category_theory.functor.epi_mono ⟷ Mathlib.CategoryTheory.Functor.EpiMono

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

@@ -260,8 +260,8 @@ instance (priority := 100) preservesMonomorphisms_of_isRightAdjoint (F : C ⥤ D
 -/
 
 #print CategoryTheory.Functor.reflectsMonomorphisms_of_faithful /-
-instance (priority := 100) reflectsMonomorphisms_of_faithful (F : C ⥤ D) [Faithful F] :
-    ReflectsMonomorphisms F
+instance (priority := 100) reflectsMonomorphisms_of_faithful (F : C ⥤ D)
+    [CategoryTheory.Functor.Faithful F] : ReflectsMonomorphisms F
     where reflects X Y f hf :=
     ⟨fun Z g h hgh =>
       F.map_injective ((cancel_mono (F.map f)).1 (by rw [← F.map_comp, hgh, F.map_comp]))⟩
@@ -269,8 +269,8 @@ instance (priority := 100) reflectsMonomorphisms_of_faithful (F : C ⥤ D) [Fait
 -/
 
 #print CategoryTheory.Functor.reflectsEpimorphisms_of_faithful /-
-instance (priority := 100) reflectsEpimorphisms_of_faithful (F : C ⥤ D) [Faithful F] :
-    ReflectsEpimorphisms F
+instance (priority := 100) reflectsEpimorphisms_of_faithful (F : C ⥤ D)
+    [CategoryTheory.Functor.Faithful F] : ReflectsEpimorphisms F
     where reflects X Y f hf :=
     ⟨fun Z g h hgh =>
       F.map_injective ((cancel_epi (F.map f)).1 (by rw [← F.map_comp, hgh, F.map_comp]))⟩
@@ -283,8 +283,8 @@ variable (F : C ⥤ D) {X Y : C} (f : X ⟶ Y)
 
 #print CategoryTheory.Functor.splitEpiEquiv /-
 /-- If `F` is a fully faithful functor, split epimorphisms are preserved and reflected by `F`. -/
-def splitEpiEquiv [Full F] [Faithful F] : SplitEpi f ≃ SplitEpi (F.map f)
-    where
+def splitEpiEquiv [CategoryTheory.Functor.Full F] [CategoryTheory.Functor.Faithful F] :
+    SplitEpi f ≃ SplitEpi (F.map f) where
   toFun f := f.map F
   invFun s := by
     refine' ⟨F.preimage s.section_, _⟩
@@ -298,8 +298,8 @@ def splitEpiEquiv [Full F] [Faithful F] : SplitEpi f ≃ SplitEpi (F.map f)
 
 #print CategoryTheory.Functor.isSplitEpi_iff /-
 @[simp]
-theorem isSplitEpi_iff [Full F] [Faithful F] : IsSplitEpi (F.map f) ↔ IsSplitEpi f :=
-  by
+theorem isSplitEpi_iff [CategoryTheory.Functor.Full F] [CategoryTheory.Functor.Faithful F] :
+    IsSplitEpi (F.map f) ↔ IsSplitEpi f := by
   constructor
   · intro h; exact is_split_epi.mk' ((split_epi_equiv F f).invFun h.exists_split_epi.some)
   · intro h; exact is_split_epi.mk' ((split_epi_equiv F f).toFun h.exists_split_epi.some)
@@ -308,7 +308,8 @@ theorem isSplitEpi_iff [Full F] [Faithful F] : IsSplitEpi (F.map f) ↔ IsSplitE
 
 #print CategoryTheory.Functor.splitMonoEquiv /-
 /-- If `F` is a fully faithful functor, split monomorphisms are preserved and reflected by `F`. -/
-def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
+def splitMonoEquiv [CategoryTheory.Functor.Full F] [CategoryTheory.Functor.Faithful F] :
+    SplitMono f ≃ SplitMono (F.map f)
     where
   toFun f := f.map F
   invFun s := by
@@ -323,7 +324,8 @@ def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
 
 #print CategoryTheory.Functor.isSplitMono_iff /-
 @[simp]
-theorem isSplitMono_iff [Full F] [Faithful F] : IsSplitMono (F.map f) ↔ IsSplitMono f :=
+theorem isSplitMono_iff [CategoryTheory.Functor.Full F] [CategoryTheory.Functor.Faithful F] :
+    IsSplitMono (F.map f) ↔ IsSplitMono f :=
   by
   constructor
   · intro h; exact is_split_mono.mk' ((split_mono_equiv F f).invFun h.exists_split_mono.some)
@@ -356,8 +358,8 @@ theorem mono_map_iff_mono [hF₁ : PreservesMonomorphisms F] [hF₂ : ReflectsMo
 #print CategoryTheory.Functor.splitEpiCategoryImpOfIsEquivalence /-
 /-- If `F : C ⥤ D` is an equivalence of categories and `C` is a `split_epi_category`,
 then `D` also is. -/
-def splitEpiCategoryImpOfIsEquivalence [IsEquivalence F] [SplitEpiCategory C] :
-    SplitEpiCategory D :=
+def splitEpiCategoryImpOfIsEquivalence [CategoryTheory.Functor.IsEquivalence F]
+    [SplitEpiCategory C] : SplitEpiCategory D :=
   ⟨fun X Y f => by
     intro
     rw [← F.inv.is_split_epi_iff f]
@@ -381,8 +383,8 @@ theorem strongEpi_map_of_strongEpi (adj : F ⊣ F') (f : A ⟶ B) [h₁ : F'.Pre
 -/
 
 #print CategoryTheory.Adjunction.strongEpi_map_of_isEquivalence /-
-instance strongEpi_map_of_isEquivalence [IsEquivalence F] (f : A ⟶ B) [h : StrongEpi f] :
-    StrongEpi (F.map f) :=
+instance strongEpi_map_of_isEquivalence [CategoryTheory.Functor.IsEquivalence F] (f : A ⟶ B)
+    [h : StrongEpi f] : StrongEpi (F.map f) :=
   F.asEquivalence.toAdjunction.strongEpi_map_of_strongEpi f
 #align category_theory.adjunction.strong_epi_map_of_is_equivalence CategoryTheory.Adjunction.strongEpi_map_of_isEquivalence
 -/
@@ -395,7 +397,7 @@ variable {C D : Type _} [Category C] [Category D] {F : C ⥤ D} {A B : C} (f : A
 
 #print CategoryTheory.Functor.strongEpi_map_iff_strongEpi_of_isEquivalence /-
 @[simp]
-theorem strongEpi_map_iff_strongEpi_of_isEquivalence [IsEquivalence F] :
+theorem strongEpi_map_iff_strongEpi_of_isEquivalence [CategoryTheory.Functor.IsEquivalence F] :
     StrongEpi (F.map f) ↔ StrongEpi f := by
   constructor
   · intro

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

@@ -228,7 +228,7 @@ theorem preservesEpimorphsisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj :
         intro Z g h H
         replace H := congr_arg (adj.hom_equiv X Z) H
         rwa [adj.hom_equiv_naturality_left, adj.hom_equiv_naturality_left, cancel_epi,
-          Equiv.apply_eq_iff_eq] at H ⟩ }
+          Equiv.apply_eq_iff_eq] at H⟩ }
 #align category_theory.functor.preserves_epimorphsisms_of_adjunction CategoryTheory.Functor.preservesEpimorphsisms_of_adjunction
 -/
 
@@ -248,7 +248,7 @@ theorem preservesMonomorphisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj :
         intro Z g h H
         replace H := congr_arg (adj.hom_equiv Z Y).symm H
         rwa [adj.hom_equiv_naturality_right_symm, adj.hom_equiv_naturality_right_symm, cancel_mono,
-          Equiv.apply_eq_iff_eq] at H ⟩ }
+          Equiv.apply_eq_iff_eq] at H⟩ }
 #align category_theory.functor.preserves_monomorphisms_of_adjunction CategoryTheory.Functor.preservesMonomorphisms_of_adjunction
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2022 Markus Himmel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Markus Himmel
 -/
-import Mathbin.CategoryTheory.EpiMono
-import Mathbin.CategoryTheory.Limits.Shapes.StrongEpi
-import Mathbin.CategoryTheory.LiftingProperties.Adjunction
+import CategoryTheory.EpiMono
+import CategoryTheory.Limits.Shapes.StrongEpi
+import CategoryTheory.LiftingProperties.Adjunction
 
 #align_import category_theory.functor.epi_mono from "leanprover-community/mathlib"@"ef7acf407d265ad4081c8998687e994fa80ba70c"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Markus Himmel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.functor.epi_mono
-! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.EpiMono
 import Mathbin.CategoryTheory.Limits.Shapes.StrongEpi
 import Mathbin.CategoryTheory.LiftingProperties.Adjunction
 
+#align_import category_theory.functor.epi_mono from "leanprover-community/mathlib"@"ef7acf407d265ad4081c8998687e994fa80ba70c"
+
 /-!
 # Preservation and reflection of monomorphisms and epimorphisms
 

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

@@ -39,10 +39,12 @@ class PreservesMonomorphisms (F : C ⥤ D) : Prop where
 #align category_theory.functor.preserves_monomorphisms CategoryTheory.Functor.PreservesMonomorphisms
 -/
 
+#print CategoryTheory.Functor.map_mono /-
 instance map_mono (F : C ⥤ D) [PreservesMonomorphisms F] {X Y : C} (f : X ⟶ Y) [Mono f] :
     Mono (F.map f) :=
   PreservesMonomorphisms.preserves f
 #align category_theory.functor.map_mono CategoryTheory.Functor.map_mono
+-/
 
 #print CategoryTheory.Functor.PreservesEpimorphisms /-
 /-- A functor preserves epimorphisms if it maps epimorphisms to epimorphisms. -/
@@ -51,10 +53,12 @@ class PreservesEpimorphisms (F : C ⥤ D) : Prop where
 #align category_theory.functor.preserves_epimorphisms CategoryTheory.Functor.PreservesEpimorphisms
 -/
 
+#print CategoryTheory.Functor.map_epi /-
 instance map_epi (F : C ⥤ D) [PreservesEpimorphisms F] {X Y : C} (f : X ⟶ Y) [Epi f] :
     Epi (F.map f) :=
   PreservesEpimorphisms.preserves f
 #align category_theory.functor.map_epi CategoryTheory.Functor.map_epi
+-/
 
 #print CategoryTheory.Functor.ReflectsMonomorphisms /-
 /-- A functor reflects monomorphisms if morphisms that are mapped to monomorphisms are themselves
@@ -64,10 +68,12 @@ class ReflectsMonomorphisms (F : C ⥤ D) : Prop where
 #align category_theory.functor.reflects_monomorphisms CategoryTheory.Functor.ReflectsMonomorphisms
 -/
 
+#print CategoryTheory.Functor.mono_of_mono_map /-
 theorem mono_of_mono_map (F : C ⥤ D) [ReflectsMonomorphisms F] {X Y : C} {f : X ⟶ Y}
     (h : Mono (F.map f)) : Mono f :=
   ReflectsMonomorphisms.reflects f h
 #align category_theory.functor.mono_of_mono_map CategoryTheory.Functor.mono_of_mono_map
+-/
 
 #print CategoryTheory.Functor.ReflectsEpimorphisms /-
 /-- A functor reflects epimorphisms if morphisms that are mapped to epimorphisms are themselves
@@ -77,10 +83,12 @@ class ReflectsEpimorphisms (F : C ⥤ D) : Prop where
 #align category_theory.functor.reflects_epimorphisms CategoryTheory.Functor.ReflectsEpimorphisms
 -/
 
+#print CategoryTheory.Functor.epi_of_epi_map /-
 theorem epi_of_epi_map (F : C ⥤ D) [ReflectsEpimorphisms F] {X Y : C} {f : X ⟶ Y}
     (h : Epi (F.map f)) : Epi f :=
   ReflectsEpimorphisms.reflects f h
 #align category_theory.functor.epi_of_epi_map CategoryTheory.Functor.epi_of_epi_map
+-/
 
