category_theory.limits.shapes.images | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

563aed34

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

f4758115

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -1149,8 +1149,9 @@ open CategoryTheory.Limits
 variable {C D : Type _} [Category C] [Category D]
 
 #print CategoryTheory.Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalence /-
-theorem hasStrongEpiMonoFactorisations_imp_of_isEquivalence (F : C ⥤ D) [IsEquivalence F]
-    [h : HasStrongEpiMonoFactorisations C] : HasStrongEpiMonoFactorisations D :=
+theorem hasStrongEpiMonoFactorisations_imp_of_isEquivalence (F : C ⥤ D)
+    [CategoryTheory.Functor.IsEquivalence F] [h : HasStrongEpiMonoFactorisations C] :
+    HasStrongEpiMonoFactorisations D :=
   ⟨fun X Y f =>
     by
     let em : strong_epi_mono_factorisation (F.inv.map f) :=

f4758115

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -114,8 +114,8 @@ theorem ext {F F' : MonoFactorisation f} (hI : F.i = F'.i) (hm : F.m = eqToHom h
     F = F' := by
   cases F; cases F'
   cases hI
-  simp at hm 
-  dsimp at F_fac' F'_fac' 
+  simp at hm
+  dsimp at F_fac' F'_fac'
   congr
   · assumption
   · skip; apply (cancel_mono F_m).1
@@ -552,7 +552,7 @@ instance [HasImage f] [∀ {Z : C} (g h : image f ⟶ Z), HasLimit (parallelPair
 #print CategoryTheory.Limits.epi_image_of_epi /-
 theorem epi_image_of_epi {X Y : C} (f : X ⟶ Y) [HasImage f] [E : Epi f] : Epi (image.ι f) :=
   by
-  rw [← image.fac f] at E 
+  rw [← image.fac f] at E
   skip
   exact epi_of_epi (factor_thru_image f) (image.ι f)
 #align category_theory.limits.epi_image_of_epi CategoryTheory.Limits.epi_image_of_epi

f4758115

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Markus Himmel
 -/
-import Mathbin.CategoryTheory.Limits.Shapes.Equalizers
-import Mathbin.CategoryTheory.Limits.Shapes.Pullbacks
-import Mathbin.CategoryTheory.Limits.Shapes.StrongEpi
+import CategoryTheory.Limits.Shapes.Equalizers
+import CategoryTheory.Limits.Shapes.Pullbacks
+import CategoryTheory.Limits.Shapes.StrongEpi
 
 #align_import category_theory.limits.shapes.images from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"

f4758115

bump to nightly-2023-09-06-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

f3106448

Diff

@@ -82,8 +82,6 @@ structure MonoFactorisation (f : X ⟶ Y) where
 #align category_theory.limits.mono_factorisation CategoryTheory.Limits.MonoFactorisation
 -/
 
-restate_axiom mono_factorisation.fac'
-
 attribute [simp, reassoc] mono_factorisation.fac
 
 attribute [instance] mono_factorisation.m_mono
@@ -199,8 +197,6 @@ structure IsImage (F : MonoFactorisation f) where
 #align category_theory.limits.is_image CategoryTheory.Limits.IsImage
 -/
 
-restate_axiom is_image.lift_fac'
-
 attribute [simp, reassoc] is_image.lift_fac
 
 namespace IsImage
@@ -765,8 +761,6 @@ instance inhabitedImageMap {f : Arrow C} [HasImage f.Hom] : Inhabited (ImageMap
 #align category_theory.limits.inhabited_image_map CategoryTheory.Limits.inhabitedImageMap
 -/
 
-restate_axiom image_map.map_ι'
-
 attribute [simp, reassoc] image_map.map_ι
 
 #print CategoryTheory.Limits.ImageMap.factor_map /-

f4758115

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.limits.shapes.images
-! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Limits.Shapes.Equalizers
 import Mathbin.CategoryTheory.Limits.Shapes.Pullbacks
 import Mathbin.CategoryTheory.Limits.Shapes.StrongEpi
 
+#align_import category_theory.limits.shapes.images from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # Categorical images

f4758115

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -176,6 +176,7 @@ def ofIsoComp {X' : C} (g : X' ⟶ X) [IsIso g] (F : MonoFactorisation (g ≫ f)
 #align category_theory.limits.mono_factorisation.of_iso_comp CategoryTheory.Limits.MonoFactorisation.ofIsoComp
 -/
 
+#print CategoryTheory.Limits.MonoFactorisation.ofArrowIso /-
 /-- If `f` and `g` are isomorphic arrows, then a mono factorisation of `f`
 gives a mono factorisation of `g` -/
 @[simps]
@@ -187,6 +188,7 @@ def ofArrowIso {f g : Arrow C} (F : MonoFactorisation f.Hom) (sq : f ⟶ g) [IsI
   m_mono := mono_comp _ _
   fac := by simp only [fac_assoc, arrow.w, is_iso.inv_comp_eq, category.assoc]
 #align category_theory.limits.mono_factorisation.of_arrow_iso CategoryTheory.Limits.MonoFactorisation.ofArrowIso
+-/
 
 end MonoFactorisation
 
@@ -264,6 +266,7 @@ theorem e_isoExt_inv : F'.e ≫ (isoExt hF hF').inv = F.e := by simp
 #align category_theory.limits.is_image.e_iso_ext_inv CategoryTheory.Limits.IsImage.e_isoExt_inv
 -/
 
+#print CategoryTheory.Limits.IsImage.ofArrowIso /-
 /-- If `f` and `g` are isomorphic arrows, then a mono factorisation of `f` that is an image
 gives a mono factorisation of `g` that is an image -/
 @[simps]
@@ -275,6 +278,7 @@ def ofArrowIso {f g : Arrow C} {F : MonoFactorisation f.Hom} (hF : IsImage F) (s
     simpa only [mono_factorisation.of_arrow_iso_m, arrow.inv_right, ← category.assoc,
       is_iso.comp_inv_eq] using hF.lift_fac (F'.of_arrow_iso (inv sq))
 #align category_theory.limits.is_image.of_arrow_iso CategoryTheory.Limits.IsImage.ofArrowIso
+-/
 
 end IsImage
 
@@ -293,6 +297,7 @@ namespace ImageFactorisation
 instance [Mono f] : Inhabited (ImageFactorisation f) :=
   ⟨⟨_, IsImage.self f⟩⟩
 
+#print CategoryTheory.Limits.ImageFactorisation.ofArrowIso /-
 /-- If `f` and `g` are isomorphic arrows, then an image factorisation of `f`
 gives an image factorisation of `g` -/
 @[simps]
@@ -301,6 +306,7 @@ def ofArrowIso {f g : Arrow C} (F : ImageFactorisation f.Hom) (sq : f ⟶ g) [Is
   f := F.f.of_arrow_iso sq
   IsImage := F.IsImage.of_arrow_iso sq
 #align category_theory.limits.image_factorisation.of_arrow_iso CategoryTheory.Limits.ImageFactorisation.ofArrowIso
+-/
 
 end ImageFactorisation
 
@@ -317,10 +323,12 @@ theorem HasImage.mk {f : X ⟶ Y} (F : ImageFactorisation f) : HasImage f :=
 #align category_theory.limits.has_image.mk CategoryTheory.Limits.HasImage.mk
 -/
 
+#print CategoryTheory.Limits.HasImage.of_arrow_iso /-
 theorem HasImage.of_arrow_iso {f g : Arrow C} [h : HasImage f.Hom] (sq : f ⟶ g) [IsIso sq] :
     HasImage g.Hom :=
   ⟨⟨h.exists_image.some.of_arrow_iso sq⟩⟩
 #align category_theory.limits.has_image.of_arrow_iso CategoryTheory.Limits.HasImage.of_arrow_iso
+-/
 
 #print CategoryTheory.Limits.mono_hasImage /-
 instance (priority := 100) mono_hasImage (f : X ⟶ Y) [Mono f] : HasImage f :=
@@ -674,11 +682,13 @@ instance image.preComp_epi_of_epi [HasImage g] [HasImage (f ≫ g)] [Epi f] :
 #align category_theory.limits.image.pre_comp_epi_of_epi CategoryTheory.Limits.image.preComp_epi_of_epi
 -/
 
+#print CategoryTheory.Limits.hasImage_iso_comp /-
 instance hasImage_iso_comp [IsIso f] [HasImage g] : HasImage (f ≫ g) :=
   HasImage.mk
     { f := (Image.monoFactorisation g).isoComp f
       IsImage := { lift := fun F' => image.lift (F'.ofIsoComp f) } }
 #align category_theory.limits.has_image_iso_comp CategoryTheory.Limits.hasImage_iso_comp
+-/
 
 #print CategoryTheory.Limits.image.isIso_precomp_iso /-
 /-- `image.pre_comp f g` is an isomorphism when `f` is an isomorphism
@@ -693,6 +703,7 @@ instance image.isIso_precomp_iso (f : X ⟶ Y) [IsIso f] [HasImage g] : IsIso (i
 #align category_theory.limits.image.is_iso_precomp_iso CategoryTheory.Limits.image.isIso_precomp_iso
 -/
 
+#print CategoryTheory.Limits.hasImage_comp_iso /-
 -- Note that in general we don't have the other comparison map you might expect
 -- `image f ⟶ image (f ≫ g)`.
 instance hasImage_comp_iso [HasImage f] [IsIso g] : HasImage (f ≫ g) :=
@@ -700,6 +711,7 @@ instance hasImage_comp_iso [HasImage f] [IsIso g] : HasImage (f ≫ g) :=
     { f := (Image.monoFactorisation f).comp_mono g
       IsImage := { lift := fun F' => image.lift F'.of_comp_iso } }
 #align category_theory.limits.has_image_comp_iso CategoryTheory.Limits.hasImage_comp_iso
+-/
 
 #print CategoryTheory.Limits.image.compIso /-
 /-- Postcomposing by an isomorphism induces an isomorphism on the image. -/
@@ -741,27 +753,34 @@ end
 
 section HasImageMap
 
+#print CategoryTheory.Limits.ImageMap /-
 /-- An image map is a morphism `image f → image g` fitting into a commutative square and satisfying
     the obvious commutativity conditions. -/
 structure ImageMap {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g) where
   map : image f.Hom ⟶ image g.Hom
   map_ι : map ≫ image.ι g.Hom = image.ι f.Hom ≫ sq.right := by obviously
 #align category_theory.limits.image_map CategoryTheory.Limits.ImageMap
+-/
 
