)
 #align category_theory.mono_over.lift_iso CategoryTheory.MonoOver.liftIso
 
 /-- `MonoOver.lift` commutes with composition of functors. -/
 def liftComp {X Z : C} {Y : D} (F : Over X ⥤ Over Y) (G : Over Y ⥤ Over Z) (h₁ h₂) :
     lift F h₁ ⋙ lift G h₂ ≅ lift (F ⋙ G) fun f => h₂ ⟨_, h₁ f⟩ :=
-  fullyFaithfulCancelRight (MonoOver.forget _) (Iso.refl _)
+  Functor.fullyFaithfulCancelRight (MonoOver.forget _) (Iso.refl _)
 #align category_theory.mono_over.lift_comp CategoryTheory.MonoOver.liftComp
 
 /-- `MonoOver.lift` preserves the identity functor. -/
 def liftId : (lift (𝟭 (Over X)) fun f => f.2) ≅ 𝟭 _ :=
-  fullyFaithfulCancelRight (MonoOver.forget _) (Iso.refl _)
+  Functor.fullyFaithfulCancelRight (MonoOver.forget _) (Iso.refl _)
 #align category_theory.mono_over.lift_id CategoryTheory.MonoOver.liftId
 
 @[simp]
@@ -275,14 +275,14 @@ theorem map_obj_arrow (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g).
   rfl
 #align category_theory.mono_over.map_obj_arrow CategoryTheory.MonoOver.map_obj_arrow
 
-instance fullMap (f : X ⟶ Y) [Mono f] : Full (map f) where
+instance fullMap (f : X ⟶ Y) [Mono f] : Functor.Full (map f) where
   preimage {g h} e := by
     refine' homMk e.left _
     rw [← cancel_mono f, assoc]
     apply w e
 #align category_theory.mono_over.full_map CategoryTheory.MonoOver.fullMap
 
-instance faithful_map (f : X ⟶ Y) [Mono f] : Faithful (map f) where
+instance faithful_map (f : X ⟶ Y) [Mono f] : Functor.Faithful (map f) where
 #align category_theory.mono_over.faithful_map CategoryTheory.MonoOver.faithful_map
 
 /-- Isomorphic objects have equivalent `MonoOver` categories.
@@ -429,7 +429,7 @@ def «exists» (f : X ⟶ Y) : MonoOver X ⥤ MonoOver Y :=
   forget _ ⋙ Over.map f ⋙ image
 #align category_theory.mono_over.exists CategoryTheory.MonoOver.exists
 
-instance faithful_exists (f : X ⟶ Y) : Faithful («exists» f) where
+instance faithful_exists (f : X ⟶ Y) : Functor.Faithful («exists» f) where
 #align category_theory.mono_over.faithful_exists CategoryTheory.MonoOver.faithful_exists
 
 /-- When `f : X ⟶ Y` is a monomorphism, `exists f` agrees with `map f`.

70fd9563

fix: change refine to exact in files where it speeds up (#11896)

See #11890 and this Zulip discussion for an in-depth explanation of why these refines and not others.

The short answer is that the files in which these replacements took place were more performant after the change than before.

514a12b4

Diff

@@ -366,7 +366,7 @@ def image : Over X ⥤ MonoOver X where
   map {f g} k := by
     apply (forget X).preimage _
     apply Over.homMk _ _
-    refine'
+    exact
       image.lift
         { I := Limits.image _
           m := image.ι g.hom
@@ -387,7 +387,7 @@ def imageForgetAdj : image ⊣ forget X :=
             apply image.fac
           invFun := fun k => by
             refine' Over.homMk _ _
-            refine'
+            exact
               image.lift
                 { I := g.obj.left
                   m := g.arrow

70fd9563

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

@@ -43,7 +43,6 @@ namespace CategoryTheory
 open CategoryTheory CategoryTheory.Category CategoryTheory.Limits
 
 variable {C : Type u₁} [Category.{v₁} C] {X Y Z : C}
-
 variable {D : Type u₂} [Category.{v₂} D]
 
 /-- The category of monomorphisms into `X` as a full subcategory of the over category.