 #print CategoryTheory.Functor.preservesMonomorphisms_comp /-
 instance preservesMonomorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [PreservesMonomorphisms F]
@@ -276,6 +284,7 @@ section
 
 variable (F : C ⥤ D) {X Y : C} (f : X ⟶ Y)
 
+#print CategoryTheory.Functor.splitEpiEquiv /-
 /-- If `F` is a fully faithful functor, split epimorphisms are preserved and reflected by `F`. -/
 def splitEpiEquiv [Full F] [Faithful F] : SplitEpi f ≃ SplitEpi (F.map f)
     where
@@ -288,7 +297,9 @@ def splitEpiEquiv [Full F] [Faithful F] : SplitEpi f ≃ SplitEpi (F.map f)
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.functor.split_epi_equiv CategoryTheory.Functor.splitEpiEquiv
+-/
 
+#print CategoryTheory.Functor.isSplitEpi_iff /-
 @[simp]
 theorem isSplitEpi_iff [Full F] [Faithful F] : IsSplitEpi (F.map f) ↔ IsSplitEpi f :=
   by
@@ -296,7 +307,9 @@ theorem isSplitEpi_iff [Full F] [Faithful F] : IsSplitEpi (F.map f) ↔ IsSplitE
   · intro h; exact is_split_epi.mk' ((split_epi_equiv F f).invFun h.exists_split_epi.some)
   · intro h; exact is_split_epi.mk' ((split_epi_equiv F f).toFun h.exists_split_epi.some)
 #align category_theory.functor.is_split_epi_iff CategoryTheory.Functor.isSplitEpi_iff
+-/
 
+#print CategoryTheory.Functor.splitMonoEquiv /-
 /-- If `F` is a fully faithful functor, split monomorphisms are preserved and reflected by `F`. -/
 def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
     where
@@ -309,7 +322,9 @@ def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.functor.split_mono_equiv CategoryTheory.Functor.splitMonoEquiv
+-/
 
+#print CategoryTheory.Functor.isSplitMono_iff /-
 @[simp]
 theorem isSplitMono_iff [Full F] [Faithful F] : IsSplitMono (F.map f) ↔ IsSplitMono f :=
   by
@@ -317,7 +332,9 @@ theorem isSplitMono_iff [Full F] [Faithful F] : IsSplitMono (F.map f) ↔ IsSpli
   · intro h; exact is_split_mono.mk' ((split_mono_equiv F f).invFun h.exists_split_mono.some)
   · intro h; exact is_split_mono.mk' ((split_mono_equiv F f).toFun h.exists_split_mono.some)
 #align category_theory.functor.is_split_mono_iff CategoryTheory.Functor.isSplitMono_iff
+-/
 
+#print CategoryTheory.Functor.epi_map_iff_epi /-
 @[simp]
 theorem epi_map_iff_epi [hF₁ : PreservesEpimorphisms F] [hF₂ : ReflectsEpimorphisms F] :
     Epi (F.map f) ↔ Epi f := by
@@ -326,7 +343,9 @@ theorem epi_map_iff_epi [hF₁ : PreservesEpimorphisms F] [hF₂ : ReflectsEpimo
   · intro h
     exact F.map_epi f
 #align category_theory.functor.epi_map_iff_epi CategoryTheory.Functor.epi_map_iff_epi
+-/
 
+#print CategoryTheory.Functor.mono_map_iff_mono /-
 @[simp]
 theorem mono_map_iff_mono [hF₁ : PreservesMonomorphisms F] [hF₂ : ReflectsMonomorphisms F] :
     Mono (F.map f) ↔ Mono f := by
@@ -335,6 +354,7 @@ theorem mono_map_iff_mono [hF₁ : PreservesMonomorphisms F] [hF₂ : ReflectsMo
   · intro h
     exact F.map_mono f
 #align category_theory.functor.mono_map_iff_mono CategoryTheory.Functor.mono_map_iff_mono
+-/
 
 #print CategoryTheory.Functor.splitEpiCategoryImpOfIsEquivalence /-
 /-- If `F : C ⥤ D` is an equivalence of categories and `C` is a `split_epi_category`,
@@ -356,15 +376,19 @@ namespace CategoryTheory.Adjunction
 
 variable {C D : Type _} [Category C] [Category D] {F : C ⥤ D} {F' : D ⥤ C} {A B : C}
 
+#print CategoryTheory.Adjunction.strongEpi_map_of_strongEpi /-
 theorem strongEpi_map_of_strongEpi (adj : F ⊣ F') (f : A ⟶ B) [h₁ : F'.PreservesMonomorphisms]
     [h₂ : F.PreservesEpimorphisms] [StrongEpi f] : StrongEpi (F.map f) :=
   ⟨inferInstance, fun X Y Z => by intro; rw [adj.has_lifting_property_iff]; infer_instance⟩
 #align category_theory.adjunction.strong_epi_map_of_strong_epi CategoryTheory.Adjunction.strongEpi_map_of_strongEpi
+-/
 
+#print CategoryTheory.Adjunction.strongEpi_map_of_isEquivalence /-
 instance strongEpi_map_of_isEquivalence [IsEquivalence F] (f : A ⟶ B) [h : StrongEpi f] :
     StrongEpi (F.map f) :=
   F.asEquivalence.toAdjunction.strongEpi_map_of_strongEpi f
 #align category_theory.adjunction.strong_epi_map_of_is_equivalence CategoryTheory.Adjunction.strongEpi_map_of_isEquivalence
+-/
 
 end CategoryTheory.Adjunction
 
@@ -372,6 +396,7 @@ namespace CategoryTheory.Functor
 
 variable {C D : Type _} [Category C] [Category D] {F : C ⥤ D} {A B : C} (f : A ⟶ B)
 
+#print CategoryTheory.Functor.strongEpi_map_iff_strongEpi_of_isEquivalence /-
 @[simp]
 theorem strongEpi_map_iff_strongEpi_of_isEquivalence [IsEquivalence F] :
     StrongEpi (F.map f) ↔ StrongEpi f := by
@@ -384,6 +409,7 @@ theorem strongEpi_map_iff_strongEpi_of_isEquivalence [IsEquivalence F] :
   · intro
     infer_instance
 #align category_theory.functor.strong_epi_map_iff_strong_epi_of_is_equivalence CategoryTheory.Functor.strongEpi_map_iff_strongEpi_of_isEquivalence
+-/
 
 end CategoryTheory.Functor
 

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

@@ -145,7 +145,7 @@ theorem preservesMonomorphisms.of_iso {F G : C ⥤ D} [PreservesMonomorphisms F]
     preserves := fun X Y f h =>
       by
       haveI : mono (F.map f ≫ (α.app Y).Hom) := mono_comp _ _
-      convert(mono_comp _ _ : mono ((α.app X).inv ≫ F.map f ≫ (α.app Y).Hom))
+      convert (mono_comp _ _ : mono ((α.app X).inv ≫ F.map f ≫ (α.app Y).Hom))
       rw [iso.eq_inv_comp, iso.app_hom, iso.app_hom, nat_trans.naturality] }
 #align category_theory.functor.preserves_monomorphisms.of_iso CategoryTheory.Functor.preservesMonomorphisms.of_iso
 -/
@@ -164,7 +164,7 @@ theorem preservesEpimorphisms.of_iso {F G : C ⥤ D} [PreservesEpimorphisms F] (
     preserves := fun X Y f h =>
       by
       haveI : epi (F.map f ≫ (α.app Y).Hom) := epi_comp _ _
-      convert(epi_comp _ _ : epi ((α.app X).inv ≫ F.map f ≫ (α.app Y).Hom))
+      convert (epi_comp _ _ : epi ((α.app X).inv ≫ F.map f ≫ (α.app Y).Hom))
       rw [iso.eq_inv_comp, iso.app_hom, iso.app_hom, nat_trans.naturality] }
 #align category_theory.functor.preserves_epimorphisms.of_iso CategoryTheory.Functor.preservesEpimorphisms.of_iso
 -/
@@ -183,7 +183,7 @@ theorem reflectsMonomorphisms.of_iso {F G : C ⥤ D} [ReflectsMonomorphisms F] (
     reflects := fun X Y f h => by
       apply F.mono_of_mono_map
       haveI : mono (G.map f ≫ (α.app Y).inv) := mono_comp _ _
-      convert(mono_comp _ _ : mono ((α.app X).Hom ≫ G.map f ≫ (α.app Y).inv))
+      convert (mono_comp _ _ : mono ((α.app X).Hom ≫ G.map f ≫ (α.app Y).inv))
       rw [← category.assoc, iso.eq_comp_inv, iso.app_hom, iso.app_hom, nat_trans.naturality] }
 #align category_theory.functor.reflects_monomorphisms.of_iso CategoryTheory.Functor.reflectsMonomorphisms.of_iso
 -/
@@ -202,7 +202,7 @@ theorem reflectsEpimorphisms.of_iso {F G : C ⥤ D} [ReflectsEpimorphisms F] (α
     reflects := fun X Y f h => by
       apply F.epi_of_epi_map
       haveI : epi (G.map f ≫ (α.app Y).inv) := epi_comp _ _
-      convert(epi_comp _ _ : epi ((α.app X).Hom ≫ G.map f ≫ (α.app Y).inv))
+      convert (epi_comp _ _ : epi ((α.app X).Hom ≫ G.map f ≫ (α.app Y).inv))
       rw [← category.assoc, iso.eq_comp_inv, iso.app_hom, iso.app_hom, nat_trans.naturality] }
 #align category_theory.functor.reflects_epimorphisms.of_iso CategoryTheory.Functor.reflectsEpimorphisms.of_iso
 -/

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

@@ -223,7 +223,7 @@ theorem preservesEpimorphsisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj :
         intro Z g h H
         replace H := congr_arg (adj.hom_equiv X Z) H
         rwa [adj.hom_equiv_naturality_left, adj.hom_equiv_naturality_left, cancel_epi,
-          Equiv.apply_eq_iff_eq] at H⟩ }
+          Equiv.apply_eq_iff_eq] at H ⟩ }
 #align category_theory.functor.preserves_epimorphsisms_of_adjunction CategoryTheory.Functor.preservesEpimorphsisms_of_adjunction
 -/
 
@@ -243,7 +243,7 @@ theorem preservesMonomorphisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj :
         intro Z g h H
         replace H := congr_arg (adj.hom_equiv Z Y).symm H
         rwa [adj.hom_equiv_naturality_right_symm, adj.hom_equiv_naturality_right_symm, cancel_mono,
-          Equiv.apply_eq_iff_eq] at H⟩ }
+          Equiv.apply_eq_iff_eq] at H ⟩ }
 #align category_theory.functor.preserves_monomorphisms_of_adjunction CategoryTheory.Functor.preservesMonomorphisms_of_adjunction
 -/
 
@@ -358,7 +358,7 @@ variable {C D : Type _} [Category C] [Category D] {F : C ⥤ D} {F' : D ⥤ C} {
 
 theorem strongEpi_map_of_strongEpi (adj : F ⊣ F') (f : A ⟶ B) [h₁ : F'.PreservesMonomorphisms]
     [h₂ : F.PreservesEpimorphisms] [StrongEpi f] : StrongEpi (F.map f) :=
-  ⟨inferInstance, fun X Y Z => by intro ; rw [adj.has_lifting_property_iff]; infer_instance⟩
+  ⟨inferInstance, fun X Y Z => by intro; rw [adj.has_lifting_property_iff]; infer_instance⟩
 #align category_theory.adjunction.strong_epi_map_of_strong_epi CategoryTheory.Adjunction.strongEpi_map_of_strongEpi
 
 instance strongEpi_map_of_isEquivalence [IsEquivalence F] (f : A ⟶ B) [h : StrongEpi f] :

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

@@ -39,12 +39,6 @@ class PreservesMonomorphisms (F : C ⥤ D) : Prop where
 #align category_theory.functor.preserves_monomorphisms CategoryTheory.Functor.PreservesMonomorphisms
 -/
 