+#print CategoryTheory.Limits.inhabitedImageMap /-
 instance inhabitedImageMap {f : Arrow C} [HasImage f.Hom] : Inhabited (ImageMap (𝟙 f)) :=
   ⟨⟨𝟙 _, by tidy⟩⟩
 #align category_theory.limits.inhabited_image_map CategoryTheory.Limits.inhabitedImageMap
+-/
 
 restate_axiom image_map.map_ι'
 
 attribute [simp, reassoc] image_map.map_ι
 
+#print CategoryTheory.Limits.ImageMap.factor_map /-
 @[simp, reassoc]
 theorem ImageMap.factor_map {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
     (m : ImageMap sq) : factorThruImage f.Hom ≫ m.map = sq.left ≫ factorThruImage g.Hom :=
   (cancel_mono (image.ι g.Hom)).1 <| by simp
 #align category_theory.limits.image_map.factor_map CategoryTheory.Limits.ImageMap.factor_map
+-/
 
+#print CategoryTheory.Limits.ImageMap.transport /-
 /-- To give an image map for a commutative square with `f` at the top and `g` at the bottom, it
     suffices to give a map between any mono factorisation of `f` and any image factorisation of
     `g`. -/
@@ -772,29 +791,39 @@ def ImageMap.transport {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f
   map := image.lift F ≫ map ≫ hF'.lift (Image.monoFactorisation g.Hom)
   map_ι := by simp [map_ι]
 #align category_theory.limits.image_map.transport CategoryTheory.Limits.ImageMap.transport
+-/
 
+#print CategoryTheory.Limits.HasImageMap /-
 /-- `has_image_map sq` means that there is an `image_map` for the square `sq`. -/
 class HasImageMap {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g) : Prop where mk' ::
   HasImageMap : Nonempty (ImageMap sq)
 #align category_theory.limits.has_image_map CategoryTheory.Limits.HasImageMap
+-/
 
+#print CategoryTheory.Limits.HasImageMap.mk /-
 theorem HasImageMap.mk {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] {sq : f ⟶ g}
     (m : ImageMap sq) : HasImageMap sq :=
   ⟨Nonempty.intro m⟩
 #align category_theory.limits.has_image_map.mk CategoryTheory.Limits.HasImageMap.mk
+-/
 
+#print CategoryTheory.Limits.HasImageMap.transport /-
 theorem HasImageMap.transport {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
     (F : MonoFactorisation f.Hom) {F' : MonoFactorisation g.Hom} (hF' : IsImage F')
     (map : F.i ⟶ F'.i) (map_ι : map ≫ F'.m = F.m ≫ sq.right) : HasImageMap sq :=
   HasImageMap.mk <| ImageMap.transport sq F hF' map_ι
 #align category_theory.limits.has_image_map.transport CategoryTheory.Limits.HasImageMap.transport
+-/
 
+#print CategoryTheory.Limits.HasImageMap.imageMap /-
 /-- Obtain an `image_map` from a `has_image_map` instance. -/
 def HasImageMap.imageMap {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
     [HasImageMap sq] : ImageMap sq :=
   Classical.choice <| @HasImageMap.hasImageMap _ _ _ _ _ _ sq _
 #align category_theory.limits.has_image_map.image_map CategoryTheory.Limits.HasImageMap.imageMap
+-/
 
+#print CategoryTheory.Limits.hasImageMapOfIsIso /-
 -- see Note [lower instance priority]
 instance (priority := 100) hasImageMapOfIsIso {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom]
     (sq : f ⟶ g) [IsIso sq] : HasImageMap sq :=
@@ -805,7 +834,9 @@ instance (priority := 100) hasImageMapOfIsIso {f g : Arrow C} [HasImage f.Hom] [
           image.lift_fac, category.assoc, ← comma.comp_right, is_iso.hom_inv_id, comma.id_right,
           category.comp_id] }
 #align category_theory.limits.has_image_map_of_is_iso CategoryTheory.Limits.hasImageMapOfIsIso
+-/
 
+#print CategoryTheory.Limits.HasImageMap.comp /-
 instance HasImageMap.comp {f g h : Arrow C} [HasImage f.Hom] [HasImage g.Hom] [HasImage h.Hom]
     (sq1 : f ⟶ g) (sq2 : g ⟶ h) [HasImageMap sq1] [HasImageMap sq2] : HasImageMap (sq1 ≫ sq2) :=
   HasImageMap.mk
@@ -813,6 +844,7 @@ instance HasImageMap.comp {f g h : Arrow C} [HasImage f.Hom] [HasImage g.Hom] [H
       map_ι := by
         simp only [image_map.map_ι, image_map.map_ι_assoc, comma.comp_right, category.assoc] }
 #align category_theory.limits.has_image_map.comp CategoryTheory.Limits.HasImageMap.comp
+-/
 
 variable {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
 
@@ -828,17 +860,23 @@ end
 
 variable [HasImageMap sq]
 
+#print CategoryTheory.Limits.image.map /-
 /-- The map on images induced by a commutative square. -/
 abbrev image.map : image f.Hom ⟶ image g.Hom :=
   (HasImageMap.imageMap sq).map
 #align category_theory.limits.image.map CategoryTheory.Limits.image.map
+-/
 
+#print CategoryTheory.Limits.image.factor_map /-
 theorem image.factor_map : factorThruImage f.Hom ≫ image.map sq = sq.left ≫ factorThruImage g.Hom :=
   by simp
 #align category_theory.limits.image.factor_map CategoryTheory.Limits.image.factor_map
+-/
 
+#print CategoryTheory.Limits.image.map_ι /-
 theorem image.map_ι : image.map sq ≫ image.ι g.Hom = image.ι f.Hom ≫ sq.right := by simp
 #align category_theory.limits.image.map_ι CategoryTheory.Limits.image.map_ι
+-/
 
 #print CategoryTheory.Limits.image.map_homMk'_ι /-
 theorem image.map_homMk'_ι {X Y P Q : C} {k : X ⟶ Y} [HasImage k] {l : P ⟶ Q} [HasImage l]
@@ -854,15 +892,19 @@ variable {h : Arrow C} [HasImage h.Hom] (sq' : g ⟶ h)
 
 variable [HasImageMap sq']
 
+#print CategoryTheory.Limits.imageMapComp /-
 /-- Image maps for composable commutative squares induce an image map in the composite square. -/
 def imageMapComp : ImageMap (sq ≫ sq') where map := image.map sq ≫ image.map sq'
 #align category_theory.limits.image_map_comp CategoryTheory.Limits.imageMapComp
+-/
 
+#print CategoryTheory.Limits.image.map_comp /-
 @[simp]
 theorem image.map_comp [HasImageMap (sq ≫ sq')] :
     image.map (sq ≫ sq') = image.map sq ≫ image.map sq' :=
   show (HasImageMap.imageMap (sq ≫ sq')).map = (imageMapComp sq sq').map by congr
 #align category_theory.limits.image.map_comp CategoryTheory.Limits.image.map_comp
+-/
 
 end
 
@@ -870,15 +912,19 @@ section
 
 variable (f)
 
+#print CategoryTheory.Limits.imageMapId /-
 /-- The identity `image f ⟶ image f` fits into the commutative square represented by the identity
     morphism `𝟙 f` in the arrow category. -/
 def imageMapId : ImageMap (𝟙 f) where map := 𝟙 (image f.Hom)
 #align category_theory.limits.image_map_id CategoryTheory.Limits.imageMapId
+-/
 
+#print CategoryTheory.Limits.image.map_id /-
 @[simp]
 theorem image.map_id [HasImageMap (𝟙 f)] : image.map (𝟙 f) = 𝟙 (image f.Hom) :=
   show (HasImageMap.imageMap (𝟙 f)).map = (imageMapId f).map by congr
 #align category_theory.limits.image.map_id CategoryTheory.Limits.image.map_id
+-/
 
 end
 
@@ -1111,6 +1157,7 @@ open CategoryTheory.Limits
 
 variable {C D : Type _} [Category C] [Category D]
 
+#print CategoryTheory.Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalence /-
 theorem hasStrongEpiMonoFactorisations_imp_of_isEquivalence (F : C ⥤ D) [IsEquivalence F]
     [h : HasStrongEpiMonoFactorisations C] : HasStrongEpiMonoFactorisations D :=
   ⟨fun X Y f =>
@@ -1128,6 +1175,7 @@ theorem hasStrongEpiMonoFactorisations_imp_of_isEquivalence (F : C ⥤ D) [IsEqu
             simpa only [category.assoc, ← F.map_comp_assoc, em.fac', is_equivalence.fun_inv_map,
               iso.inv_hom_id_app, iso.inv_hom_id_app_assoc] using category.comp_id _ }⟩
 #align category_theory.functor.has_strong_epi_mono_factorisations_imp_of_is_equivalence CategoryTheory.Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalence
+-/
 
 end CategoryTheory.Functor

f4758115

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -541,7 +541,6 @@ theorem image.ext [HasImage f] {W : C} {g h : image f ⟶ W} [HasLimit (parallel
     _ = v ≫ q ≫ h := by rw [equalizer.condition g h]
     _ = 𝟙 (image f) ≫ h := by rw [← category.assoc, t]
     _ = h := by rw [category.id_comp]
-    
 #align category_theory.limits.image.ext CategoryTheory.Limits.image.ext
 -/

f4758115

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -119,8 +119,8 @@ theorem ext {F F' : MonoFactorisation f} (hI : F.i = F'.i) (hm : F.m = eqToHom h
     F = F' := by
   cases F; cases F'
   cases hI
-  simp at hm
-  dsimp at F_fac' F'_fac'
+  simp at hm 
+  dsimp at F_fac' F'_fac' 
   congr
   · assumption
   · skip; apply (cancel_mono F_m).1
@@ -552,7 +552,7 @@ instance [HasImage f] [∀ {Z : C} (g h : image f ⟶ Z), HasLimit (parallelPair
 #print CategoryTheory.Limits.epi_image_of_epi /-
 theorem epi_image_of_epi {X Y : C} (f : X ⟶ Y) [HasImage f] [E : Epi f] : Epi (image.ι f) :=
   by
-  rw [← image.fac f] at E
+  rw [← image.fac f] at E 
   skip
   exact epi_of_epi (factor_thru_image f) (image.ι f)
 #align category_theory.limits.epi_image_of_epi CategoryTheory.Limits.epi_image_of_epi

f4758115

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -176,12 +176,6 @@ def ofIsoComp {X' : C} (g : X' ⟶ X) [IsIso g] (F : MonoFactorisation (g ≫ f)
 #align category_theory.limits.mono_factorisation.of_iso_comp CategoryTheory.Limits.MonoFactorisation.ofIsoComp
 -/
 