70fd9563

chore: tidy various files (#8880)

d510164f

Diff

@@ -191,10 +191,10 @@ are equivalent to monomorphisms over the source of `f`.
 -/
 def slice {A : C} {f : Over A}
     (h₁ : ∀ (g : MonoOver f),
-    Mono ((Over.iteratedSliceEquiv f).functor.obj ((forget f).obj g)).hom)
+      Mono ((Over.iteratedSliceEquiv f).functor.obj ((forget f).obj g)).hom)
     (h₂ : ∀ (g : MonoOver f.left),
-    Mono ((Over.iteratedSliceEquiv f).inverse.obj ((forget f.left).obj g)).hom) :
-  MonoOver f ≌ MonoOver f.left where
+      Mono ((Over.iteratedSliceEquiv f).inverse.obj ((forget f.left).obj g)).hom) :
+    MonoOver f ≌ MonoOver f.left where
   functor := MonoOver.lift f.iteratedSliceEquiv.functor h₁
   inverse := MonoOver.lift f.iteratedSliceEquiv.inverse h₂
   unitIso :=

70fd9563

feat(CategoryTheory/Sites): internal hom of (pre)sheaves (#8622)

In this PR, we define a presheaf presheafHom F G when F and G are presheaves Cᵒᵖ ⥤ A and show that it is a sheaf when G is a sheaf (for a certain Grothendieck topology on C).

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

c28500a0

Diff

@@ -257,11 +257,15 @@ def mapComp (f : X ⟶ Y) (g : Y ⟶ Z) [Mono f] [Mono g] : map (f ≫ g) ≅ ma
   liftIso _ _ (Over.mapComp _ _) ≪≫ (liftComp _ _ _ _).symm
 #align category_theory.mono_over.map_comp CategoryTheory.MonoOver.mapComp
 
+variable (X)
+
 /-- `MonoOver.map` preserves the identity (up to a natural isomorphism). -/
 def mapId : map (𝟙 X) ≅ 𝟭 _ :=
-  liftIso _ _ Over.mapId ≪≫ liftId
+  liftIso _ _ (Over.mapId X) ≪≫ liftId
 #align category_theory.mono_over.map_id CategoryTheory.MonoOver.mapId
 
+variable {X}
+
 @[simp]
 theorem map_obj_left (f : X ⟶ Y) [Mono f] (g : MonoOver X) : ((map f).obj g : C) = g.obj.left :=
   rfl
@@ -288,8 +292,8 @@ instance faithful_map (f : X ⟶ Y) [Mono f] : Faithful (map f) where
 def mapIso {A B : C} (e : A ≅ B) : MonoOver A ≌ MonoOver B where
   functor := map e.hom
   inverse := map e.inv
-  unitIso := ((mapComp _ _).symm ≪≫ eqToIso (by simp) ≪≫ mapId).symm
-  counitIso := (mapComp _ _).symm ≪≫ eqToIso (by simp) ≪≫ mapId
+  unitIso := ((mapComp _ _).symm ≪≫ eqToIso (by simp) ≪≫ (mapId _)).symm
+  counitIso := (mapComp _ _).symm ≪≫ eqToIso (by simp) ≪≫ (mapId _)
 #align category_theory.mono_over.map_iso CategoryTheory.MonoOver.mapIso
 
 section

70fd9563

chore: fix some cases in names (#7469)

And fix some names in comments where this revealed issues

be0d066c

Diff

@@ -420,7 +420,7 @@ section Exists
 variable [HasImages C]
 
 /-- In the case where `f` is not a monomorphism but `C` has images,
-we can still take the "forward map" under it, which agrees with `mono_over.map f`.
+we can still take the "forward map" under it, which agrees with `MonoOver.map f`.
 -/
 def «exists» (f : X ⟶ Y) : MonoOver X ⥤ MonoOver Y :=
   forget _ ⋙ Over.map f ⋙ image

70fd9563

chore: exactly 4 spaces in theorems (#7328)

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

d3263b23

Diff

@@ -190,9 +190,9 @@ theorem lift_obj_arrow {Y : D} (F : Over Y ⥤ Over X)
 are equivalent to monomorphisms over the source of `f`.
 -/
 def slice {A : C} {f : Over A}
-  (h₁ : ∀ (g : MonoOver f),
+    (h₁ : ∀ (g : MonoOver f),
     Mono ((Over.iteratedSliceEquiv f).functor.obj ((forget f).obj g)).hom)
-  (h₂ : ∀ (g : MonoOver f.left),
+    (h₂ : ∀ (g : MonoOver f.left),
     Mono ((Over.iteratedSliceEquiv f).inverse.obj ((forget f.left).obj g)).hom) :
   MonoOver f ≌ MonoOver f.left where
   functor := MonoOver.lift f.iteratedSliceEquiv.functor h₁

70fd9563

chore: avoid lean3 style have/suffices (#6964)

Many proofs use the "stream of consciousness" style from Lean 3, rather than have ... := or suffices ... from/by.

This PR updates a fraction of these to the preferred Lean 4 style.

I think a good goal would be to delete the "deferred" versions of have, suffices, and let at the bottom of Mathlib.Tactic.Have

(Anyone who would like to contribute more cleanup is welcome to push directly to this branch.)