-/- warning: category_theory.functor.map_mono -> CategoryTheory.Functor.map_mono is a dubious translation:
-lean 3 declaration is
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 instance map_mono (F : C ⥤ D) [PreservesMonomorphisms F] {X Y : C} (f : X ⟶ Y) [Mono f] :
     Mono (F.map f) :=
   PreservesMonomorphisms.preserves f
@@ -57,12 +51,6 @@ class PreservesEpimorphisms (F : C ⥤ D) : Prop where
 #align category_theory.functor.preserves_epimorphisms CategoryTheory.Functor.PreservesEpimorphisms
 -/
 
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 instance map_epi (F : C ⥤ D) [PreservesEpimorphisms F] {X Y : C} (f : X ⟶ Y) [Epi f] :
     Epi (F.map f) :=
   PreservesEpimorphisms.preserves f
@@ -76,12 +64,6 @@ class ReflectsMonomorphisms (F : C ⥤ D) : Prop where
 #align category_theory.functor.reflects_monomorphisms CategoryTheory.Functor.ReflectsMonomorphisms
 -/
 
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 theorem mono_of_mono_map (F : C ⥤ D) [ReflectsMonomorphisms F] {X Y : C} {f : X ⟶ Y}
     (h : Mono (F.map f)) : Mono f :=
   ReflectsMonomorphisms.reflects f h
@@ -95,12 +77,6 @@ class ReflectsEpimorphisms (F : C ⥤ D) : Prop where
 #align category_theory.functor.reflects_epimorphisms CategoryTheory.Functor.ReflectsEpimorphisms
 -/
 
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 theorem epi_of_epi_map (F : C ⥤ D) [ReflectsEpimorphisms F] {X Y : C} {f : X ⟶ Y}
     (h : Epi (F.map f)) : Epi f :=
   ReflectsEpimorphisms.reflects f h
@@ -300,12 +276,6 @@ section
 
 variable (F : C ⥤ D) {X Y : C} (f : X ⟶ Y)
 
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 /-- If `F` is a fully faithful functor, split epimorphisms are preserved and reflected by `F`. -/
 def splitEpiEquiv [Full F] [Faithful F] : SplitEpi f ≃ SplitEpi (F.map f)
     where
@@ -319,12 +289,6 @@ def splitEpiEquiv [Full F] [Faithful F] : SplitEpi f ≃ SplitEpi (F.map f)
   right_inv := by tidy
 #align category_theory.functor.split_epi_equiv CategoryTheory.Functor.splitEpiEquiv
 
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 @[simp]
 theorem isSplitEpi_iff [Full F] [Faithful F] : IsSplitEpi (F.map f) ↔ IsSplitEpi f :=
   by
@@ -333,12 +297,6 @@ theorem isSplitEpi_iff [Full F] [Faithful F] : IsSplitEpi (F.map f) ↔ IsSplitE
   · intro h; exact is_split_epi.mk' ((split_epi_equiv F f).toFun h.exists_split_epi.some)
 #align category_theory.functor.is_split_epi_iff CategoryTheory.Functor.isSplitEpi_iff
 
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 /-- If `F` is a fully faithful functor, split monomorphisms are preserved and reflected by `F`. -/
 def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
     where
@@ -352,12 +310,6 @@ def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
   right_inv := by tidy
 #align category_theory.functor.split_mono_equiv CategoryTheory.Functor.splitMonoEquiv
 
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 @[simp]
 theorem isSplitMono_iff [Full F] [Faithful F] : IsSplitMono (F.map f) ↔ IsSplitMono f :=
   by
@@ -366,12 +318,6 @@ theorem isSplitMono_iff [Full F] [Faithful F] : IsSplitMono (F.map f) ↔ IsSpli
   · intro h; exact is_split_mono.mk' ((split_mono_equiv F f).toFun h.exists_split_mono.some)
 #align category_theory.functor.is_split_mono_iff CategoryTheory.Functor.isSplitMono_iff
 
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 @[simp]
 theorem epi_map_iff_epi [hF₁ : PreservesEpimorphisms F] [hF₂ : ReflectsEpimorphisms F] :
     Epi (F.map f) ↔ Epi f := by
@@ -381,12 +327,6 @@ theorem epi_map_iff_epi [hF₁ : PreservesEpimorphisms F] [hF₂ : ReflectsEpimo
     exact F.map_epi f
 #align category_theory.functor.epi_map_iff_epi CategoryTheory.Functor.epi_map_iff_epi
 
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 @[simp]
 theorem mono_map_iff_mono [hF₁ : PreservesMonomorphisms F] [hF₂ : ReflectsMonomorphisms F] :
     Mono (F.map f) ↔ Mono f := by
@@ -416,23 +356,11 @@ namespace CategoryTheory.Adjunction
 
 variable {C D : Type _} [Category C] [Category D] {F : C ⥤ D} {F' : D ⥤ C} {A B : C}
 
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 theorem strongEpi_map_of_strongEpi (adj : F ⊣ F') (f : A ⟶ B) [h₁ : F'.PreservesMonomorphisms]
     [h₂ : F.PreservesEpimorphisms] [StrongEpi f] : StrongEpi (F.map f) :=
   ⟨inferInstance, fun X Y Z => by intro ; rw [adj.has_lifting_property_iff]; infer_instance⟩
 #align category_theory.adjunction.strong_epi_map_of_strong_epi CategoryTheory.Adjunction.strongEpi_map_of_strongEpi
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.adjunction.strong_epi_map_of_is_equivalence CategoryTheory.Adjunction.strongEpi_map_of_isEquivalenceₓ'. -/
 instance strongEpi_map_of_isEquivalence [IsEquivalence F] (f : A ⟶ B) [h : StrongEpi f] :
     StrongEpi (F.map f) :=
   F.asEquivalence.toAdjunction.strongEpi_map_of_strongEpi f
@@ -444,12 +372,6 @@ namespace CategoryTheory.Functor
 
 variable {C D : Type _} [Category C] [Category D] {F : C ⥤ D} {A B : C} (f : A ⟶ B)
 
-/- warning: category_theory.functor.strong_epi_map_iff_strong_epi_of_is_equivalence -> CategoryTheory.Functor.strongEpi_map_iff_strongEpi_of_isEquivalence is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align category_theory.functor.strong_epi_map_iff_strong_epi_of_is_equivalence CategoryTheory.Functor.strongEpi_map_iff_strongEpi_of_isEquivalenceₓ'. -/
 @[simp]
 theorem strongEpi_map_iff_strongEpi_of_isEquivalence [IsEquivalence F] :
     StrongEpi (F.map f) ↔ StrongEpi f := by

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

@@ -109,18 +109,14 @@ theorem epi_of_epi_map (F : C ⥤ D) [ReflectsEpimorphisms F] {X Y : C} {f : X 
 #print CategoryTheory.Functor.preservesMonomorphisms_comp /-
 instance preservesMonomorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [PreservesMonomorphisms F]
     [PreservesMonomorphisms G] : PreservesMonomorphisms (F ⋙ G)
-    where preserves X Y f h := by
-    rw [comp_map]
-    exact inferInstance
+    where preserves X Y f h := by rw [comp_map]; exact inferInstance
 #align category_theory.functor.preserves_monomorphisms_comp CategoryTheory.Functor.preservesMonomorphisms_comp
 -/
 
 #print CategoryTheory.Functor.preservesEpimorphisms_comp /-
 instance preservesEpimorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [PreservesEpimorphisms F]
     [PreservesEpimorphisms G] : PreservesEpimorphisms (F ⋙ G)
-    where preserves X Y f h := by
-    rw [comp_map]
-    exact inferInstance
+    where preserves X Y f h := by rw [comp_map]; exact inferInstance
 #align category_theory.functor.preserves_epimorphisms_comp CategoryTheory.Functor.preservesEpimorphisms_comp
 -/
 
@@ -333,10 +329,8 @@ Case conversion may be inaccurate. Consider using '#align category_theory.functo
 theorem isSplitEpi_iff [Full F] [Faithful F] : IsSplitEpi (F.map f) ↔ IsSplitEpi f :=
   by
   constructor
-  · intro h
-    exact is_split_epi.mk' ((split_epi_equiv F f).invFun h.exists_split_epi.some)
-  · intro h
-    exact is_split_epi.mk' ((split_epi_equiv F f).toFun h.exists_split_epi.some)
+  · intro h; exact is_split_epi.mk' ((split_epi_equiv F f).invFun h.exists_split_epi.some)
+  · intro h; exact is_split_epi.mk' ((split_epi_equiv F f).toFun h.exists_split_epi.some)
 #align category_theory.functor.is_split_epi_iff CategoryTheory.Functor.isSplitEpi_iff
 
 /- warning: category_theory.functor.split_mono_equiv -> CategoryTheory.Functor.splitMonoEquiv is a dubious translation:
@@ -368,10 +362,8 @@ Case conversion may be inaccurate. Consider using '#align category_theory.functo
 theorem isSplitMono_iff [Full F] [Faithful F] : IsSplitMono (F.map f) ↔ IsSplitMono f :=
   by
   constructor
-  · intro h
-    exact is_split_mono.mk' ((split_mono_equiv F f).invFun h.exists_split_mono.some)
-  · intro h
-    exact is_split_mono.mk' ((split_mono_equiv F f).toFun h.exists_split_mono.some)
+  · intro h; exact is_split_mono.mk' ((split_mono_equiv F f).invFun h.exists_split_mono.some)
+  · intro h; exact is_split_mono.mk' ((split_mono_equiv F f).toFun h.exists_split_mono.some)
 #align category_theory.functor.is_split_mono_iff CategoryTheory.Functor.isSplitMono_iff
 
 /- warning: category_theory.functor.epi_map_iff_epi -> CategoryTheory.Functor.epi_map_iff_epi is a dubious translation:
@@ -432,10 +424,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.adjunction.strong_epi_map_of_strong_epi CategoryTheory.Adjunction.strongEpi_map_of_strongEpiₓ'. -/
 theorem strongEpi_map_of_strongEpi (adj : F ⊣ F') (f : A ⟶ B) [h₁ : F'.PreservesMonomorphisms]
     [h₂ : F.PreservesEpimorphisms] [StrongEpi f] : StrongEpi (F.map f) :=
-  ⟨inferInstance, fun X Y Z => by
-    intro
-    rw [adj.has_lifting_property_iff]
-    infer_instance⟩
+  ⟨inferInstance, fun X Y Z => by intro ; rw [adj.has_lifting_property_iff]; infer_instance⟩
 #align category_theory.adjunction.strong_epi_map_of_strong_epi CategoryTheory.Adjunction.strongEpi_map_of_strongEpi
 
 /- warning: category_theory.adjunction.strong_epi_map_of_is_equivalence -> CategoryTheory.Adjunction.strongEpi_map_of_isEquivalence is a dubious translation:

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -173,7 +173,7 @@ theorem preservesMonomorphisms.of_iso {F G : C ⥤ D} [PreservesMonomorphisms F]
     preserves := fun X Y f h =>
       by
       haveI : mono (F.map f ≫ (α.app Y).Hom) := mono_comp _ _
-      convert (mono_comp _ _ : mono ((α.app X).inv ≫ F.map f ≫ (α.app Y).Hom))
+      convert(mono_comp _ _ : mono ((α.app X).inv ≫ F.map f ≫ (α.app Y).Hom))
       rw [iso.eq_inv_comp, iso.app_hom, iso.app_hom, nat_trans.naturality] }
 #align category_theory.functor.preserves_monomorphisms.of_iso CategoryTheory.Functor.preservesMonomorphisms.of_iso
 -/
@@ -192,7 +192,7 @@ theorem preservesEpimorphisms.of_iso {F G : C ⥤ D} [PreservesEpimorphisms F] (
     preserves := fun X Y f h =>
       by
       haveI : epi (F.map f ≫ (α.app Y).Hom) := epi_comp _ _
-      convert (epi_comp _ _ : epi ((α.app X).inv ≫ F.map f ≫ (α.app Y).Hom))
+      convert(epi_comp _ _ : epi ((α.app X).inv ≫ F.map f ≫ (α.app Y).Hom))
       rw [iso.eq_inv_comp, iso.app_hom, iso.app_hom, nat_trans.naturality] }
 #align category_theory.functor.preserves_epimorphisms.of_iso CategoryTheory.Functor.preservesEpimorphisms.of_iso
 -/
@@ -211,7 +211,7 @@ theorem reflectsMonomorphisms.of_iso {F G : C ⥤ D} [ReflectsMonomorphisms F] (
     reflects := fun X Y f h => by
       apply F.mono_of_mono_map
       haveI : mono (G.map f ≫ (α.app Y).inv) := mono_comp _ _
-      convert (mono_comp _ _ : mono ((α.app X).Hom ≫ G.map f ≫ (α.app Y).inv))
+      convert(mono_comp _ _ : mono ((α.app X).Hom ≫ G.map f ≫ (α.app Y).inv))
       rw [← category.assoc, iso.eq_comp_inv, iso.app_hom, iso.app_hom, nat_trans.naturality] }
 #align category_theory.functor.reflects_monomorphisms.of_iso CategoryTheory.Functor.reflectsMonomorphisms.of_iso
 -/
@@ -230,7 +230,7 @@ theorem reflectsEpimorphisms.of_iso {F G : C ⥤ D} [ReflectsEpimorphisms F] (α
     reflects := fun X Y f h => by
       apply F.epi_of_epi_map
       haveI : epi (G.map f ≫ (α.app Y).inv) := epi_comp _ _
-      convert (epi_comp _ _ : epi ((α.app X).Hom ≫ G.map f ≫ (α.app Y).inv))
+      convert(epi_comp _ _ : epi ((α.app X).Hom ≫ G.map f ≫ (α.app Y).inv))
       rw [← category.assoc, iso.eq_comp_inv, iso.app_hom, iso.app_hom, nat_trans.naturality] }
 #align category_theory.functor.reflects_epimorphisms.of_iso CategoryTheory.Functor.reflectsEpimorphisms.of_iso
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Markus Himmel
 
 ! This file was ported from Lean 3 source module category_theory.functor.epi_mono
-! leanprover-community/mathlib commit 563aed347eb59dc4181cb732cda0d124d736eaa3
+! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
 ! 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.LiftingProperties.Adjunction
 /-!
 # Preservation and reflection of monomorphisms and epimorphisms
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We provide typeclasses that state that a functor preserves or reflects monomorphisms or
 epimorphisms.
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

@@ -29,93 +29,142 @@ namespace CategoryTheory.Functor
 variable {C : Type u₁} [Category.{v₁} C] {D : Type u₂} [Category.{v₂} D] {E : Type u₃}
   [Category.{v₃} E]
 
+#print CategoryTheory.Functor.PreservesMonomorphisms /-
 /-- A functor preserves monomorphisms if it maps monomorphisms to monomorphisms. -/
 class PreservesMonomorphisms (F : C ⥤ D) : Prop where
   preserves : ∀ {X Y : C} (f : X ⟶ Y) [Mono f], Mono (F.map f)
 #align category_theory.functor.preserves_monomorphisms CategoryTheory.Functor.PreservesMonomorphisms
+-/
 
+/- warning: category_theory.functor.map_mono -> CategoryTheory.Functor.map_mono is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_mono CategoryTheory.Functor.map_monoₓ'. -/
 instance map_mono (F : C ⥤ D) [PreservesMonomorphisms F] {X Y : C} (f : X ⟶ Y) [Mono f] :
     Mono (F.map f) :=
   PreservesMonomorphisms.preserves f
 #align category_theory.functor.map_mono CategoryTheory.Functor.map_mono
 
+#print CategoryTheory.Functor.PreservesEpimorphisms /-
 /-- A functor preserves epimorphisms if it maps epimorphisms to epimorphisms. -/
 class PreservesEpimorphisms (F : C ⥤ D) : Prop where
   preserves : ∀ {X Y : C} (f : X ⟶ Y) [Epi f], Epi (F.map f)
 #align category_theory.functor.preserves_epimorphisms CategoryTheory.Functor.PreservesEpimorphisms
+-/
 
+/- warning: category_theory.functor.map_epi -> CategoryTheory.Functor.map_epi is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_epi CategoryTheory.Functor.map_epiₓ'. -/
 instance map_epi (F : C ⥤ D) [PreservesEpimorphisms F] {X Y : C} (f : X ⟶ Y) [Epi f] :
     Epi (F.map f) :=
   PreservesEpimorphisms.preserves f
 #align category_theory.functor.map_epi CategoryTheory.Functor.map_epi
 
+#print CategoryTheory.Functor.ReflectsMonomorphisms /-
 /-- A functor reflects monomorphisms if morphisms that are mapped to monomorphisms are themselves
     monomorphisms. -/
 class ReflectsMonomorphisms (F : C ⥤ D) : Prop where
   reflects : ∀ {X Y : C} (f : X ⟶ Y), Mono (F.map f) → Mono f
 #align category_theory.functor.reflects_monomorphisms CategoryTheory.Functor.ReflectsMonomorphisms
+-/
 
+/- warning: category_theory.functor.mono_of_mono_map -> CategoryTheory.Functor.mono_of_mono_map is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) [_inst_4 : CategoryTheory.Functor.ReflectsMonomorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] {X : C} {Y : C} {f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y}, (CategoryTheory.Mono.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X Y f)) -> (CategoryTheory.Mono.{u1, u3} C _inst_1 X Y f)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) [_inst_4 : CategoryTheory.Functor.ReflectsMonomorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] {X : C} {Y : C} {f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y}, (CategoryTheory.Mono.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X Y f)) -> (CategoryTheory.Mono.{u1, u3} C _inst_1 X Y f)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.mono_of_mono_map CategoryTheory.Functor.mono_of_mono_mapₓ'. -/
 theorem mono_of_mono_map (F : C ⥤ D) [ReflectsMonomorphisms F] {X Y : C} {f : X ⟶ Y}
     (h : Mono (F.map f)) : Mono f :=
   ReflectsMonomorphisms.reflects f h
 #align category_theory.functor.mono_of_mono_map CategoryTheory.Functor.mono_of_mono_map
 
+#print CategoryTheory.Functor.ReflectsEpimorphisms /-
 /-- A functor reflects epimorphisms if morphisms that are mapped to epimorphisms are themselves
     epimorphisms. -/
 class ReflectsEpimorphisms (F : C ⥤ D) : Prop where
   reflects : ∀ {X Y : C} (f : X ⟶ Y), Epi (F.map f) → Epi f
 #align category_theory.functor.reflects_epimorphisms CategoryTheory.Functor.ReflectsEpimorphisms
+-/
 
+/- warning: category_theory.functor.epi_of_epi_map -> CategoryTheory.Functor.epi_of_epi_map is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) [_inst_4 : CategoryTheory.Functor.ReflectsEpimorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] {X : C} {Y : C} {f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y}, (CategoryTheory.Epi.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X Y f)) -> (CategoryTheory.Epi.{u1, u3} C _inst_1 X Y f)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) [_inst_4 : CategoryTheory.Functor.ReflectsEpimorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] {X : C} {Y : C} {f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y}, (CategoryTheory.Epi.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X Y f)) -> (CategoryTheory.Epi.{u1, u3} C _inst_1 X Y f)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.epi_of_epi_map CategoryTheory.Functor.epi_of_epi_mapₓ'. -/
 theorem epi_of_epi_map (F : C ⥤ D) [ReflectsEpimorphisms F] {X Y : C} {f : X ⟶ Y}
     (h : Epi (F.map f)) : Epi f :=
   ReflectsEpimorphisms.reflects f h
 #align category_theory.functor.epi_of_epi_map CategoryTheory.Functor.epi_of_epi_map
 
+#print CategoryTheory.Functor.preservesMonomorphisms_comp /-
 instance preservesMonomorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [PreservesMonomorphisms F]
     [PreservesMonomorphisms G] : PreservesMonomorphisms (F ⋙ G)
     where preserves X Y f h := by
     rw [comp_map]
     exact inferInstance
 #align category_theory.functor.preserves_monomorphisms_comp CategoryTheory.Functor.preservesMonomorphisms_comp
+-/
 
+#print CategoryTheory.Functor.preservesEpimorphisms_comp /-
 instance preservesEpimorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [PreservesEpimorphisms F]
     [PreservesEpimorphisms G] : PreservesEpimorphisms (F ⋙ G)
     where preserves X Y f h := by
     rw [comp_map]
     exact inferInstance
 #align category_theory.functor.preserves_epimorphisms_comp CategoryTheory.Functor.preservesEpimorphisms_comp
+-/
 
+#print CategoryTheory.Functor.reflectsMonomorphisms_comp /-
 instance reflectsMonomorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [ReflectsMonomorphisms F]
     [ReflectsMonomorphisms G] : ReflectsMonomorphisms (F ⋙ G)
     where reflects X Y f h := F.mono_of_mono_map (G.mono_of_mono_map h)
 #align category_theory.functor.reflects_monomorphisms_comp CategoryTheory.Functor.reflectsMonomorphisms_comp
+-/
 
+#print CategoryTheory.Functor.reflectsEpimorphisms_comp /-
 instance reflectsEpimorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [ReflectsEpimorphisms F]
     [ReflectsEpimorphisms G] : ReflectsEpimorphisms (F ⋙ G)
     where reflects X Y f h := F.epi_of_epi_map (G.epi_of_epi_map h)
 #align category_theory.functor.reflects_epimorphisms_comp CategoryTheory.Functor.reflectsEpimorphisms_comp
+-/
 
+#print CategoryTheory.Functor.preservesEpimorphisms_of_preserves_of_reflects /-
 theorem preservesEpimorphisms_of_preserves_of_reflects (F : C ⥤ D) (G : D ⥤ E)
     [PreservesEpimorphisms (F ⋙ G)] [ReflectsEpimorphisms G] : PreservesEpimorphisms F :=
   ⟨fun X Y f hf => G.epi_of_epi_map <| show Epi ((F ⋙ G).map f) from inferInstance⟩
 #align category_theory.functor.preserves_epimorphisms_of_preserves_of_reflects CategoryTheory.Functor.preservesEpimorphisms_of_preserves_of_reflects
+-/
 
+#print CategoryTheory.Functor.preservesMonomorphisms_of_preserves_of_reflects /-
 theorem preservesMonomorphisms_of_preserves_of_reflects (F : C ⥤ D) (G : D ⥤ E)
     [PreservesMonomorphisms (F ⋙ G)] [ReflectsMonomorphisms G] : PreservesMonomorphisms F :=
   ⟨fun X Y f hf => G.mono_of_mono_map <| show Mono ((F ⋙ G).map f) from inferInstance⟩
 #align category_theory.functor.preserves_monomorphisms_of_preserves_of_reflects CategoryTheory.Functor.preservesMonomorphisms_of_preserves_of_reflects
+-/
 
+#print CategoryTheory.Functor.reflectsEpimorphisms_of_preserves_of_reflects /-
 theorem reflectsEpimorphisms_of_preserves_of_reflects (F : C ⥤ D) (G : D ⥤ E)
     [PreservesEpimorphisms G] [ReflectsEpimorphisms (F ⋙ G)] : ReflectsEpimorphisms F :=
   ⟨fun X Y f hf => (F ⋙ G).epi_of_epi_map <| show Epi (G.map (F.map f)) from inferInstance⟩
 #align category_theory.functor.reflects_epimorphisms_of_preserves_of_reflects CategoryTheory.Functor.reflectsEpimorphisms_of_preserves_of_reflects
+-/
 