-/- warning: category_theory.limits.mono_factorisation.of_arrow_iso -> CategoryTheory.Limits.MonoFactorisation.ofArrowIso is a dubious translation:
-lean 3 declaration is
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 /-- If `f` and `g` are isomorphic arrows, then a mono factorisation of `f`
 gives a mono factorisation of `g` -/
 @[simps]
@@ -270,12 +264,6 @@ theorem e_isoExt_inv : F'.e ≫ (isoExt hF hF').inv = F.e := by simp
 #align category_theory.limits.is_image.e_iso_ext_inv CategoryTheory.Limits.IsImage.e_isoExt_inv
 -/
 
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 /-- If `f` and `g` are isomorphic arrows, then a mono factorisation of `f` that is an image
 gives a mono factorisation of `g` that is an image -/
 @[simps]
@@ -305,12 +293,6 @@ namespace ImageFactorisation
 instance [Mono f] : Inhabited (ImageFactorisation f) :=
   ⟨⟨_, IsImage.self f⟩⟩
 
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 /-- If `f` and `g` are isomorphic arrows, then an image factorisation of `f`
 gives an image factorisation of `g` -/
 @[simps]
@@ -335,12 +317,6 @@ theorem HasImage.mk {f : X ⟶ Y} (F : ImageFactorisation f) : HasImage f :=
 #align category_theory.limits.has_image.mk CategoryTheory.Limits.HasImage.mk
 -/
 
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 theorem HasImage.of_arrow_iso {f g : Arrow C} [h : HasImage f.Hom] (sq : f ⟶ g) [IsIso sq] :
     HasImage g.Hom :=
   ⟨⟨h.exists_image.some.of_arrow_iso sq⟩⟩
@@ -699,12 +675,6 @@ instance image.preComp_epi_of_epi [HasImage g] [HasImage (f ≫ g)] [Epi f] :
 #align category_theory.limits.image.pre_comp_epi_of_epi CategoryTheory.Limits.image.preComp_epi_of_epi
 -/
 
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 instance hasImage_iso_comp [IsIso f] [HasImage g] : HasImage (f ≫ g) :=
   HasImage.mk
     { f := (Image.monoFactorisation g).isoComp f
@@ -724,12 +694,6 @@ instance image.isIso_precomp_iso (f : X ⟶ Y) [IsIso f] [HasImage g] : IsIso (i
 #align category_theory.limits.image.is_iso_precomp_iso CategoryTheory.Limits.image.isIso_precomp_iso
 -/
 
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 -- Note that in general we don't have the other comparison map you might expect
 -- `image f ⟶ image (f ≫ g)`.
 instance hasImage_comp_iso [HasImage f] [IsIso g] : HasImage (f ≫ g) :=
@@ -778,12 +742,6 @@ end
 
 section HasImageMap
 
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 /-- An image map is a morphism `image f → image g` fitting into a commutative square and satisfying
     the obvious commutativity conditions. -/
 structure ImageMap {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g) where
@@ -791,12 +749,6 @@ structure ImageMap {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶
   map_ι : map ≫ image.ι g.Hom = image.ι f.Hom ≫ sq.right := by obviously
 #align category_theory.limits.image_map CategoryTheory.Limits.ImageMap
 
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 instance inhabitedImageMap {f : Arrow C} [HasImage f.Hom] : Inhabited (ImageMap (𝟙 f)) :=
   ⟨⟨𝟙 _, by tidy⟩⟩
 #align category_theory.limits.inhabited_image_map CategoryTheory.Limits.inhabitedImageMap
@@ -805,18 +757,12 @@ restate_axiom image_map.map_ι'
 
 attribute [simp, reassoc] image_map.map_ι
 
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 @[simp, reassoc]
 theorem ImageMap.factor_map {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
     (m : ImageMap sq) : factorThruImage f.Hom ≫ m.map = sq.left ≫ factorThruImage g.Hom :=
   (cancel_mono (image.ι g.Hom)).1 <| by simp
 #align category_theory.limits.image_map.factor_map CategoryTheory.Limits.ImageMap.factor_map
 
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 /-- To give an image map for a commutative square with `f` at the top and `g` at the bottom, it
     suffices to give a map between any mono factorisation of `f` and any image factorisation of
     `g`. -/
@@ -828,55 +774,28 @@ def ImageMap.transport {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f
   map_ι := by simp [map_ι]
 #align category_theory.limits.image_map.transport CategoryTheory.Limits.ImageMap.transport
 
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 /-- `has_image_map sq` means that there is an `image_map` for the square `sq`. -/
 class HasImageMap {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g) : Prop where mk' ::
   HasImageMap : Nonempty (ImageMap sq)
 #align category_theory.limits.has_image_map CategoryTheory.Limits.HasImageMap
 
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 theorem HasImageMap.mk {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] {sq : f ⟶ g}
     (m : ImageMap sq) : HasImageMap sq :=
   ⟨Nonempty.intro m⟩
 #align category_theory.limits.has_image_map.mk CategoryTheory.Limits.HasImageMap.mk
 
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 theorem HasImageMap.transport {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
     (F : MonoFactorisation f.Hom) {F' : MonoFactorisation g.Hom} (hF' : IsImage F')
     (map : F.i ⟶ F'.i) (map_ι : map ≫ F'.m = F.m ≫ sq.right) : HasImageMap sq :=
   HasImageMap.mk <| ImageMap.transport sq F hF' map_ι
 #align category_theory.limits.has_image_map.transport CategoryTheory.Limits.HasImageMap.transport
 
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 /-- Obtain an `image_map` from a `has_image_map` instance. -/
 def HasImageMap.imageMap {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
     [HasImageMap sq] : ImageMap sq :=
   Classical.choice <| @HasImageMap.hasImageMap _ _ _ _ _ _ sq _
 #align category_theory.limits.has_image_map.image_map CategoryTheory.Limits.HasImageMap.imageMap
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image_map_of_is_iso CategoryTheory.Limits.hasImageMapOfIsIsoₓ'. -/
 -- see Note [lower instance priority]
 instance (priority := 100) hasImageMapOfIsIso {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom]
     (sq : f ⟶ g) [IsIso sq] : HasImageMap sq :=
@@ -888,12 +807,6 @@ instance (priority := 100) hasImageMapOfIsIso {f g : Arrow C} [HasImage f.Hom] [
           category.comp_id] }
 #align category_theory.limits.has_image_map_of_is_iso CategoryTheory.Limits.hasImageMapOfIsIso
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image_map.comp CategoryTheory.Limits.HasImageMap.compₓ'. -/
 instance HasImageMap.comp {f g h : Arrow C} [HasImage f.Hom] [HasImage g.Hom] [HasImage h.Hom]
     (sq1 : f ⟶ g) (sq2 : g ⟶ h) [HasImageMap sq1] [HasImageMap sq2] : HasImageMap (sq1 ≫ sq2) :=
   HasImageMap.mk
@@ -916,24 +829,15 @@ end
 
 variable [HasImageMap sq]
 
-/- warning: category_theory.limits.image.map -> CategoryTheory.Limits.image.map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map CategoryTheory.Limits.image.mapₓ'. -/
 /-- The map on images induced by a commutative square. -/
 abbrev image.map : image f.Hom ⟶ image g.Hom :=
   (HasImageMap.imageMap sq).map
 #align category_theory.limits.image.map CategoryTheory.Limits.image.map
 
-/- warning: category_theory.limits.image.factor_map -> CategoryTheory.Limits.image.factor_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.factor_map CategoryTheory.Limits.image.factor_mapₓ'. -/
 theorem image.factor_map : factorThruImage f.Hom ≫ image.map sq = sq.left ≫ factorThruImage g.Hom :=
   by simp
 #align category_theory.limits.image.factor_map CategoryTheory.Limits.image.factor_map
 
-/- warning: category_theory.limits.image.map_ι -> CategoryTheory.Limits.image.map_ι is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map_ι CategoryTheory.Limits.image.map_ιₓ'. -/
 theorem image.map_ι : image.map sq ≫ image.ι g.Hom = image.ι f.Hom ≫ sq.right := by simp
 #align category_theory.limits.image.map_ι CategoryTheory.Limits.image.map_ι
 
@@ -951,19 +855,10 @@ variable {h : Arrow C} [HasImage h.Hom] (sq' : g ⟶ h)
 
 variable [HasImageMap sq']
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.limits.image_map_comp CategoryTheory.Limits.imageMapCompₓ'. -/
 /-- Image maps for composable commutative squares induce an image map in the composite square. -/
 def imageMapComp : ImageMap (sq ≫ sq') where map := image.map sq ≫ image.map sq'
 #align category_theory.limits.image_map_comp CategoryTheory.Limits.imageMapComp
 
-/- warning: category_theory.limits.image.map_comp -> CategoryTheory.Limits.image.map_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map_comp CategoryTheory.Limits.image.map_compₓ'. -/
 @[simp]
 theorem image.map_comp [HasImageMap (sq ≫ sq')] :
     image.map (sq ≫ sq') = image.map sq ≫ image.map sq' :=
@@ -976,20 +871,11 @@ section
 
 variable (f)
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.limits.image_map_id CategoryTheory.Limits.imageMapIdₓ'. -/
 /-- The identity `image f ⟶ image f` fits into the commutative square represented by the identity
     morphism `𝟙 f` in the arrow category. -/
 def imageMapId : ImageMap (𝟙 f) where map := 𝟙 (image f.Hom)
 #align category_theory.limits.image_map_id CategoryTheory.Limits.imageMapId
 
-/- warning: category_theory.limits.image.map_id -> CategoryTheory.Limits.image.map_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map_id CategoryTheory.Limits.image.map_idₓ'. -/
 @[simp]
 theorem image.map_id [HasImageMap (𝟙 f)] : image.map (𝟙 f) = 𝟙 (image f.Hom) :=
   show (HasImageMap.imageMap (𝟙 f)).map = (imageMapId f).map by congr
@@ -1226,12 +1112,6 @@ open CategoryTheory.Limits
 
 variable {C D : Type _} [Category C] [Category D]
 