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

bdc47f68

Diff

@@ -434,8 +434,8 @@ instance faithful_exists (f : X ⟶ Y) : Faithful («exists» f) where
 def existsIsoMap (f : X ⟶ Y) [Mono f] : «exists» f ≅ map f :=
   NatIso.ofComponents (by
     intro Z
-    suffices : (forget _).obj ((«exists» f).obj Z) ≅ (forget _).obj ((map f).obj Z)
-    apply (forget _).preimageIso this
+    suffices (forget _).obj ((«exists» f).obj Z) ≅ (forget _).obj ((map f).obj Z) by
+      apply (forget _).preimageIso this
     apply Over.isoMk _ _
     apply imageMonoIsoSource (Z.arrow ≫ f)
     apply imageMonoIsoSource_hom_self)

70fd9563

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.subobject.mono_over
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Limits.Over
 import Mathlib.CategoryTheory.Limits.Shapes.Images
 import Mathlib.CategoryTheory.Adjunction.Reflective
 
+#align_import category_theory.subobject.mono_over from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 # Monomorphisms over a fixed object

70fd9563

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

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

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

5b958613

Diff

@@ -127,14 +127,15 @@ theorem w {f g : MonoOver X} (k : f ⟶ g) : k.left ≫ g.arrow = f.arrow :=
 #align category_theory.mono_over.w CategoryTheory.MonoOver.w
 
 /-- Convenience constructor for a morphism in monomorphisms over `X`. -/
-abbrev homMk {f g : MonoOver X} (h : f.obj.left ⟶ g.obj.left) (w : h ≫ g.arrow = f.arrow) : f ⟶ g :=
+abbrev homMk {f g : MonoOver X} (h : f.obj.left ⟶ g.obj.left)
+    (w : h ≫ g.arrow = f.arrow := by aesop_cat) : f ⟶ g :=
   Over.homMk h w
 #align category_theory.mono_over.hom_mk CategoryTheory.MonoOver.homMk
 
 /-- Convenience constructor for an isomorphism in monomorphisms over `X`. -/
 @[simps]
-def isoMk {f g : MonoOver X} (h : f.obj.left ≅ g.obj.left) (w : h.hom ≫ g.arrow = f.arrow) : f ≅ g
-    where
+def isoMk {f g : MonoOver X} (h : f.obj.left ≅ g.obj.left)
+    (w : h.hom ≫ g.arrow = f.arrow := by aesop_cat) : f ≅ g where
   hom := homMk h.hom w
   inv := homMk h.inv (by rw [h.inv_comp_eq, w])
 #align category_theory.mono_over.iso_mk CategoryTheory.MonoOver.isoMk
@@ -143,7 +144,7 @@ def isoMk {f g : MonoOver X} (h : f.obj.left ≅ g.obj.left) (w : h.hom ≫ g.ar
     package it as an isomorphism. -/
 @[simp]
 def mk'ArrowIso {X : C} (f : MonoOver X) : mk' f.arrow ≅ f :=
-  isoMk (Iso.refl _) (by simp)
+  isoMk (Iso.refl _)
 #align category_theory.mono_over.mk'_arrow_iso CategoryTheory.MonoOver.mk'ArrowIso
 
 /-- Lift a functor between over categories to a functor between `MonoOver` categories,
@@ -151,8 +152,8 @@ given suitable evidence that morphisms are taken to monomorphisms.
 -/
 @[simps]
 def lift {Y : D} (F : Over Y ⥤ Over X)
-    (h : ∀ f : MonoOver Y, Mono (F.obj ((MonoOver.forget Y).obj f)).hom) : MonoOver Y ⥤ MonoOver X
-    where
+    (h : ∀ f : MonoOver Y, Mono (F.obj ((MonoOver.forget Y).obj f)).hom) :
+    MonoOver Y ⥤ MonoOver X where
   obj f := ⟨_, h f⟩
   map k := (MonoOver.forget X).preimage ((MonoOver.forget Y ⋙ F).map k)
 #align category_theory.mono_over.lift CategoryTheory.MonoOver.lift
@@ -311,10 +312,8 @@ def congr (e : C ≌ D) : MonoOver X ≌ MonoOver (e.functor.obj X) where
         dsimp
         infer_instance) ⋙
       (mapIso (e.unitIso.symm.app X)).functor
-  unitIso := NatIso.ofComponents (fun Y => isoMk (e.unitIso.app Y)
-    (by aesop_cat)) (by aesop_cat)
-  counitIso := NatIso.ofComponents (fun Y => isoMk (e.counitIso.app Y)
-    (by aesop_cat)) (by aesop_cat)
+  unitIso := NatIso.ofComponents fun Y => isoMk (e.unitIso.app Y)
+  counitIso := NatIso.ofComponents fun Y => isoMk (e.counitIso.app Y)
 #align category_theory.mono_over.congr CategoryTheory.MonoOver.congr
 