+#print CategoryTheory.Functor.reflectsMonomorphisms_of_preserves_of_reflects /-
 theorem reflectsMonomorphisms_of_preserves_of_reflects (F : C ⥤ D) (G : D ⥤ E)
     [PreservesMonomorphisms G] [ReflectsMonomorphisms (F ⋙ G)] : ReflectsMonomorphisms F :=
   ⟨fun X Y f hf => (F ⋙ G).mono_of_mono_map <| show Mono (G.map (F.map f)) from inferInstance⟩
 #align category_theory.functor.reflects_monomorphisms_of_preserves_of_reflects CategoryTheory.Functor.reflectsMonomorphisms_of_preserves_of_reflects
+-/
 
-theorem PreservesMonomorphisms.of_iso {F G : C ⥤ D} [PreservesMonomorphisms F] (α : F ≅ G) :
+#print CategoryTheory.Functor.preservesMonomorphisms.of_iso /-
+theorem preservesMonomorphisms.of_iso {F G : C ⥤ D} [PreservesMonomorphisms F] (α : F ≅ G) :
     PreservesMonomorphisms G :=
   {
     preserves := fun X Y f h =>
@@ -123,14 +172,18 @@ theorem PreservesMonomorphisms.of_iso {F G : C ⥤ D} [PreservesMonomorphisms F]
       haveI : mono (F.map f ≫ (α.app Y).Hom) := mono_comp _ _
       convert (mono_comp _ _ : mono ((α.app X).inv ≫ F.map f ≫ (α.app Y).Hom))
       rw [iso.eq_inv_comp, iso.app_hom, iso.app_hom, nat_trans.naturality] }
-#align category_theory.functor.preserves_monomorphisms.of_iso CategoryTheory.Functor.PreservesMonomorphisms.of_iso
+#align category_theory.functor.preserves_monomorphisms.of_iso CategoryTheory.Functor.preservesMonomorphisms.of_iso
+-/
 
-theorem PreservesMonomorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
+#print CategoryTheory.Functor.preservesMonomorphisms.iso_iff /-
+theorem preservesMonomorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
     PreservesMonomorphisms F ↔ PreservesMonomorphisms G :=
   ⟨fun h => preserves_monomorphisms.of_iso α, fun h => preserves_monomorphisms.of_iso α.symm⟩
-#align category_theory.functor.preserves_monomorphisms.iso_iff CategoryTheory.Functor.PreservesMonomorphisms.iso_iff
+#align category_theory.functor.preserves_monomorphisms.iso_iff CategoryTheory.Functor.preservesMonomorphisms.iso_iff
+-/
 
-theorem PreservesEpimorphisms.of_iso {F G : C ⥤ D} [PreservesEpimorphisms F] (α : F ≅ G) :
+#print CategoryTheory.Functor.preservesEpimorphisms.of_iso /-
+theorem preservesEpimorphisms.of_iso {F G : C ⥤ D} [PreservesEpimorphisms F] (α : F ≅ G) :
     PreservesEpimorphisms G :=
   {
     preserves := fun X Y f h =>
@@ -138,14 +191,18 @@ theorem PreservesEpimorphisms.of_iso {F G : C ⥤ D} [PreservesEpimorphisms F] (
       haveI : epi (F.map f ≫ (α.app Y).Hom) := epi_comp _ _
       convert (epi_comp _ _ : epi ((α.app X).inv ≫ F.map f ≫ (α.app Y).Hom))
       rw [iso.eq_inv_comp, iso.app_hom, iso.app_hom, nat_trans.naturality] }
-#align category_theory.functor.preserves_epimorphisms.of_iso CategoryTheory.Functor.PreservesEpimorphisms.of_iso
+#align category_theory.functor.preserves_epimorphisms.of_iso CategoryTheory.Functor.preservesEpimorphisms.of_iso
+-/
 
-theorem PreservesEpimorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
+#print CategoryTheory.Functor.preservesEpimorphisms.iso_iff /-
+theorem preservesEpimorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
     PreservesEpimorphisms F ↔ PreservesEpimorphisms G :=
   ⟨fun h => preserves_epimorphisms.of_iso α, fun h => preserves_epimorphisms.of_iso α.symm⟩
-#align category_theory.functor.preserves_epimorphisms.iso_iff CategoryTheory.Functor.PreservesEpimorphisms.iso_iff
+#align category_theory.functor.preserves_epimorphisms.iso_iff CategoryTheory.Functor.preservesEpimorphisms.iso_iff
+-/
 
-theorem ReflectsMonomorphisms.of_iso {F G : C ⥤ D} [ReflectsMonomorphisms F] (α : F ≅ G) :
+#print CategoryTheory.Functor.reflectsMonomorphisms.of_iso /-
+theorem reflectsMonomorphisms.of_iso {F G : C ⥤ D} [ReflectsMonomorphisms F] (α : F ≅ G) :
     ReflectsMonomorphisms G :=
   {
     reflects := fun X Y f h => by
@@ -153,14 +210,18 @@ theorem ReflectsMonomorphisms.of_iso {F G : C ⥤ D} [ReflectsMonomorphisms F] (
       haveI : mono (G.map f ≫ (α.app Y).inv) := mono_comp _ _
       convert (mono_comp _ _ : mono ((α.app X).Hom ≫ G.map f ≫ (α.app Y).inv))
       rw [← category.assoc, iso.eq_comp_inv, iso.app_hom, iso.app_hom, nat_trans.naturality] }
-#align category_theory.functor.reflects_monomorphisms.of_iso CategoryTheory.Functor.ReflectsMonomorphisms.of_iso
+#align category_theory.functor.reflects_monomorphisms.of_iso CategoryTheory.Functor.reflectsMonomorphisms.of_iso
+-/
 
-theorem ReflectsMonomorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
+#print CategoryTheory.Functor.reflectsMonomorphisms.iso_iff /-
+theorem reflectsMonomorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
     ReflectsMonomorphisms F ↔ ReflectsMonomorphisms G :=
   ⟨fun h => reflects_monomorphisms.of_iso α, fun h => reflects_monomorphisms.of_iso α.symm⟩
-#align category_theory.functor.reflects_monomorphisms.iso_iff CategoryTheory.Functor.ReflectsMonomorphisms.iso_iff
+#align category_theory.functor.reflects_monomorphisms.iso_iff CategoryTheory.Functor.reflectsMonomorphisms.iso_iff
+-/
 
-theorem ReflectsEpimorphisms.of_iso {F G : C ⥤ D} [ReflectsEpimorphisms F] (α : F ≅ G) :
+#print CategoryTheory.Functor.reflectsEpimorphisms.of_iso /-
+theorem reflectsEpimorphisms.of_iso {F G : C ⥤ D} [ReflectsEpimorphisms F] (α : F ≅ G) :
     ReflectsEpimorphisms G :=
   {
     reflects := fun X Y f h => by
@@ -168,14 +229,18 @@ theorem ReflectsEpimorphisms.of_iso {F G : C ⥤ D} [ReflectsEpimorphisms F] (α
       haveI : epi (G.map f ≫ (α.app Y).inv) := epi_comp _ _
       convert (epi_comp _ _ : epi ((α.app X).Hom ≫ G.map f ≫ (α.app Y).inv))
       rw [← category.assoc, iso.eq_comp_inv, iso.app_hom, iso.app_hom, nat_trans.naturality] }
-#align category_theory.functor.reflects_epimorphisms.of_iso CategoryTheory.Functor.ReflectsEpimorphisms.of_iso
+#align category_theory.functor.reflects_epimorphisms.of_iso CategoryTheory.Functor.reflectsEpimorphisms.of_iso
+-/
 
-theorem ReflectsEpimorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
+#print CategoryTheory.Functor.reflectsEpimorphisms.iso_iff /-
+theorem reflectsEpimorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
     ReflectsEpimorphisms F ↔ ReflectsEpimorphisms G :=
   ⟨fun h => reflects_epimorphisms.of_iso α, fun h => reflects_epimorphisms.of_iso α.symm⟩
-#align category_theory.functor.reflects_epimorphisms.iso_iff CategoryTheory.Functor.ReflectsEpimorphisms.iso_iff
+#align category_theory.functor.reflects_epimorphisms.iso_iff CategoryTheory.Functor.reflectsEpimorphisms.iso_iff
+-/
 
-theorem preserves_epimorphsisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj : F ⊣ G) :
+#print CategoryTheory.Functor.preservesEpimorphsisms_of_adjunction /-
+theorem preservesEpimorphsisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj : F ⊣ G) :
     PreservesEpimorphisms F :=
   {
     preserves := fun X Y f hf =>
@@ -184,13 +249,17 @@ theorem preserves_epimorphsisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj :
         replace H := congr_arg (adj.hom_equiv X Z) H
         rwa [adj.hom_equiv_naturality_left, adj.hom_equiv_naturality_left, cancel_epi,
           Equiv.apply_eq_iff_eq] at H⟩ }
-#align category_theory.functor.preserves_epimorphsisms_of_adjunction CategoryTheory.Functor.preserves_epimorphsisms_of_adjunction
+#align category_theory.functor.preserves_epimorphsisms_of_adjunction CategoryTheory.Functor.preservesEpimorphsisms_of_adjunction
+-/
 
+#print CategoryTheory.Functor.preservesEpimorphisms_of_isLeftAdjoint /-
 instance (priority := 100) preservesEpimorphisms_of_isLeftAdjoint (F : C ⥤ D) [IsLeftAdjoint F] :
     PreservesEpimorphisms F :=
-  preserves_epimorphsisms_of_adjunction (Adjunction.ofLeftAdjoint F)
+  preservesEpimorphsisms_of_adjunction (Adjunction.ofLeftAdjoint F)
 #align category_theory.functor.preserves_epimorphisms_of_is_left_adjoint CategoryTheory.Functor.preservesEpimorphisms_of_isLeftAdjoint
+-/
 
+#print CategoryTheory.Functor.preservesMonomorphisms_of_adjunction /-
 theorem preservesMonomorphisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj : F ⊣ G) :
     PreservesMonomorphisms G :=
   {
@@ -201,30 +270,43 @@ theorem preservesMonomorphisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj :
         rwa [adj.hom_equiv_naturality_right_symm, adj.hom_equiv_naturality_right_symm, cancel_mono,
           Equiv.apply_eq_iff_eq] at H⟩ }
 #align category_theory.functor.preserves_monomorphisms_of_adjunction CategoryTheory.Functor.preservesMonomorphisms_of_adjunction
+-/
 
+#print CategoryTheory.Functor.preservesMonomorphisms_of_isRightAdjoint /-
 instance (priority := 100) preservesMonomorphisms_of_isRightAdjoint (F : C ⥤ D) [IsRightAdjoint F] :
     PreservesMonomorphisms F :=
   preservesMonomorphisms_of_adjunction (Adjunction.ofRightAdjoint F)
 #align category_theory.functor.preserves_monomorphisms_of_is_right_adjoint CategoryTheory.Functor.preservesMonomorphisms_of_isRightAdjoint
+-/
 
+#print CategoryTheory.Functor.reflectsMonomorphisms_of_faithful /-
 instance (priority := 100) reflectsMonomorphisms_of_faithful (F : C ⥤ D) [Faithful F] :
     ReflectsMonomorphisms F
     where reflects X Y f hf :=
     ⟨fun Z g h hgh =>
       F.map_injective ((cancel_mono (F.map f)).1 (by rw [← F.map_comp, hgh, F.map_comp]))⟩
 #align category_theory.functor.reflects_monomorphisms_of_faithful CategoryTheory.Functor.reflectsMonomorphisms_of_faithful
+-/
 
+#print CategoryTheory.Functor.reflectsEpimorphisms_of_faithful /-
 instance (priority := 100) reflectsEpimorphisms_of_faithful (F : C ⥤ D) [Faithful F] :
     ReflectsEpimorphisms F
     where reflects X Y f hf :=
     ⟨fun Z g h hgh =>
       F.map_injective ((cancel_epi (F.map f)).1 (by rw [← F.map_comp, hgh, F.map_comp]))⟩
 #align category_theory.functor.reflects_epimorphisms_of_faithful CategoryTheory.Functor.reflectsEpimorphisms_of_faithful
+-/
 
 section
 
 variable (F : C ⥤ D) {X Y : C} (f : X ⟶ Y)
 