-/- warning: category_theory.functor.has_strong_epi_mono_factorisations_imp_of_is_equivalence -> CategoryTheory.Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalence is a dubious translation:
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-  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) [_inst_3 : CategoryTheory.IsEquivalence.{u3, u4, u1, u2} C _inst_1 D _inst_2 F] [h : CategoryTheory.Limits.HasStrongEpiMonoFactorisations.{u3, u1} C _inst_1], CategoryTheory.Limits.HasStrongEpiMonoFactorisations.{u4, u2} D _inst_2
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-Case conversion may be inaccurate. Consider using '#align category_theory.functor.has_strong_epi_mono_factorisations_imp_of_is_equivalence CategoryTheory.Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalenceₓ'. -/
 theorem hasStrongEpiMonoFactorisations_imp_of_isEquivalence (F : C ⥤ D) [IsEquivalence F]
     [h : HasStrongEpiMonoFactorisations C] : HasStrongEpiMonoFactorisations D :=
   ⟨fun X Y f =>

f4758115

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -123,8 +123,7 @@ theorem ext {F F' : MonoFactorisation f} (hI : F.i = F'.i) (hm : F.m = eqToHom h
   dsimp at F_fac' F'_fac'
   congr
   · assumption
-  · skip
-    apply (cancel_mono F_m).1
+  · skip; apply (cancel_mono F_m).1
     rw [F_fac', hm, F'_fac']
 #align category_theory.limits.mono_factorisation.ext CategoryTheory.Limits.MonoFactorisation.ext
 -/
@@ -463,10 +462,8 @@ theorem IsImage.lift_ι {F : MonoFactorisation f} (hF : IsImage F) :
 -- (they then automatically commute with the `e`s)
 -- and show that an `image_of f` gives an initial object there
 -- (uniqueness of the lift comes for free).
-instance image.lift_mono (F' : MonoFactorisation f) : Mono (image.lift F') :=
-  by
-  apply mono_of_mono _ F'.m
-  simpa using mono_factorisation.m_mono _
+instance image.lift_mono (F' : MonoFactorisation f) : Mono (image.lift F') := by
+  apply mono_of_mono _ F'.m; simpa using mono_factorisation.m_mono _
 #align category_theory.limits.image.lift_mono CategoryTheory.Limits.image.lift_mono
 -/
 
@@ -558,10 +555,7 @@ theorem image.ext [HasImage f] {W : C} {g h : image f ⟶ W} [HasLimit (parallel
   let v := image.lift F'
   have t₀ : v ≫ q ≫ image.ι f = image.ι f := image.lift_fac F'
   have t : v ≫ q = 𝟙 (image f) :=
-    (cancel_mono_id (image.ι f)).1
-      (by
-        convert t₀ using 1
-        rw [category.assoc])
+    (cancel_mono_id (image.ι f)).1 (by convert t₀ using 1; rw [category.assoc])
   -- The proof from wikipedia next proves `q ≫ v = 𝟙 _`,
   -- and concludes that `equalizer g h ≅ image f`,
   -- but this isn't necessary.
@@ -590,10 +584,7 @@ theorem epi_image_of_epi {X Y : C} (f : X ⟶ Y) [HasImage f] [E : Epi f] : Epi
 
 #print CategoryTheory.Limits.epi_of_epi_image /-
 theorem epi_of_epi_image {X Y : C} (f : X ⟶ Y) [HasImage f] [Epi (image.ι f)]
-    [Epi (factorThruImage f)] : Epi f :=
-  by
-  rw [← image.fac f]
-  apply epi_comp
+    [Epi (factorThruImage f)] : Epi f := by rw [← image.fac f]; apply epi_comp
 #align category_theory.limits.epi_of_epi_image CategoryTheory.Limits.epi_of_epi_image
 -/
 
@@ -632,9 +623,7 @@ def image.eqToIso (h : f = f') : image f ≅ image f' :=
 the image inclusion maps commute with `image.eq_to_iso`.
 -/
 theorem image.eq_fac [HasEqualizers C] (h : f = f') :
-    image.ι f = (image.eqToIso h).Hom ≫ image.ι f' :=
-  by
-  ext
+    image.ι f = (image.eqToIso h).Hom ≫ image.ι f' := by ext;
   simp [image.eq_to_iso, image.eq_to_hom]
 #align category_theory.limits.image.eq_fac CategoryTheory.Limits.image.eq_fac
 -/
@@ -731,11 +720,7 @@ instance image.isIso_precomp_iso (f : X ⟶ Y) [IsIso f] [HasImage g] : IsIso (i
         { i := image (f ≫ g)
           m := image.ι (f ≫ g)
           e := inv f ≫ factorThruImage (f ≫ g) },
-      ⟨by
-        ext
-        simp [image.pre_comp], by
-        ext
-        simp [image.pre_comp]⟩⟩⟩
+      ⟨by ext; simp [image.pre_comp], by ext; simp [image.pre_comp]⟩⟩⟩
 #align category_theory.limits.image.is_iso_precomp_iso CategoryTheory.Limits.image.isIso_precomp_iso
 -/
 
@@ -765,20 +750,14 @@ def image.compIso [HasImage f] [IsIso g] : image f ≅ image (f ≫ g)
 #print CategoryTheory.Limits.image.compIso_hom_comp_image_ι /-
 @[simp, reassoc]
 theorem image.compIso_hom_comp_image_ι [HasImage f] [IsIso g] :
-    (image.compIso f g).Hom ≫ image.ι (f ≫ g) = image.ι f ≫ g :=
-  by
-  ext
-  simp [image.comp_iso]
+    (image.compIso f g).Hom ≫ image.ι (f ≫ g) = image.ι f ≫ g := by ext; simp [image.comp_iso]
 #align category_theory.limits.image.comp_iso_hom_comp_image_ι CategoryTheory.Limits.image.compIso_hom_comp_image_ι
 -/
 
 #print CategoryTheory.Limits.image.compIso_inv_comp_image_ι /-
 @[simp, reassoc]
 theorem image.compIso_inv_comp_image_ι [HasImage f] [IsIso g] :
-    (image.compIso f g).inv ≫ image.ι f = image.ι (f ≫ g) ≫ inv g :=
-  by
-  ext
-  simp [image.comp_iso]
+    (image.compIso f g).inv ≫ image.ι f = image.ι (f ≫ g) ≫ inv g := by ext; simp [image.comp_iso]
 #align category_theory.limits.image.comp_iso_inv_comp_image_ι CategoryTheory.Limits.image.compIso_inv_comp_image_ι
 -/
 
@@ -1137,9 +1116,7 @@ section HasStrongEpiImages
     strong epi-mono factorisation. -/
 theorem strongEpi_of_strongEpiMonoFactorisation {X Y : C} {f : X ⟶ Y}
     (F : StrongEpiMonoFactorisation f) {F' : MonoFactorisation f} (hF' : IsImage F') :
-    StrongEpi F'.e := by
-  rw [← is_image.e_iso_ext_hom F.to_mono_is_image hF']
-  apply strong_epi_comp
+    StrongEpi F'.e := by rw [← is_image.e_iso_ext_hom F.to_mono_is_image hF']; apply strong_epi_comp
 #align category_theory.limits.strong_epi_of_strong_epi_mono_factorisation CategoryTheory.Limits.strongEpi_of_strongEpiMonoFactorisation
 -/
 
@@ -1198,8 +1175,7 @@ instance (priority := 100) hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers [
                   e := pullback.lift _ _ sq.w } ≫
               pullback.fst
           fac_left' := by simp only [image.fac_lift_assoc, pullback.lift_fst]
-          fac_right' := by
-            ext
+          fac_right' := by ext;
             simp only [sq.w, category.assoc, image.fac_lift_assoc, pullback.lift_fst_assoc] }
 #align category_theory.limits.has_strong_epi_images_of_has_pullbacks_of_has_equalizers CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers
 -/

f4758115

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -827,10 +827,7 @@ restate_axiom image_map.map_ι'
 attribute [simp, reassoc] image_map.map_ι
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.image_map.factor_map CategoryTheory.Limits.ImageMap.factor_mapₓ'. -/
 @[simp, reassoc]
 theorem ImageMap.factor_map {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
@@ -839,10 +836,7 @@ theorem ImageMap.factor_map {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (s
 #align category_theory.limits.image_map.factor_map CategoryTheory.Limits.ImageMap.factor_map
 
 /- warning: category_theory.limits.image_map.transport -> CategoryTheory.Limits.ImageMap.transport is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.image_map.transport CategoryTheory.Limits.ImageMap.transportₓ'. -/
 /-- To give an image map for a commutative square with `f` at the top and `g` at the bottom, it
     suffices to give a map between any mono factorisation of `f` and any image factorisation of
@@ -878,10 +872,7 @@ theorem HasImageMap.mk {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] {sq : f
 #align category_theory.limits.has_image_map.mk CategoryTheory.Limits.HasImageMap.mk
 
 /- warning: category_theory.limits.has_image_map.transport -> CategoryTheory.Limits.HasImageMap.transport is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image_map.transport CategoryTheory.Limits.HasImageMap.transportₓ'. -/
 theorem HasImageMap.transport {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
     (F : MonoFactorisation f.Hom) {F' : MonoFactorisation g.Hom} (hF' : IsImage F')
@@ -947,10 +938,7 @@ end
 variable [HasImageMap sq]
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map CategoryTheory.Limits.image.mapₓ'. -/
 /-- The map on images induced by a commutative square. -/
 abbrev image.map : image f.Hom ⟶ image g.Hom :=
@@ -958,20 +946,14 @@ abbrev image.map : image f.Hom ⟶ image g.Hom :=
 #align category_theory.limits.image.map CategoryTheory.Limits.image.map
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.factor_map CategoryTheory.Limits.image.factor_mapₓ'. -/
 theorem image.factor_map : factorThruImage f.Hom ≫ image.map sq = sq.left ≫ factorThruImage g.Hom :=
   by simp
 #align category_theory.limits.image.factor_map CategoryTheory.Limits.image.factor_map
 