 end
@@ -436,15 +435,13 @@ instance faithful_exists (f : X ⟶ Y) : Faithful («exists» f) where
 /-- When `f : X ⟶ Y` is a monomorphism, `exists f` agrees with `map f`.
 -/
 def existsIsoMap (f : X ⟶ Y) [Mono f] : «exists» f ≅ map f :=
-  NatIso.ofComponents
-    (by
-      intro Z
-      suffices : (forget _).obj ((«exists» f).obj Z) ≅ (forget _).obj ((map f).obj Z)
-      apply (forget _).preimageIso this
-      apply Over.isoMk _ _
-      apply imageMonoIsoSource (Z.arrow ≫ f)
-      apply imageMonoIsoSource_hom_self)
-    (fun _ => Subsingleton.elim _ _)
+  NatIso.ofComponents (by
+    intro Z
+    suffices : (forget _).obj ((«exists» f).obj Z) ≅ (forget _).obj ((map f).obj Z)
+    apply (forget _).preimageIso this
+    apply Over.isoMk _ _
+    apply imageMonoIsoSource (Z.arrow ≫ f)
+    apply imageMonoIsoSource_hom_self)
 #align category_theory.mono_over.exists_iso_map CategoryTheory.MonoOver.existsIsoMap
 
 /-- `exists` is adjoint to `pullback` when images exist -/

70fd9563

chore: tidy various files (#3848)

66cb7cc4

Diff

@@ -423,24 +423,23 @@ section Exists
 
 variable [HasImages C]
 
--- porting note: renamed `exists` as `exists_` because it is a reserved word
 /-- In the case where `f` is not a monomorphism but `C` has images,
 we can still take the "forward map" under it, which agrees with `mono_over.map f`.
 -/
-def exists_ (f : X ⟶ Y) : MonoOver X ⥤ MonoOver Y :=
+def «exists» (f : X ⟶ Y) : MonoOver X ⥤ MonoOver Y :=
   forget _ ⋙ Over.map f ⋙ image
-#align category_theory.mono_over.exists CategoryTheory.MonoOver.exists_
+#align category_theory.mono_over.exists CategoryTheory.MonoOver.exists
 
-instance faithful_exists (f : X ⟶ Y) : Faithful (exists_ f) where
+instance faithful_exists (f : X ⟶ Y) : Faithful («exists» f) where
 #align category_theory.mono_over.faithful_exists CategoryTheory.MonoOver.faithful_exists
 
-/-- When `f : X ⟶ Y` is a monomorphism, `exists_ f` agrees with `map f`.
+/-- When `f : X ⟶ Y` is a monomorphism, `exists f` agrees with `map f`.
 -/
-def existsIsoMap (f : X ⟶ Y) [Mono f] : exists_ f ≅ map f :=
+def existsIsoMap (f : X ⟶ Y) [Mono f] : «exists» f ≅ map f :=
   NatIso.ofComponents
     (by
       intro Z
-      suffices : (forget _).obj ((exists_ f).obj Z) ≅ (forget _).obj ((map f).obj Z)
+      suffices : (forget _).obj ((«exists» f).obj Z) ≅ (forget _).obj ((map f).obj Z)
       apply (forget _).preimageIso this
       apply Over.isoMk _ _
       apply imageMonoIsoSource (Z.arrow ≫ f)
@@ -449,7 +448,7 @@ def existsIsoMap (f : X ⟶ Y) [Mono f] : exists_ f ≅ map f :=
 #align category_theory.mono_over.exists_iso_map CategoryTheory.MonoOver.existsIsoMap
 
 /-- `exists` is adjoint to `pullback` when images exist -/
-def existsPullbackAdj (f : X ⟶ Y) [HasPullbacks C] : exists_ f ⊣ pullback f :=
+def existsPullbackAdj (f : X ⟶ Y) [HasPullbacks C] : «exists» f ⊣ pullback f :=
   Adjunction.restrictFullyFaithful (forget X) (𝟭 _) ((Over.mapPullbackAdj f).comp imageForgetAdj)
     (Iso.refl _) (Iso.refl _)
 #align category_theory.mono_over.exists_pullback_adj CategoryTheory.MonoOver.existsPullbackAdj

70fd9563

feat: port CategoryTheory.Subobject.MonoOver (#3423)

Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>

85848f29

`category_theory.subobject.mono_over` ⟷ `Mathlib.CategoryTheory.Subobject.MonoOver`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 140

category_theory.subobject.mono_over ⟷ Mathlib.CategoryTheory.Subobject.MonoOver

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 140

`category_theory.subobject.mono_over` ⟷ `Mathlib.CategoryTheory.Subobject.MonoOver`