+/- warning: category_theory.functor.split_epi_equiv -> CategoryTheory.Functor.splitEpiEquiv is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Full.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [_inst_5 : CategoryTheory.Faithful.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Equiv.{succ u1, succ u2} (CategoryTheory.SplitEpi.{u1, u3} C _inst_1 X Y f) (CategoryTheory.SplitEpi.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X Y f))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Full.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [_inst_5 : CategoryTheory.Faithful.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Equiv.{succ u1, succ u2} (CategoryTheory.SplitEpi.{u1, u3} C _inst_1 X Y f) (CategoryTheory.SplitEpi.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X Y f))
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.split_epi_equiv CategoryTheory.Functor.splitEpiEquivₓ'. -/
 /-- If `F` is a fully faithful functor, split epimorphisms are preserved and reflected by `F`. -/
 def splitEpiEquiv [Full F] [Faithful F] : SplitEpi f ≃ SplitEpi (F.map f)
     where
@@ -238,6 +320,12 @@ def splitEpiEquiv [Full F] [Faithful F] : SplitEpi f ≃ SplitEpi (F.map f)
   right_inv := by tidy
 #align category_theory.functor.split_epi_equiv CategoryTheory.Functor.splitEpiEquiv
 
+/- warning: category_theory.functor.is_split_epi_iff -> CategoryTheory.Functor.isSplitEpi_iff is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Full.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [_inst_5 : CategoryTheory.Faithful.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Iff (CategoryTheory.IsSplitEpi.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X Y f)) (CategoryTheory.IsSplitEpi.{u1, u3} C _inst_1 X Y f)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Full.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [_inst_5 : CategoryTheory.Faithful.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Iff (CategoryTheory.IsSplitEpi.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X Y f)) (CategoryTheory.IsSplitEpi.{u1, u3} C _inst_1 X Y f)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.is_split_epi_iff CategoryTheory.Functor.isSplitEpi_iffₓ'. -/
 @[simp]
 theorem isSplitEpi_iff [Full F] [Faithful F] : IsSplitEpi (F.map f) ↔ IsSplitEpi f :=
   by
@@ -248,6 +336,12 @@ theorem isSplitEpi_iff [Full F] [Faithful F] : IsSplitEpi (F.map f) ↔ IsSplitE
     exact is_split_epi.mk' ((split_epi_equiv F f).toFun h.exists_split_epi.some)
 #align category_theory.functor.is_split_epi_iff CategoryTheory.Functor.isSplitEpi_iff
 
+/- warning: category_theory.functor.split_mono_equiv -> CategoryTheory.Functor.splitMonoEquiv is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Full.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [_inst_5 : CategoryTheory.Faithful.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Equiv.{succ u1, succ u2} (CategoryTheory.SplitMono.{u1, u3} C _inst_1 X Y f) (CategoryTheory.SplitMono.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X Y f))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Full.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [_inst_5 : CategoryTheory.Faithful.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Equiv.{succ u1, succ u2} (CategoryTheory.SplitMono.{u1, u3} C _inst_1 X Y f) (CategoryTheory.SplitMono.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X Y f))
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.split_mono_equiv CategoryTheory.Functor.splitMonoEquivₓ'. -/
 /-- If `F` is a fully faithful functor, split monomorphisms are preserved and reflected by `F`. -/
 def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
     where
@@ -261,6 +355,12 @@ def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
   right_inv := by tidy
 #align category_theory.functor.split_mono_equiv CategoryTheory.Functor.splitMonoEquiv
 
+/- warning: category_theory.functor.is_split_mono_iff -> CategoryTheory.Functor.isSplitMono_iff is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Full.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [_inst_5 : CategoryTheory.Faithful.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Iff (CategoryTheory.IsSplitMono.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X Y f)) (CategoryTheory.IsSplitMono.{u1, u3} C _inst_1 X Y f)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [_inst_4 : CategoryTheory.Full.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [_inst_5 : CategoryTheory.Faithful.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Iff (CategoryTheory.IsSplitMono.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X Y f)) (CategoryTheory.IsSplitMono.{u1, u3} C _inst_1 X Y f)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.is_split_mono_iff CategoryTheory.Functor.isSplitMono_iffₓ'. -/
 @[simp]
 theorem isSplitMono_iff [Full F] [Faithful F] : IsSplitMono (F.map f) ↔ IsSplitMono f :=
   by
@@ -271,6 +371,12 @@ theorem isSplitMono_iff [Full F] [Faithful F] : IsSplitMono (F.map f) ↔ IsSpli
     exact is_split_mono.mk' ((split_mono_equiv F f).toFun h.exists_split_mono.some)
 #align category_theory.functor.is_split_mono_iff CategoryTheory.Functor.isSplitMono_iff
 
+/- warning: category_theory.functor.epi_map_iff_epi -> CategoryTheory.Functor.epi_map_iff_epi is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [hF₁ : CategoryTheory.Functor.PreservesEpimorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [hF₂ : CategoryTheory.Functor.ReflectsEpimorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Iff (CategoryTheory.Epi.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X Y f)) (CategoryTheory.Epi.{u1, u3} C _inst_1 X Y f)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [hF₁ : CategoryTheory.Functor.PreservesEpimorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [hF₂ : CategoryTheory.Functor.ReflectsEpimorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Iff (CategoryTheory.Epi.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X Y f)) (CategoryTheory.Epi.{u1, u3} C _inst_1 X Y f)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.epi_map_iff_epi CategoryTheory.Functor.epi_map_iff_epiₓ'. -/
 @[simp]
 theorem epi_map_iff_epi [hF₁ : PreservesEpimorphisms F] [hF₂ : ReflectsEpimorphisms F] :
     Epi (F.map f) ↔ Epi f := by
@@ -280,6 +386,12 @@ theorem epi_map_iff_epi [hF₁ : PreservesEpimorphisms F] [hF₂ : ReflectsEpimo
     exact F.map_epi f
 #align category_theory.functor.epi_map_iff_epi CategoryTheory.Functor.epi_map_iff_epi
 
+/- warning: category_theory.functor.mono_map_iff_mono -> CategoryTheory.Functor.mono_map_iff_mono is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [hF₁ : CategoryTheory.Functor.PreservesMonomorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [hF₂ : CategoryTheory.Functor.ReflectsMonomorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Iff (CategoryTheory.Mono.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X Y f)) (CategoryTheory.Mono.{u1, u3} C _inst_1 X Y f)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [hF₁ : CategoryTheory.Functor.PreservesMonomorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F] [hF₂ : CategoryTheory.Functor.ReflectsMonomorphisms.{u1, u2, u3, u4} C _inst_1 D _inst_2 F], Iff (CategoryTheory.Mono.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X Y f)) (CategoryTheory.Mono.{u1, u3} C _inst_1 X Y f)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.mono_map_iff_mono CategoryTheory.Functor.mono_map_iff_monoₓ'. -/
 @[simp]
 theorem mono_map_iff_mono [hF₁ : PreservesMonomorphisms F] [hF₂ : ReflectsMonomorphisms F] :
     Mono (F.map f) ↔ Mono f := by
@@ -289,6 +401,7 @@ theorem mono_map_iff_mono [hF₁ : PreservesMonomorphisms F] [hF₂ : ReflectsMo
     exact F.map_mono f
 #align category_theory.functor.mono_map_iff_mono CategoryTheory.Functor.mono_map_iff_mono
 
+#print CategoryTheory.Functor.splitEpiCategoryImpOfIsEquivalence /-
 /-- If `F : C ⥤ D` is an equivalence of categories and `C` is a `split_epi_category`,
 then `D` also is. -/
 def splitEpiCategoryImpOfIsEquivalence [IsEquivalence F] [SplitEpiCategory C] :
@@ -298,6 +411,7 @@ def splitEpiCategoryImpOfIsEquivalence [IsEquivalence F] [SplitEpiCategory C] :
     rw [← F.inv.is_split_epi_iff f]
     apply is_split_epi_of_epi⟩
 #align category_theory.functor.split_epi_category_imp_of_is_equivalence CategoryTheory.Functor.splitEpiCategoryImpOfIsEquivalence
+-/
 
 end
 
@@ -307,6 +421,12 @@ namespace CategoryTheory.Adjunction
 
 variable {C D : Type _} [Category C] [Category D] {F : C ⥤ D} {F' : D ⥤ C} {A B : C}
 
+/- warning: category_theory.adjunction.strong_epi_map_of_strong_epi -> CategoryTheory.Adjunction.strongEpi_map_of_strongEpi is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} {D : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u3, u1} C] [_inst_2 : CategoryTheory.Category.{u4, u2} D] {F : CategoryTheory.Functor.{u3, u4, u1, u2} C _inst_1 D _inst_2} {F' : CategoryTheory.Functor.{u4, u3, u2, u1} D _inst_2 C _inst_1} {A : C} {B : C}, (CategoryTheory.Adjunction.{u3, u4, u1, u2} C _inst_1 D _inst_2 F F') -> (forall (f : Quiver.Hom.{succ u3, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} C (CategoryTheory.Category.toCategoryStruct.{u3, u1} C _inst_1)) A B) [h₁ : CategoryTheory.Functor.PreservesMonomorphisms.{u4, u3, u2, u1} D _inst_2 C _inst_1 F'] [h₂ : CategoryTheory.Functor.PreservesEpimorphisms.{u3, u4, u1, u2} C _inst_1 D _inst_2 F] [_inst_3 : CategoryTheory.StrongEpi.{u3, u1} C _inst_1 A B f], CategoryTheory.StrongEpi.{u4, u2} D _inst_2 (CategoryTheory.Functor.obj.{u3, u4, u1, u2} C _inst_1 D _inst_2 F A) (CategoryTheory.Functor.obj.{u3, u4, u1, u2} C _inst_1 D _inst_2 F B) (CategoryTheory.Functor.map.{u3, u4, u1, u2} C _inst_1 D _inst_2 F A B f))
+but is expected to have type
+  forall {C : Type.{u2}} {D : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u4, u2} C] [_inst_2 : CategoryTheory.Category.{u3, u1} D] {F : CategoryTheory.Functor.{u4, u3, u2, u1} C _inst_1 D _inst_2} {F' : CategoryTheory.Functor.{u3, u4, u1, u2} D _inst_2 C _inst_1} {A : C} {B : C}, (CategoryTheory.Adjunction.{u4, u3, u2, u1} C _inst_1 D _inst_2 F F') -> (forall (f : Quiver.Hom.{succ u4, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u2} C (CategoryTheory.Category.toCategoryStruct.{u4, u2} C _inst_1)) A B) [h₁ : CategoryTheory.Functor.PreservesMonomorphisms.{u3, u4, u1, u2} D _inst_2 C _inst_1 F'] [h₂ : CategoryTheory.Functor.PreservesEpimorphisms.{u4, u3, u2, u1} C _inst_1 D _inst_2 F] [_inst_3 : CategoryTheory.StrongEpi.{u4, u2} C _inst_1 A B f], CategoryTheory.StrongEpi.{u3, u1} D _inst_2 (Prefunctor.obj.{succ u4, succ u3, u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u2} C (CategoryTheory.Category.toCategoryStruct.{u4, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} D (CategoryTheory.Category.toCategoryStruct.{u3, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u3, u2, u1} C _inst_1 D _inst_2 F) A) (Prefunctor.obj.{succ u4, succ u3, u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u2} C (CategoryTheory.Category.toCategoryStruct.{u4, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} D (CategoryTheory.Category.toCategoryStruct.{u3, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u3, u2, u1} C _inst_1 D _inst_2 F) B) (Prefunctor.map.{succ u4, succ u3, u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u2} C (CategoryTheory.Category.toCategoryStruct.{u4, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} D (CategoryTheory.Category.toCategoryStruct.{u3, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u3, u2, u1} C _inst_1 D _inst_2 F) A B f))
+Case conversion may be inaccurate. Consider using '#align category_theory.adjunction.strong_epi_map_of_strong_epi CategoryTheory.Adjunction.strongEpi_map_of_strongEpiₓ'. -/
 theorem strongEpi_map_of_strongEpi (adj : F ⊣ F') (f : A ⟶ B) [h₁ : F'.PreservesMonomorphisms]
     [h₂ : F.PreservesEpimorphisms] [StrongEpi f] : StrongEpi (F.map f) :=
   ⟨inferInstance, fun X Y Z => by
@@ -315,6 +435,12 @@ theorem strongEpi_map_of_strongEpi (adj : F ⊣ F') (f : A ⟶ B) [h₁ : F'.Pre
     infer_instance⟩
 #align category_theory.adjunction.strong_epi_map_of_strong_epi CategoryTheory.Adjunction.strongEpi_map_of_strongEpi
 