 /- warning: category_theory.limits.image.map_ι -> CategoryTheory.Limits.image.map_ι is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map_ι CategoryTheory.Limits.image.map_ιₓ'. -/
 theorem image.map_ι : image.map sq ≫ image.ι g.Hom = image.ι f.Hom ≫ sq.right := by simp
 #align category_theory.limits.image.map_ι CategoryTheory.Limits.image.map_ι
@@ -1001,10 +983,7 @@ def imageMapComp : ImageMap (sq ≫ sq') where map := image.map sq ≫ image.map
 #align category_theory.limits.image_map_comp CategoryTheory.Limits.imageMapComp
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map_comp CategoryTheory.Limits.image.map_compₓ'. -/
 @[simp]
 theorem image.map_comp [HasImageMap (sq ≫ sq')] :
@@ -1030,10 +1009,7 @@ def imageMapId : ImageMap (𝟙 f) where map := 𝟙 (image f.Hom)
 #align category_theory.limits.image_map_id CategoryTheory.Limits.imageMapId
 
 /- warning: category_theory.limits.image.map_id -> CategoryTheory.Limits.image.map_id is a dubious translation:
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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_5 : CategoryTheory.Limits.HasImageMap.{u1, u2} C _inst_1 f f _inst_2 _inst_2 (CategoryTheory.CategoryStruct.id.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1)) f)], Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C 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u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1)) f) _inst_5) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Limits.image.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f) _inst_2))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map_id CategoryTheory.Limits.image.map_idₓ'. -/
 @[simp]
 theorem image.map_id [HasImageMap (𝟙 f)] : image.map (𝟙 f) = 𝟙 (image f.Hom) :=

f4758115

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -87,7 +87,7 @@ structure MonoFactorisation (f : X ⟶ Y) where
 
 restate_axiom mono_factorisation.fac'
 
-attribute [simp, reassoc.1] mono_factorisation.fac
+attribute [simp, reassoc] mono_factorisation.fac
 
 attribute [instance] mono_factorisation.m_mono
 
@@ -209,12 +209,12 @@ structure IsImage (F : MonoFactorisation f) where
 
 restate_axiom is_image.lift_fac'
 
-attribute [simp, reassoc.1] is_image.lift_fac
+attribute [simp, reassoc] is_image.lift_fac
 
 namespace IsImage
 
 #print CategoryTheory.Limits.IsImage.fac_lift /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem fac_lift {F : MonoFactorisation f} (hF : IsImage F) (F' : MonoFactorisation f) :
     F.e ≫ hF.lift F' = F'.e :=
   (cancel_mono F'.m).1 <| by simp
@@ -412,7 +412,7 @@ theorem as_factorThruImage : (Image.monoFactorisation f).e = factorThruImage f :
 -/
 
 #print CategoryTheory.Limits.image.fac /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem image.fac : factorThruImage f ≫ image.ι f = f :=
   (Image.monoFactorisation f).fac
 #align category_theory.limits.image.fac CategoryTheory.Limits.image.fac
@@ -429,14 +429,14 @@ def image.lift (F' : MonoFactorisation f) : image f ⟶ F'.i :=
 -/
 
 #print CategoryTheory.Limits.image.lift_fac /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem image.lift_fac (F' : MonoFactorisation f) : image.lift F' ≫ F'.m = image.ι f :=
   (Image.isImage f).lift_fac F'
 #align category_theory.limits.image.lift_fac CategoryTheory.Limits.image.lift_fac
 -/
 
 #print CategoryTheory.Limits.image.fac_lift /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem image.fac_lift (F' : MonoFactorisation f) : factorThruImage f ≫ image.lift F' = F'.e :=
   (Image.isImage f).fac_lift F'
 #align category_theory.limits.image.fac_lift CategoryTheory.Limits.image.fac_lift
@@ -450,7 +450,7 @@ theorem image.isImage_lift (F : MonoFactorisation f) : (Image.isImage f).lift F
 -/
 
 #print CategoryTheory.Limits.IsImage.lift_ι /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem IsImage.lift_ι {F : MonoFactorisation f} (hF : IsImage F) :
     hF.lift (Image.monoFactorisation f) ≫ image.ι f = F.m :=
   hF.lift_fac _
@@ -521,14 +521,14 @@ def imageMonoIsoSource [Mono f] : image f ≅ X :=
 -/
 
 #print CategoryTheory.Limits.imageMonoIsoSource_inv_ι /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem imageMonoIsoSource_inv_ι [Mono f] : (imageMonoIsoSource f).inv ≫ image.ι f = f := by
   simp [image_mono_iso_source]
 #align category_theory.limits.image_mono_iso_source_inv_ι CategoryTheory.Limits.imageMonoIsoSource_inv_ι
 -/
 
 #print CategoryTheory.Limits.imageMonoIsoSource_hom_self /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem imageMonoIsoSource_hom_self [Mono f] : (imageMonoIsoSource f).Hom ≫ f = image.ι f :=
   by
   conv =>
@@ -656,14 +656,14 @@ def image.preComp [HasImage g] [HasImage (f ≫ g)] : image (f ≫ g) ⟶ image
 -/
 
 #print CategoryTheory.Limits.image.preComp_ι /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem image.preComp_ι [HasImage g] [HasImage (f ≫ g)] :
     image.preComp f g ≫ image.ι g = image.ι (f ≫ g) := by simp [image.pre_comp]
 #align category_theory.limits.image.pre_comp_ι CategoryTheory.Limits.image.preComp_ι
 -/
 
 #print CategoryTheory.Limits.image.factorThruImage_preComp /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem image.factorThruImage_preComp [HasImage g] [HasImage (f ≫ g)] :
     factorThruImage (f ≫ g) ≫ image.preComp f g = f ≫ factorThruImage g := by simp [image.pre_comp]
 #align category_theory.limits.image.factor_thru_image_pre_comp CategoryTheory.Limits.image.factorThruImage_preComp
@@ -763,7 +763,7 @@ def image.compIso [HasImage f] [IsIso g] : image f ≅ image (f ≫ g)
 -/
 
 #print CategoryTheory.Limits.image.compIso_hom_comp_image_ι /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem image.compIso_hom_comp_image_ι [HasImage f] [IsIso g] :
     (image.compIso f g).Hom ≫ image.ι (f ≫ g) = image.ι f ≫ g :=
   by
@@ -773,7 +773,7 @@ theorem image.compIso_hom_comp_image_ι [HasImage f] [IsIso g] :
 -/
 
 #print CategoryTheory.Limits.image.compIso_inv_comp_image_ι /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem image.compIso_inv_comp_image_ι [HasImage f] [IsIso g] :
     (image.compIso f g).inv ≫ image.ι f = image.ι (f ≫ g) ≫ inv g :=
   by
@@ -824,7 +824,7 @@ instance inhabitedImageMap {f : Arrow C} [HasImage f.Hom] : Inhabited (ImageMap
 
 restate_axiom image_map.map_ι'
 
-attribute [simp, reassoc.1] image_map.map_ι
+attribute [simp, reassoc] image_map.map_ι
 
 /- warning: category_theory.limits.image_map.factor_map -> CategoryTheory.Limits.ImageMap.factor_map is a dubious translation:
 lean 3 declaration is
@@ -832,7 +832,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)] (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1))) f g) (m : CategoryTheory.Limits.ImageMap.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Limits.image.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) _inst_3)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Limits.image.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f) _inst_2) (CategoryTheory.Limits.image.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) _inst_3) (CategoryTheory.Limits.factorThruImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f) _inst_2) (CategoryTheory.Limits.ImageMap.map.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq m)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) (CategoryTheory.Limits.image.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) _inst_3) (CategoryTheory.CommaMorphism.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f g sq) (CategoryTheory.Limits.factorThruImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) _inst_3))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.image_map.factor_map CategoryTheory.Limits.ImageMap.factor_mapₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem ImageMap.factor_map {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
     (m : ImageMap sq) : factorThruImage f.Hom ≫ m.map = sq.left ≫ factorThruImage g.Hom :=
   (cancel_mono (image.ι g.Hom)).1 <| by simp

f4758115

bump to nightly-2023-04-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

ff662d55

Diff

@@ -505,7 +505,7 @@ class HasImages : Prop where
 #align category_theory.limits.has_images CategoryTheory.Limits.HasImages
 -/
 
-attribute [instance] has_images.has_image
+attribute [instance 100] has_images.has_image
 
 end
 
@@ -1055,7 +1055,7 @@ class HasImageMaps where
 #align category_theory.limits.has_image_maps CategoryTheory.Limits.HasImageMaps
 -/
 
-attribute [instance] has_image_maps.has_image_map
+attribute [instance 100] has_image_maps.has_image_map
 
 end

f4758115

bump to nightly-2023-03-09-03

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

061741a1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Markus Himmel
 
 ! This file was ported from Lean 3 source module category_theory.limits.shapes.images
-! leanprover-community/mathlib commit 563aed347eb59dc4181cb732cda0d124d736eaa3
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! 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.Limits.Shapes.StrongEpi
 /-!
 # Categorical images
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define the categorical image of `f` as a factorisation `f = e ≫ m` through a monomorphism `m`,
 so that `m` factors through the `m'` in any other such factorisation.

563aed34

bump to nightly-2023-03-07-20

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

c0bba963

Diff

@@ -71,6 +71,7 @@ variable {C : Type u} [Category.{v} C]
 
 variable {X Y : C} (f : X ⟶ Y)
 
+#print CategoryTheory.Limits.MonoFactorisation /-
 /-- A factorisation of a morphism `f = e ≫ m`, with `m` monic. -/
 structure MonoFactorisation (f : X ⟶ Y) where
   i : C
@@ -79,6 +80,7 @@ structure MonoFactorisation (f : X ⟶ Y) where
   e : X ⟶ I
   fac : e ≫ m = f := by obviously
 #align category_theory.limits.mono_factorisation CategoryTheory.Limits.MonoFactorisation
+-/
 
 restate_axiom mono_factorisation.fac'
 
@@ -90,12 +92,14 @@ attribute [instance] mono_factorisation.m_mono
 
 namespace MonoFactorisation
 
+#print CategoryTheory.Limits.MonoFactorisation.self /-
 /-- The obvious factorisation of a monomorphism through itself. -/
 def self [Mono f] : MonoFactorisation f where
   i := X
   m := f
   e := 𝟙 X
 #align category_theory.limits.mono_factorisation.self CategoryTheory.Limits.MonoFactorisation.self
+-/
 
 -- I'm not sure we really need this, but the linter says that an inhabited instance
 -- ought to exist...
@@ -104,6 +108,7 @@ instance [Mono f] : Inhabited (MonoFactorisation f) :=
 
 variable {f}
 
+#print CategoryTheory.Limits.MonoFactorisation.ext /-
 /-- The morphism `m` in a factorisation `f = e ≫ m` through a monomorphism is uniquely
 determined. -/
 @[ext]
@@ -119,7 +124,9 @@ theorem ext {F F' : MonoFactorisation f} (hI : F.i = F'.i) (hm : F.m = eqToHom h
     apply (cancel_mono F_m).1
     rw [F_fac', hm, F'_fac']
 #align category_theory.limits.mono_factorisation.ext CategoryTheory.Limits.MonoFactorisation.ext
+-/
 
+#print CategoryTheory.Limits.MonoFactorisation.compMono /-
 /-- Any mono factorisation of `f` gives a mono factorisation of `f ≫ g` when `g` is a mono. -/
 @[simps]
 def compMono (F : MonoFactorisation f) {Y' : C} (g : Y ⟶ Y') [Mono g] : MonoFactorisation (f ≫ g)
@@ -129,7 +136,9 @@ def compMono (F : MonoFactorisation f) {Y' : C} (g : Y ⟶ Y') [Mono g] : MonoFa
   m_mono := mono_comp _ _
   e := F.e
 #align category_theory.limits.mono_factorisation.comp_mono CategoryTheory.Limits.MonoFactorisation.compMono
+-/
 
+#print CategoryTheory.Limits.MonoFactorisation.ofCompIso /-
 /-- A mono factorisation of `f ≫ g`, where `g` is an isomorphism,
 gives a mono factorisation of `f`. -/
 @[simps]
@@ -140,7 +149,9 @@ def ofCompIso {Y' : C} {g : Y ⟶ Y'} [IsIso g] (F : MonoFactorisation (f ≫ g)
   m_mono := mono_comp _ _
   e := F.e
 #align category_theory.limits.mono_factorisation.of_comp_iso CategoryTheory.Limits.MonoFactorisation.ofCompIso
+-/
 
+#print CategoryTheory.Limits.MonoFactorisation.isoComp /-
 /-- Any mono factorisation of `f` gives a mono factorisation of `g ≫ f`. -/
 @[simps]
 def isoComp (F : MonoFactorisation f) {X' : C} (g : X' ⟶ X) : MonoFactorisation (g ≫ f)
@@ -149,7 +160,9 @@ def isoComp (F : MonoFactorisation f) {X' : C} (g : X' ⟶ X) : MonoFactorisatio
   m := F.m
   e := g ≫ F.e
 #align category_theory.limits.mono_factorisation.iso_comp CategoryTheory.Limits.MonoFactorisation.isoComp
+-/
 
+#print CategoryTheory.Limits.MonoFactorisation.ofIsoComp /-
 /-- A mono factorisation of `g ≫ f`, where `g` is an isomorphism,
 gives a mono factorisation of `f`. -/
 @[simps]
@@ -159,7 +172,14 @@ def ofIsoComp {X' : C} (g : X' ⟶ X) [IsIso g] (F : MonoFactorisation (g ≫ f)
   m := F.m
   e := inv g ≫ F.e
 #align category_theory.limits.mono_factorisation.of_iso_comp CategoryTheory.Limits.MonoFactorisation.ofIsoComp
+-/
 
+/- warning: category_theory.limits.mono_factorisation.of_arrow_iso -> CategoryTheory.Limits.MonoFactorisation.ofArrowIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1}, (CategoryTheory.Limits.MonoFactorisation.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) -> (forall (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1))) f g) [_inst_2 : CategoryTheory.IsIso.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1) f g sq], CategoryTheory.Limits.MonoFactorisation.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1}, (CategoryTheory.Limits.MonoFactorisation.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) -> (forall (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1))) f g) [_inst_2 : CategoryTheory.IsIso.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1) f g sq], CategoryTheory.Limits.MonoFactorisation.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.mono_factorisation.of_arrow_iso CategoryTheory.Limits.MonoFactorisation.ofArrowIsoₓ'. -/
 /-- If `f` and `g` are isomorphic arrows, then a mono factorisation of `f`
 gives a mono factorisation of `g` -/
 @[simps]
@@ -176,11 +196,13 @@ end MonoFactorisation
 
 variable {f}
 
+#print CategoryTheory.Limits.IsImage /-
 /-- Data exhibiting that a given factorisation through a mono is initial. -/
 structure IsImage (F : MonoFactorisation f) where
   lift : ∀ F' : MonoFactorisation f, F.i ⟶ F'.i
-  lift_fac' : ∀ F' : MonoFactorisation f, lift F' ≫ F'.m = F.m := by obviously
+  lift_fac : ∀ F' : MonoFactorisation f, lift F' ≫ F'.m = F.m := by obviously
 #align category_theory.limits.is_image CategoryTheory.Limits.IsImage
+-/
 
 restate_axiom is_image.lift_fac'
 
@@ -188,24 +210,29 @@ attribute [simp, reassoc.1] is_image.lift_fac
 
 namespace IsImage
 
+#print CategoryTheory.Limits.IsImage.fac_lift /-
 @[simp, reassoc.1]
 theorem fac_lift {F : MonoFactorisation f} (hF : IsImage F) (F' : MonoFactorisation f) :
     F.e ≫ hF.lift F' = F'.e :=
   (cancel_mono F'.m).1 <| by simp
 #align category_theory.limits.is_image.fac_lift CategoryTheory.Limits.IsImage.fac_lift
+-/
 
 variable (f)
 
+#print CategoryTheory.Limits.IsImage.self /-
 /-- The trivial factorisation of a monomorphism satisfies the universal property. -/
 @[simps]
 def self [Mono f] : IsImage (MonoFactorisation.self f) where lift F' := F'.e
 #align category_theory.limits.is_image.self CategoryTheory.Limits.IsImage.self
+-/
 
 instance [Mono f] : Inhabited (IsImage (MonoFactorisation.self f)) :=
   ⟨self f⟩
 
 variable {f}
 
+#print CategoryTheory.Limits.IsImage.isoExt /-
 -- TODO this is another good candidate for a future `unique_up_to_canonical_iso`.
 /-- Two factorisations through monomorphisms satisfying the universal property
 must factor through isomorphic objects. -/
@@ -217,21 +244,36 @@ def isoExt {F F' : MonoFactorisation f} (hF : IsImage F) (hF' : IsImage F') : F.
   hom_inv_id' := (cancel_mono F.m).1 (by simp)
   inv_hom_id' := (cancel_mono F'.m).1 (by simp)
 #align category_theory.limits.is_image.iso_ext CategoryTheory.Limits.IsImage.isoExt
+-/
 
 variable {F F' : MonoFactorisation f} (hF : IsImage F) (hF' : IsImage F')
 
+#print CategoryTheory.Limits.IsImage.isoExt_hom_m /-
 theorem isoExt_hom_m : (isoExt hF hF').Hom ≫ F'.m = F.m := by simp
 #align category_theory.limits.is_image.iso_ext_hom_m CategoryTheory.Limits.IsImage.isoExt_hom_m
+-/
 
+#print CategoryTheory.Limits.IsImage.isoExt_inv_m /-
 theorem isoExt_inv_m : (isoExt hF hF').inv ≫ F.m = F'.m := by simp
 #align category_theory.limits.is_image.iso_ext_inv_m CategoryTheory.Limits.IsImage.isoExt_inv_m
+-/
 
+#print CategoryTheory.Limits.IsImage.e_isoExt_hom /-
 theorem e_isoExt_hom : F.e ≫ (isoExt hF hF').Hom = F'.e := by simp
 #align category_theory.limits.is_image.e_iso_ext_hom CategoryTheory.Limits.IsImage.e_isoExt_hom
+-/
 
+#print CategoryTheory.Limits.IsImage.e_isoExt_inv /-
 theorem e_isoExt_inv : F'.e ≫ (isoExt hF hF').inv = F.e := by simp
 #align category_theory.limits.is_image.e_iso_ext_inv CategoryTheory.Limits.IsImage.e_isoExt_inv
+-/
 
+/- warning: category_theory.limits.is_image.of_arrow_iso -> CategoryTheory.Limits.IsImage.ofArrowIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} {F : CategoryTheory.Limits.MonoFactorisation.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)}, (CategoryTheory.Limits.IsImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f) F) -> (forall (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1))) f g) [_inst_2 : CategoryTheory.IsIso.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1) f g sq], CategoryTheory.Limits.IsImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) (CategoryTheory.Limits.MonoFactorisation.ofArrowIso.{u1, u2} C _inst_1 f g F sq _inst_2))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} {F : CategoryTheory.Limits.MonoFactorisation.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)}, (CategoryTheory.Limits.IsImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f) F) -> (forall (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1))) f g) [_inst_2 : CategoryTheory.IsIso.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1) f g sq], CategoryTheory.Limits.IsImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) (CategoryTheory.Limits.MonoFactorisation.ofArrowIso.{u1, u2} C _inst_1 f g F sq _inst_2))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_image.of_arrow_iso CategoryTheory.Limits.IsImage.ofArrowIsoₓ'. -/
 /-- If `f` and `g` are isomorphic arrows, then a mono factorisation of `f` that is an image
 gives a mono factorisation of `g` that is an image -/
 @[simps]
@@ -239,7 +281,7 @@ def ofArrowIso {f g : Arrow C} {F : MonoFactorisation f.Hom} (hF : IsImage F) (s
     [IsIso sq] : IsImage (F.of_arrow_iso sq)
     where
   lift F' := hF.lift (F'.of_arrow_iso (inv sq))
-  lift_fac' F' := by
+  lift_fac F' := by
     simpa only [mono_factorisation.of_arrow_iso_m, arrow.inv_right, ← category.assoc,
       is_iso.comp_inv_eq] using hF.lift_fac (F'.of_arrow_iso (inv sq))
 #align category_theory.limits.is_image.of_arrow_iso CategoryTheory.Limits.IsImage.ofArrowIso
@@ -248,17 +290,25 @@ end IsImage
 
 variable (f)
 