+/- warning: category_theory.adjunction.strong_epi_map_of_is_equivalence -> CategoryTheory.Adjunction.strongEpi_map_of_isEquivalence is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} {D : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u3, u1} C] [_inst_2 : CategoryTheory.Category.{u4, u2} D] {F : CategoryTheory.Functor.{u3, u4, u1, u2} C _inst_1 D _inst_2} {A : C} {B : C} [_inst_3 : CategoryTheory.IsEquivalence.{u3, u4, u1, u2} C _inst_1 D _inst_2 F] (f : Quiver.Hom.{succ u3, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} C (CategoryTheory.Category.toCategoryStruct.{u3, u1} C _inst_1)) A B) [h : CategoryTheory.StrongEpi.{u3, u1} C _inst_1 A B f], CategoryTheory.StrongEpi.{u4, u2} D _inst_2 (CategoryTheory.Functor.obj.{u3, u4, u1, u2} C _inst_1 D _inst_2 F A) (CategoryTheory.Functor.obj.{u3, u4, u1, u2} C _inst_1 D _inst_2 F B) (CategoryTheory.Functor.map.{u3, u4, u1, u2} C _inst_1 D _inst_2 F A B f)
+but is expected to have type
+  forall {C : Type.{u1}} {D : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u3, u1} C] [_inst_2 : CategoryTheory.Category.{u4, u2} D] {F : CategoryTheory.Functor.{u3, u4, u1, u2} C _inst_1 D _inst_2} {A : C} {B : C} [_inst_3 : CategoryTheory.IsEquivalence.{u3, u4, u1, u2} C _inst_1 D _inst_2 F] (f : Quiver.Hom.{succ u3, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} C (CategoryTheory.Category.toCategoryStruct.{u3, u1} C _inst_1)) A B) [h : CategoryTheory.StrongEpi.{u3, u1} C _inst_1 A B f], CategoryTheory.StrongEpi.{u4, u2} D _inst_2 (Prefunctor.obj.{succ u3, succ u4, u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} C (CategoryTheory.Category.toCategoryStruct.{u3, u1} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u4, u2} D (CategoryTheory.Category.toCategoryStruct.{u4, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u3, u4, u1, u2} C _inst_1 D _inst_2 F) A) (Prefunctor.obj.{succ u3, succ u4, u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} C (CategoryTheory.Category.toCategoryStruct.{u3, u1} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u4, u2} D (CategoryTheory.Category.toCategoryStruct.{u4, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u3, u4, u1, u2} C _inst_1 D _inst_2 F) B) (Prefunctor.map.{succ u3, succ u4, u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} C (CategoryTheory.Category.toCategoryStruct.{u3, u1} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u4, u2} D (CategoryTheory.Category.toCategoryStruct.{u4, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u3, u4, u1, u2} C _inst_1 D _inst_2 F) A B f)
+Case conversion may be inaccurate. Consider using '#align category_theory.adjunction.strong_epi_map_of_is_equivalence CategoryTheory.Adjunction.strongEpi_map_of_isEquivalenceₓ'. -/
 instance strongEpi_map_of_isEquivalence [IsEquivalence F] (f : A ⟶ B) [h : StrongEpi f] :
     StrongEpi (F.map f) :=
   F.asEquivalence.toAdjunction.strongEpi_map_of_strongEpi f
@@ -326,6 +452,12 @@ namespace CategoryTheory.Functor
 
 variable {C D : Type _} [Category C] [Category D] {F : C ⥤ D} {A B : C} (f : A ⟶ B)
 
+/- warning: category_theory.functor.strong_epi_map_iff_strong_epi_of_is_equivalence -> CategoryTheory.Functor.strongEpi_map_iff_strongEpi_of_isEquivalence is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} {D : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u3, u1} C] [_inst_2 : CategoryTheory.Category.{u4, u2} D] {F : CategoryTheory.Functor.{u3, u4, u1, u2} C _inst_1 D _inst_2} {A : C} {B : C} (f : Quiver.Hom.{succ u3, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} C (CategoryTheory.Category.toCategoryStruct.{u3, u1} C _inst_1)) A B) [_inst_3 : CategoryTheory.IsEquivalence.{u3, u4, u1, u2} C _inst_1 D _inst_2 F], Iff (CategoryTheory.StrongEpi.{u4, u2} D _inst_2 (CategoryTheory.Functor.obj.{u3, u4, u1, u2} C _inst_1 D _inst_2 F A) (CategoryTheory.Functor.obj.{u3, u4, u1, u2} C _inst_1 D _inst_2 F B) (CategoryTheory.Functor.map.{u3, u4, u1, u2} C _inst_1 D _inst_2 F A B f)) (CategoryTheory.StrongEpi.{u3, u1} C _inst_1 A B f)
+but is expected to have type
+  forall {C : Type.{u2}} {D : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u4, u2} C] [_inst_2 : CategoryTheory.Category.{u3, u1} D] {F : CategoryTheory.Functor.{u4, u3, u2, u1} C _inst_1 D _inst_2} {A : C} {B : C} (f : Quiver.Hom.{succ u4, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u2} C (CategoryTheory.Category.toCategoryStruct.{u4, u2} C _inst_1)) A B) [_inst_3 : CategoryTheory.IsEquivalence.{u4, u3, u2, u1} C _inst_1 D _inst_2 F], Iff (CategoryTheory.StrongEpi.{u3, u1} D _inst_2 (Prefunctor.obj.{succ u4, succ u3, u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u2} C (CategoryTheory.Category.toCategoryStruct.{u4, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} D (CategoryTheory.Category.toCategoryStruct.{u3, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u3, u2, u1} C _inst_1 D _inst_2 F) A) (Prefunctor.obj.{succ u4, succ u3, u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u2} C (CategoryTheory.Category.toCategoryStruct.{u4, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} D (CategoryTheory.Category.toCategoryStruct.{u3, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u3, u2, u1} C _inst_1 D _inst_2 F) B) (Prefunctor.map.{succ u4, succ u3, u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u4, u2} C (CategoryTheory.Category.toCategoryStruct.{u4, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u3, u1} D (CategoryTheory.Category.toCategoryStruct.{u3, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u3, u2, u1} C _inst_1 D _inst_2 F) A B f)) (CategoryTheory.StrongEpi.{u4, u2} C _inst_1 A B f)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.strong_epi_map_iff_strong_epi_of_is_equivalence CategoryTheory.Functor.strongEpi_map_iff_strongEpi_of_isEquivalenceₓ'. -/
 @[simp]
 theorem strongEpi_map_iff_strongEpi_of_isEquivalence [IsEquivalence F] :
     StrongEpi (F.map f) ↔ StrongEpi f := by

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

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>

@@ -221,20 +221,15 @@ section
 variable (F : C ⥤ D) {X Y : C} (f : X ⟶ Y)
 
 /-- If `F` is a fully faithful functor, split epimorphisms are preserved and reflected by `F`. -/
-def splitEpiEquiv [Full F] [Faithful F] : SplitEpi f ≃ SplitEpi (F.map f)
+noncomputable def splitEpiEquiv [Full F] [Faithful F] : SplitEpi f ≃ SplitEpi (F.map f)
     where
   toFun f := f.map F
-  invFun s := by
-    refine' ⟨F.preimage s.section_, _⟩
+  invFun s := ⟨F.preimage s.section_, by
     apply F.map_injective
-    simp only [map_comp, image_preimage, map_id]
-    apply SplitEpi.id
+    simp only [map_comp, map_preimage, map_id]
+    apply SplitEpi.id⟩
   left_inv := by aesop_cat
-  right_inv := by
-      simp only [Function.RightInverse,Function.LeftInverse]
-      intro x
-      simp only [SplitEpi.map, preimage]
-      aesop_cat
+  right_inv x := by aesop_cat
 #align category_theory.functor.split_epi_equiv CategoryTheory.Functor.splitEpiEquiv
 
 @[simp]
@@ -247,20 +242,15 @@ theorem isSplitEpi_iff [Full F] [Faithful F] : IsSplitEpi (F.map f) ↔ IsSplitE
 #align category_theory.functor.is_split_epi_iff CategoryTheory.Functor.isSplitEpi_iff
 
 /-- If `F` is a fully faithful functor, split monomorphisms are preserved and reflected by `F`. -/
-def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
+noncomputable def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
     where
   toFun f := f.map F
-  invFun s := by
-    refine' ⟨F.preimage s.retraction, _⟩
+  invFun s := ⟨F.preimage s.retraction, by
     apply F.map_injective
-    simp only [map_comp, image_preimage, map_id]
-    apply SplitMono.id
+    simp only [map_comp, map_preimage, map_id]
+    apply SplitMono.id⟩
   left_inv := by aesop_cat
-  right_inv := by
-    simp only [Function.RightInverse, Function.LeftInverse]
-    intro x
-    simp only [SplitMono.map,preimage]
-    aesop_cat
+  right_inv x := by aesop_cat
 #align category_theory.functor.split_mono_equiv CategoryTheory.Functor.splitMonoEquiv
 
 @[simp]

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

@@ -316,7 +316,7 @@ theorem strongEpi_map_of_strongEpi (adj : F ⊣ F') (f : A ⟶ B) [h₁ : F'.Pre
     infer_instance⟩
 #align category_theory.adjunction.strong_epi_map_of_strong_epi CategoryTheory.Adjunction.strongEpi_map_of_strongEpi
 
-instance strongEpi_map_of_isEquivalence [IsEquivalence F] (f : A ⟶ B) [_h : StrongEpi f] :
+instance strongEpi_map_of_isEquivalence [F.IsEquivalence] (f : A ⟶ B) [_h : StrongEpi f] :
     StrongEpi (F.map f) :=
   F.asEquivalence.toAdjunction.strongEpi_map_of_strongEpi f
 #align category_theory.adjunction.strong_epi_map_of_is_equivalence CategoryTheory.Adjunction.strongEpi_map_of_isEquivalence

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

@@ -321,6 +321,12 @@ instance strongEpi_map_of_isEquivalence [IsEquivalence F] (f : A ⟶ B) [_h : St
   F.asEquivalence.toAdjunction.strongEpi_map_of_strongEpi f
 #align category_theory.adjunction.strong_epi_map_of_is_equivalence CategoryTheory.Adjunction.strongEpi_map_of_isEquivalence
 
+instance (adj : F ⊣ F') {X : C} {Y : D} (f : F.obj X ⟶ Y) [hf : Mono f] [F.ReflectsMonomorphisms] :
+    Mono (adj.homEquiv _ _ f) :=
+  F.mono_of_mono_map <| by
+    rw [← (homEquiv adj X Y).symm_apply_apply f] at hf
+    exact mono_of_mono_fac adj.homEquiv_counit.symm
+
 end CategoryTheory.Adjunction
 
 namespace CategoryTheory.Functor

@@ -203,15 +203,15 @@ instance (priority := 100) preservesMonomorphisms_of_isRightAdjoint (F : C ⥤ D
 #align category_theory.functor.preserves_monomorphisms_of_is_right_adjoint CategoryTheory.Functor.preservesMonomorphisms_of_isRightAdjoint
 
 instance (priority := 100) reflectsMonomorphisms_of_faithful (F : C ⥤ D) [Faithful F] :
-    ReflectsMonomorphisms F
-    where reflects {X} {Y} f hf :=
+    ReflectsMonomorphisms F where
+  reflects {X} {Y} f hf :=
     ⟨fun {Z} g h hgh =>
       F.map_injective ((cancel_mono (F.map f)).1 (by rw [← F.map_comp, hgh, F.map_comp]))⟩
 #align category_theory.functor.reflects_monomorphisms_of_faithful CategoryTheory.Functor.reflectsMonomorphisms_of_faithful
 
 instance (priority := 100) reflectsEpimorphisms_of_faithful (F : C ⥤ D) [Faithful F] :
-    ReflectsEpimorphisms F
-    where reflects {X} {Y} f hf :=
+    ReflectsEpimorphisms F where
+  reflects {X} {Y} f hf :=
     ⟨fun {Z} g h hgh =>
       F.map_injective ((cancel_epi (F.map f)).1 (by rw [← F.map_comp, hgh, F.map_comp]))⟩
 #align category_theory.functor.reflects_epimorphisms_of_faithful CategoryTheory.Functor.reflectsEpimorphisms_of_faithful

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

This has nice performance benefits.