+#print CategoryTheory.Limits.ImageFactorisation /-
 /-- Data exhibiting that a morphism `f` has an image. -/
 structure ImageFactorisation (f : X ⟶ Y) where
   f : MonoFactorisation f
   IsImage : IsImage F
 #align category_theory.limits.image_factorisation CategoryTheory.Limits.ImageFactorisation
+-/
 
 namespace ImageFactorisation
 
 instance [Mono f] : Inhabited (ImageFactorisation f) :=
   ⟨⟨_, IsImage.self f⟩⟩
 
+/- warning: category_theory.limits.image_factorisation.of_arrow_iso -> CategoryTheory.Limits.ImageFactorisation.ofArrowIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1}, (CategoryTheory.Limits.ImageFactorisation.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) -> (forall (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1))) f g) [_inst_2 : CategoryTheory.IsIso.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1) f g sq], CategoryTheory.Limits.ImageFactorisation.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1}, (CategoryTheory.Limits.ImageFactorisation.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) -> (forall (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1))) f g) [_inst_2 : CategoryTheory.IsIso.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1) f g sq], CategoryTheory.Limits.ImageFactorisation.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.image_factorisation.of_arrow_iso CategoryTheory.Limits.ImageFactorisation.ofArrowIsoₓ'. -/
 /-- If `f` and `g` are isomorphic arrows, then an image factorisation of `f`
 gives an image factorisation of `g` -/
 @[simps]
@@ -270,102 +320,141 @@ def ofArrowIso {f g : Arrow C} (F : ImageFactorisation f.Hom) (sq : f ⟶ g) [Is
 
 end ImageFactorisation
 
+#print CategoryTheory.Limits.HasImage /-
 /-- `has_image f` means that there exists an image factorisation of `f`. -/
 class HasImage (f : X ⟶ Y) : Prop where mk' ::
   exists_image : Nonempty (ImageFactorisation f)
 #align category_theory.limits.has_image CategoryTheory.Limits.HasImage
+-/
 
+#print CategoryTheory.Limits.HasImage.mk /-
 theorem HasImage.mk {f : X ⟶ Y} (F : ImageFactorisation f) : HasImage f :=
   ⟨Nonempty.intro F⟩
 #align category_theory.limits.has_image.mk CategoryTheory.Limits.HasImage.mk
+-/
 
+/- warning: category_theory.limits.has_image.of_arrow_iso -> CategoryTheory.Limits.HasImage.of_arrow_iso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [h : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1))) f g) [_inst_2 : CategoryTheory.IsIso.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1) f g sq], CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [h : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1))) f g) [_inst_2 : CategoryTheory.IsIso.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1) f g sq], CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image.of_arrow_iso CategoryTheory.Limits.HasImage.of_arrow_isoₓ'. -/
 theorem HasImage.of_arrow_iso {f g : Arrow C} [h : HasImage f.Hom] (sq : f ⟶ g) [IsIso sq] :
     HasImage g.Hom :=
   ⟨⟨h.exists_image.some.of_arrow_iso sq⟩⟩
 #align category_theory.limits.has_image.of_arrow_iso CategoryTheory.Limits.HasImage.of_arrow_iso
 
+#print CategoryTheory.Limits.mono_hasImage /-
 instance (priority := 100) mono_hasImage (f : X ⟶ Y) [Mono f] : HasImage f :=
   HasImage.mk ⟨_, IsImage.self f⟩
 #align category_theory.limits.mono_has_image CategoryTheory.Limits.mono_hasImage
+-/
 
 section
 
 variable [HasImage f]
 
+#print CategoryTheory.Limits.Image.monoFactorisation /-
 /-- Some factorisation of `f` through a monomorphism (selected with choice). -/
 def Image.monoFactorisation : MonoFactorisation f :=
   (Classical.choice HasImage.exists_image).f
 #align category_theory.limits.image.mono_factorisation CategoryTheory.Limits.Image.monoFactorisation
+-/
 
+#print CategoryTheory.Limits.Image.isImage /-
 /-- The witness of the universal property for the chosen factorisation of `f` through
 a monomorphism. -/
 def Image.isImage : IsImage (Image.monoFactorisation f) :=
   (Classical.choice HasImage.exists_image).IsImage
 #align category_theory.limits.image.is_image CategoryTheory.Limits.Image.isImage
+-/
 
+#print CategoryTheory.Limits.image /-
 /-- The categorical image of a morphism. -/
 def image : C :=
   (Image.monoFactorisation f).i
 #align category_theory.limits.image CategoryTheory.Limits.image
+-/
 
+#print CategoryTheory.Limits.image.ι /-
 /-- The inclusion of the image of a morphism into the target. -/
 def image.ι : image f ⟶ Y :=
   (Image.monoFactorisation f).m
 #align category_theory.limits.image.ι CategoryTheory.Limits.image.ι
+-/
 
+#print CategoryTheory.Limits.image.as_ι /-
 @[simp]
 theorem image.as_ι : (Image.monoFactorisation f).m = image.ι f :=
   rfl
 #align category_theory.limits.image.as_ι CategoryTheory.Limits.image.as_ι
+-/
 
 instance : Mono (image.ι f) :=
   (Image.monoFactorisation f).m_mono
 
+#print CategoryTheory.Limits.factorThruImage /-
 /-- The map from the source to the image of a morphism. -/
 def factorThruImage : X ⟶ image f :=
   (Image.monoFactorisation f).e
 #align category_theory.limits.factor_thru_image CategoryTheory.Limits.factorThruImage
+-/
 
+#print CategoryTheory.Limits.as_factorThruImage /-
 /-- Rewrite in terms of the `factor_thru_image` interface. -/
 @[simp]
 theorem as_factorThruImage : (Image.monoFactorisation f).e = factorThruImage f :=
   rfl
 #align category_theory.limits.as_factor_thru_image CategoryTheory.Limits.as_factorThruImage
+-/
 
+#print CategoryTheory.Limits.image.fac /-
 @[simp, reassoc.1]
 theorem image.fac : factorThruImage f ≫ image.ι f = f :=
   (Image.monoFactorisation f).fac
 #align category_theory.limits.image.fac CategoryTheory.Limits.image.fac
+-/
 
 variable {f}
 
+#print CategoryTheory.Limits.image.lift /-
 /-- Any other factorisation of the morphism `f` through a monomorphism receives a map from the
 image. -/
 def image.lift (F' : MonoFactorisation f) : image f ⟶ F'.i :=
   (Image.isImage f).lift F'
 #align category_theory.limits.image.lift CategoryTheory.Limits.image.lift
+-/
 
+#print CategoryTheory.Limits.image.lift_fac /-
 @[simp, reassoc.1]
 theorem image.lift_fac (F' : MonoFactorisation f) : image.lift F' ≫ F'.m = image.ι f :=
-  (Image.isImage f).lift_fac' F'
+  (Image.isImage f).lift_fac F'
 #align category_theory.limits.image.lift_fac CategoryTheory.Limits.image.lift_fac
+-/
 
+#print CategoryTheory.Limits.image.fac_lift /-
 @[simp, reassoc.1]
 theorem image.fac_lift (F' : MonoFactorisation f) : factorThruImage f ≫ image.lift F' = F'.e :=
   (Image.isImage f).fac_lift F'
 #align category_theory.limits.image.fac_lift CategoryTheory.Limits.image.fac_lift
+-/
 
+#print CategoryTheory.Limits.image.isImage_lift /-
 @[simp]
 theorem image.isImage_lift (F : MonoFactorisation f) : (Image.isImage f).lift F = image.lift F :=
   rfl
 #align category_theory.limits.image.is_image_lift CategoryTheory.Limits.image.isImage_lift
+-/
 
+#print CategoryTheory.Limits.IsImage.lift_ι /-
 @[simp, reassoc.1]
 theorem IsImage.lift_ι {F : MonoFactorisation f} (hF : IsImage F) :
     hF.lift (Image.monoFactorisation f) ≫ image.ι f = F.m :=
   hF.lift_fac _
 #align category_theory.limits.is_image.lift_ι CategoryTheory.Limits.IsImage.lift_ι
+-/
 
+#print CategoryTheory.Limits.image.lift_mono /-
 -- TODO we could put a category structure on `mono_factorisation f`,
 -- with the morphisms being `g : I ⟶ I'` commuting with the `m`s
 -- (they then automatically commute with the `e`s)
@@ -376,11 +465,14 @@ instance image.lift_mono (F' : MonoFactorisation f) : Mono (image.lift F') :=
   apply mono_of_mono _ F'.m
   simpa using mono_factorisation.m_mono _
 #align category_theory.limits.image.lift_mono CategoryTheory.Limits.image.lift_mono
+-/
 
+#print CategoryTheory.Limits.HasImage.uniq /-
 theorem HasImage.uniq (F' : MonoFactorisation f) (l : image f ⟶ F'.i) (w : l ≫ F'.m = image.ι f) :
     l = image.lift F' :=
   (cancel_mono F'.m).1 (by simp [w])
 #align category_theory.limits.has_image.uniq CategoryTheory.Limits.HasImage.uniq
+-/
 
 /-- If `has_image g`, then `has_image (f ≫ g)` when `f` is an isomorphism. -/
 instance {X Y Z : C} (f : X ⟶ Y) [IsIso f] (g : Y ⟶ Z) [HasImage g] : HasImage (f ≫ g)
@@ -403,10 +495,12 @@ section
 
 variable (C)
 
+#print CategoryTheory.Limits.HasImages /-
 /-- `has_images` asserts that every morphism has an image. -/
 class HasImages : Prop where
   HasImage : ∀ {X Y : C} (f : X ⟶ Y), HasImage f
 #align category_theory.limits.has_images CategoryTheory.Limits.HasImages
+-/
 
 attribute [instance] has_images.has_image
 
@@ -416,16 +510,21 @@ section
 
 variable (f)
 
+#print CategoryTheory.Limits.imageMonoIsoSource /-
 /-- The image of a monomorphism is isomorphic to the source. -/
 def imageMonoIsoSource [Mono f] : image f ≅ X :=
   IsImage.isoExt (Image.isImage f) (IsImage.self f)
 #align category_theory.limits.image_mono_iso_source CategoryTheory.Limits.imageMonoIsoSource
+-/
 