@@ -306,7 +306,7 @@ end CategoryTheory.Functor
 
 namespace CategoryTheory.Adjunction
 
-variable {C D : Type _} [Category C] [Category D] {F : C ⥤ D} {F' : D ⥤ C} {A B : C}
+variable {C D : Type*} [Category C] [Category D] {F : C ⥤ D} {F' : D ⥤ C} {A B : C}
 
 theorem strongEpi_map_of_strongEpi (adj : F ⊣ F') (f : A ⟶ B) [h₁ : F'.PreservesMonomorphisms]
     [h₂ : F.PreservesEpimorphisms] [StrongEpi f] : StrongEpi (F.map f) :=
@@ -325,7 +325,7 @@ end CategoryTheory.Adjunction
 
 namespace CategoryTheory.Functor
 
-variable {C D : Type _} [Category C] [Category D] {F : C ⥤ D} {A B : C} (f : A ⟶ B)
+variable {C D : Type*} [Category C] [Category D] {F : C ⥤ D} {A B : C} (f : A ⟶ B)
 
 @[simp]
 theorem strongEpi_map_iff_strongEpi_of_isEquivalence [IsEquivalence F] :

@@ -292,7 +292,7 @@ theorem mono_map_iff_mono [hF₁ : PreservesMonomorphisms F] [hF₂ : ReflectsMo
 
 /-- If `F : C ⥤ D` is an equivalence of categories and `C` is a `split_epi_category`,
 then `D` also is. -/
-def splitEpiCategoryImpOfIsEquivalence [IsEquivalence F] [SplitEpiCategory C] :
+theorem splitEpiCategoryImpOfIsEquivalence [IsEquivalence F] [SplitEpiCategory C] :
     SplitEpiCategory D :=
   ⟨fun {X} {Y} f => by
     intro

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Markus Himmel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.functor.epi_mono
-! leanprover-community/mathlib commit 32253a1a1071173b33dc7d6a218cf722c6feb514
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.EpiMono
 import Mathlib.CategoryTheory.Limits.Shapes.StrongEpi
 import Mathlib.CategoryTheory.LiftingProperties.Adjunction
 
+#align_import category_theory.functor.epi_mono from "leanprover-community/mathlib"@"32253a1a1071173b33dc7d6a218cf722c6feb514"
+
 /-!
 # Preservation and reflection of monomorphisms and epimorphisms
 

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

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

@@ -123,9 +123,7 @@ theorem reflectsMonomorphisms_of_preserves_of_reflects (F : C ⥤ D) (G : D ⥤
 
 theorem preservesMonomorphisms.of_iso {F G : C ⥤ D} [PreservesMonomorphisms F] (α : F ≅ G) :
     PreservesMonomorphisms G :=
-  {
-    preserves := fun {X} {Y} f h =>
-      by
+  { preserves := fun {X} {Y} f h => by
       haveI : Mono (F.map f ≫ (α.app Y).hom) := mono_comp _ _
       convert (mono_comp _ _ : Mono ((α.app X).inv ≫ F.map f ≫ (α.app Y).hom))
       rw [Iso.eq_inv_comp, Iso.app_hom, Iso.app_hom, NatTrans.naturality] }
@@ -138,9 +136,7 @@ theorem preservesMonomorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
 
 theorem preservesEpimorphisms.of_iso {F G : C ⥤ D} [PreservesEpimorphisms F] (α : F ≅ G) :
     PreservesEpimorphisms G :=
-  {
-    preserves := fun {X} {Y} f h =>
-      by
+  { preserves := fun {X} {Y} f h => by
       haveI : Epi (F.map f ≫ (α.app Y).hom) := epi_comp _ _
       convert (epi_comp _ _ : Epi ((α.app X).inv ≫ F.map f ≫ (α.app Y).hom))
       rw [Iso.eq_inv_comp, Iso.app_hom, Iso.app_hom, NatTrans.naturality] }
@@ -153,8 +149,7 @@ theorem preservesEpimorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
 
 theorem reflectsMonomorphisms.of_iso {F G : C ⥤ D} [ReflectsMonomorphisms F] (α : F ≅ G) :
     ReflectsMonomorphisms G :=
-  {
-    reflects := fun {X} {Y} f h => by
+  { reflects := fun {X} {Y} f h => by
       apply F.mono_of_mono_map
       haveI : Mono (G.map f ≫ (α.app Y).inv) := mono_comp _ _
       convert (mono_comp _ _ : Mono ((α.app X).hom ≫ G.map f ≫ (α.app Y).inv))
@@ -168,8 +163,7 @@ theorem reflectsMonomorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
 
 theorem reflectsEpimorphisms.of_iso {F G : C ⥤ D} [ReflectsEpimorphisms F] (α : F ≅ G) :
     ReflectsEpimorphisms G :=
-  {
-    reflects := fun {X} {Y} f h => by
+  { reflects := fun {X} {Y} f h => by
       apply F.epi_of_epi_map
       haveI : Epi (G.map f ≫ (α.app Y).inv) := epi_comp _ _
       convert (epi_comp _ _ : Epi ((α.app X).hom ≫ G.map f ≫ (α.app Y).inv))
@@ -183,8 +177,7 @@ theorem reflectsEpimorphisms.iso_iff {F G : C ⥤ D} (α : F ≅ G) :
 
 theorem preservesEpimorphsisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj : F ⊣ G) :
     PreservesEpimorphisms F :=
-  {
-    preserves := fun {X} {Y} f hf =>
+  { preserves := fun {X} {Y} f hf =>
       ⟨by
         intro Z g h H
         replace H := congr_arg (adj.homEquiv X Z) H
@@ -199,8 +192,7 @@ instance (priority := 100) preservesEpimorphisms_of_isLeftAdjoint (F : C ⥤ D)
 
 theorem preservesMonomorphisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj : F ⊣ G) :
     PreservesMonomorphisms G :=
-  {
-    preserves := fun {X} {Y} f hf =>
+  { preserves := fun {X} {Y} f hf =>
       ⟨by
         intro Z g h H
         replace H := congr_arg (adj.homEquiv Z Y).symm H

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -272,7 +272,6 @@ def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
     intro x
     simp only [SplitMono.map,preimage]
     aesop_cat
-
 #align category_theory.functor.split_mono_equiv CategoryTheory.Functor.splitMonoEquiv
 
 @[simp]

vscode is already configured by .vscode/settings.json to trim these on save. It's not clear how they've managed to stick around.

By doing this all in one PR now, it avoids getting random whitespace diffs in PRs later.

This was done with a regex search in vscode,

@@ -55,7 +55,7 @@ instance map_epi (F : C ⥤ D) [PreservesEpimorphisms F] {X Y : C} (f : X ⟶ Y)
     monomorphisms. -/
 class ReflectsMonomorphisms (F : C ⥤ D) : Prop where
    /-- A functor reflects monomorphisms if morphisms that are mapped to monomorphisms are themselves
-    monomorphisms. -/ 
+    monomorphisms. -/
   reflects : ∀ {X Y : C} (f : X ⟶ Y), Mono (F.map f) → Mono f
 #align category_theory.functor.reflects_monomorphisms CategoryTheory.Functor.ReflectsMonomorphisms
 
@@ -78,26 +78,26 @@ theorem epi_of_epi_map (F : C ⥤ D) [ReflectsEpimorphisms F] {X Y : C} {f : X 
 #align category_theory.functor.epi_of_epi_map CategoryTheory.Functor.epi_of_epi_map
 
 instance preservesMonomorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [PreservesMonomorphisms F]
-    [PreservesMonomorphisms G] : PreservesMonomorphisms (F ⋙ G) where 
+    [PreservesMonomorphisms G] : PreservesMonomorphisms (F ⋙ G) where
   preserves f h := by
     rw [comp_map]
     exact inferInstance
 #align category_theory.functor.preserves_monomorphisms_comp CategoryTheory.Functor.preservesMonomorphisms_comp
 
 instance preservesEpimorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [PreservesEpimorphisms F]
-    [PreservesEpimorphisms G] : PreservesEpimorphisms (F ⋙ G) where 
+    [PreservesEpimorphisms G] : PreservesEpimorphisms (F ⋙ G) where
   preserves f h := by
     rw [comp_map]
     exact inferInstance
 #align category_theory.functor.preserves_epimorphisms_comp CategoryTheory.Functor.preservesEpimorphisms_comp
 
 instance reflectsMonomorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [ReflectsMonomorphisms F]
-    [ReflectsMonomorphisms G] : ReflectsMonomorphisms (F ⋙ G) where 
+    [ReflectsMonomorphisms G] : ReflectsMonomorphisms (F ⋙ G) where
   reflects _ h := F.mono_of_mono_map (G.mono_of_mono_map h)
 #align category_theory.functor.reflects_monomorphisms_comp CategoryTheory.Functor.reflectsMonomorphisms_comp
 
 instance reflectsEpimorphisms_comp (F : C ⥤ D) (G : D ⥤ E) [ReflectsEpimorphisms F]
-    [ReflectsEpimorphisms G] : ReflectsEpimorphisms (F ⋙ G) where 
+    [ReflectsEpimorphisms G] : ReflectsEpimorphisms (F ⋙ G) where
   reflects _ h := F.epi_of_epi_map (G.epi_of_epi_map h)
 #align category_theory.functor.reflects_epimorphisms_comp CategoryTheory.Functor.reflectsEpimorphisms_comp
 
@@ -241,11 +241,11 @@ def splitEpiEquiv [Full F] [Faithful F] : SplitEpi f ≃ SplitEpi (F.map f)
     simp only [map_comp, image_preimage, map_id]
     apply SplitEpi.id
   left_inv := by aesop_cat
-  right_inv := by 
+  right_inv := by
       simp only [Function.RightInverse,Function.LeftInverse]
-      intro x 
+      intro x
       simp only [SplitEpi.map, preimage]
-      aesop_cat 
+      aesop_cat
 #align category_theory.functor.split_epi_equiv CategoryTheory.Functor.splitEpiEquiv
 
 @[simp]
@@ -267,7 +267,7 @@ def splitMonoEquiv [Full F] [Faithful F] : SplitMono f ≃ SplitMono (F.map f)
     simp only [map_comp, image_preimage, map_id]
     apply SplitMono.id
   left_inv := by aesop_cat
-  right_inv := by 
+  right_inv := by
     simp only [Function.RightInverse, Function.LeftInverse]
     intro x
     simp only [SplitMono.map,preimage]
@@ -353,4 +353,3 @@ theorem strongEpi_map_iff_strongEpi_of_isEquivalence [IsEquivalence F] :
 #align category_theory.functor.strong_epi_map_iff_strong_epi_of_is_equivalence CategoryTheory.Functor.strongEpi_map_iff_strongEpi_of_isEquivalence
 
 end CategoryTheory.Functor
-

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: thorimur <68410468+thorimur@users.noreply.github.com>