+#print CategoryTheory.Limits.imageMonoIsoSource_inv_ι /-
 @[simp, reassoc.1]
 theorem imageMonoIsoSource_inv_ι [Mono f] : (imageMonoIsoSource f).inv ≫ image.ι f = f := by
   simp [image_mono_iso_source]
 #align category_theory.limits.image_mono_iso_source_inv_ι CategoryTheory.Limits.imageMonoIsoSource_inv_ι
+-/
 
+#print CategoryTheory.Limits.imageMonoIsoSource_hom_self /-
 @[simp, reassoc.1]
 theorem imageMonoIsoSource_hom_self [Mono f] : (imageMonoIsoSource f).Hom ≫ f = image.ι f :=
   by
@@ -436,7 +535,9 @@ theorem imageMonoIsoSource_hom_self [Mono f] : (imageMonoIsoSource f).Hom ≫ f
     rw [← image_mono_iso_source_inv_ι f]
   rw [← category.assoc, iso.hom_inv_id, category.id_comp]
 #align category_theory.limits.image_mono_iso_source_hom_self CategoryTheory.Limits.imageMonoIsoSource_hom_self
+-/
 
+#print CategoryTheory.Limits.image.ext /-
 -- This is the proof that `factor_thru_image f` is an epimorphism
 -- from https://en.wikipedia.org/wiki/Image_%28category_theory%29, which is in turn taken from:
 -- Mitchell, Barry (1965), Theory of categories, MR 0202787, p.12, Proposition 10.1
@@ -469,24 +570,29 @@ theorem image.ext [HasImage f] {W : C} {g h : image f ⟶ W} [HasLimit (parallel
     _ = h := by rw [category.id_comp]
     
 #align category_theory.limits.image.ext CategoryTheory.Limits.image.ext
+-/
 
 instance [HasImage f] [∀ {Z : C} (g h : image f ⟶ Z), HasLimit (parallelPair g h)] :
     Epi (factorThruImage f) :=
   ⟨fun Z g h w => image.ext f w⟩
 
+#print CategoryTheory.Limits.epi_image_of_epi /-
 theorem epi_image_of_epi {X Y : C} (f : X ⟶ Y) [HasImage f] [E : Epi f] : Epi (image.ι f) :=
   by
   rw [← image.fac f] at E
   skip
   exact epi_of_epi (factor_thru_image f) (image.ι f)
 #align category_theory.limits.epi_image_of_epi CategoryTheory.Limits.epi_image_of_epi
+-/
 
+#print CategoryTheory.Limits.epi_of_epi_image /-
 theorem epi_of_epi_image {X Y : C} (f : X ⟶ Y) [HasImage f] [Epi (image.ι f)]
     [Epi (factorThruImage f)] : Epi f :=
   by
   rw [← image.fac f]
   apply epi_comp
 #align category_theory.limits.epi_of_epi_image CategoryTheory.Limits.epi_of_epi_image
+-/
 
 end
 
@@ -494,6 +600,7 @@ section
 
 variable {f} {f' : X ⟶ Y} [HasImage f] [HasImage f']
 
+#print CategoryTheory.Limits.image.eqToHom /-
 /-- An equation between morphisms gives a comparison map between the images
 (which momentarily we prove is an iso).
 -/
@@ -503,17 +610,21 @@ def image.eqToHom (h : f = f') : image f ⟶ image f' :=
       m := image.ι f'
       e := factorThruImage f' }
 #align category_theory.limits.image.eq_to_hom CategoryTheory.Limits.image.eqToHom
+-/
 
 instance (h : f = f') : IsIso (image.eqToHom h) :=
   ⟨⟨image.eqToHom h.symm,
       ⟨(cancel_mono (image.ι f)).1 (by simp [image.eq_to_hom]),
         (cancel_mono (image.ι f')).1 (by simp [image.eq_to_hom])⟩⟩⟩
 
+#print CategoryTheory.Limits.image.eqToIso /-
 /-- An equation between morphisms gives an isomorphism between the images. -/
 def image.eqToIso (h : f = f') : image f ≅ image f' :=
   asIso (image.eqToHom h)
 #align category_theory.limits.image.eq_to_iso CategoryTheory.Limits.image.eqToIso
+-/
 
+#print CategoryTheory.Limits.image.eq_fac /-
 /-- As long as the category has equalizers,
 the image inclusion maps commute with `image.eq_to_iso`.
 -/
@@ -523,6 +634,7 @@ theorem image.eq_fac [HasEqualizers C] (h : f = f') :
   ext
   simp [image.eq_to_iso, image.eq_to_hom]
 #align category_theory.limits.image.eq_fac CategoryTheory.Limits.image.eq_fac
+-/
 
 end
 
@@ -530,6 +642,7 @@ section
 
 variable {Z : C} (g : Y ⟶ Z)
 
+#print CategoryTheory.Limits.image.preComp /-
 /-- The comparison map `image (f ≫ g) ⟶ image g`. -/
 def image.preComp [HasImage g] [HasImage (f ≫ g)] : image (f ≫ g) ⟶ image g :=
   image.lift
@@ -537,17 +650,23 @@ def image.preComp [HasImage g] [HasImage (f ≫ g)] : image (f ≫ g) ⟶ image
       m := image.ι g
       e := f ≫ factorThruImage g }
 #align category_theory.limits.image.pre_comp CategoryTheory.Limits.image.preComp
+-/
 
+#print CategoryTheory.Limits.image.preComp_ι /-
 @[simp, reassoc.1]
 theorem image.preComp_ι [HasImage g] [HasImage (f ≫ g)] :
     image.preComp f g ≫ image.ι g = image.ι (f ≫ g) := by simp [image.pre_comp]
 #align category_theory.limits.image.pre_comp_ι CategoryTheory.Limits.image.preComp_ι
+-/
 
+#print CategoryTheory.Limits.image.factorThruImage_preComp /-
 @[simp, reassoc.1]
 theorem image.factorThruImage_preComp [HasImage g] [HasImage (f ≫ g)] :
     factorThruImage (f ≫ g) ≫ image.preComp f g = f ≫ factorThruImage g := by simp [image.pre_comp]
 #align category_theory.limits.image.factor_thru_image_pre_comp CategoryTheory.Limits.image.factorThruImage_preComp
+-/
 
+#print CategoryTheory.Limits.image.preComp_mono /-
 /-- `image.pre_comp f g` is a monomorphism.
 -/
 instance image.preComp_mono [HasImage g] [HasImage (f ≫ g)] : Mono (image.preComp f g) :=
@@ -556,7 +675,9 @@ instance image.preComp_mono [HasImage g] [HasImage (f ≫ g)] : Mono (image.preC
   simp only [image.pre_comp_ι]
   infer_instance
 #align category_theory.limits.image.pre_comp_mono CategoryTheory.Limits.image.preComp_mono
+-/
 
+#print CategoryTheory.Limits.image.preComp_comp /-
 /-- The two step comparison map
   `image (f ≫ (g ≫ h)) ⟶ image (g ≫ h) ⟶ image h`
 agrees with the one step comparison map
@@ -570,9 +691,11 @@ theorem image.preComp_comp {W : C} (h : Z ⟶ W) [HasImage (g ≫ h)] [HasImage
   apply (cancel_mono (image.ι h)).1
   simp [image.pre_comp, image.eq_to_hom]
 #align category_theory.limits.image.pre_comp_comp CategoryTheory.Limits.image.preComp_comp
+-/
 
 variable [HasEqualizers C]
 
+#print CategoryTheory.Limits.image.preComp_epi_of_epi /-
 /-- `image.pre_comp f g` is an epimorphism when `f` is an epimorphism
 (we need `C` to have equalizers to prove this).
 -/
@@ -582,13 +705,21 @@ instance image.preComp_epi_of_epi [HasImage g] [HasImage (f ≫ g)] [Epi f] :
   apply epi_of_epi_fac (image.factor_thru_image_pre_comp _ _)
   exact epi_comp _ _
 #align category_theory.limits.image.pre_comp_epi_of_epi CategoryTheory.Limits.image.preComp_epi_of_epi
+-/
 
+/- warning: category_theory.limits.has_image_iso_comp -> CategoryTheory.Limits.hasImage_iso_comp is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) {Z : C} (g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z) [_inst_2 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.IsIso.{u1, u2} C _inst_1 X Y f] [_inst_4 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 Y Z g], CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) X Y Z f g)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) {Z : C} (g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z) [_inst_2 : CategoryTheory.IsIso.{u1, u2} C _inst_1 X Y f] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 Y Z g], CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) X Y Z f g)
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image_iso_comp CategoryTheory.Limits.hasImage_iso_compₓ'. -/
 instance hasImage_iso_comp [IsIso f] [HasImage g] : HasImage (f ≫ g) :=
   HasImage.mk
     { f := (Image.monoFactorisation g).isoComp f
       IsImage := { lift := fun F' => image.lift (F'.ofIsoComp f) } }
 #align category_theory.limits.has_image_iso_comp CategoryTheory.Limits.hasImage_iso_comp
 
+#print CategoryTheory.Limits.image.isIso_precomp_iso /-
 /-- `image.pre_comp f g` is an isomorphism when `f` is an isomorphism
 (we need `C` to have equalizers to prove this).
 -/
@@ -603,7 +734,14 @@ instance image.isIso_precomp_iso (f : X ⟶ Y) [IsIso f] [HasImage g] : IsIso (i
         ext
         simp [image.pre_comp]⟩⟩⟩
 #align category_theory.limits.image.is_iso_precomp_iso CategoryTheory.Limits.image.isIso_precomp_iso
+-/
 
+/- warning: category_theory.limits.has_image_comp_iso -> CategoryTheory.Limits.hasImage_comp_iso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) {Z : C} (g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z) [_inst_2 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 X Y f] [_inst_4 : CategoryTheory.IsIso.{u1, u2} C _inst_1 Y Z g], CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) X Y Z f g)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) {Z : C} (g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z) [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 X Y f] [_inst_3 : CategoryTheory.IsIso.{u1, u2} C _inst_1 Y Z g], CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 X Z (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) X Y Z f g)
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image_comp_iso CategoryTheory.Limits.hasImage_comp_isoₓ'. -/
 -- Note that in general we don't have the other comparison map you might expect
 -- `image f ⟶ image (f ≫ g)`.
 instance hasImage_comp_iso [HasImage f] [IsIso g] : HasImage (f ≫ g) :=
@@ -612,13 +750,16 @@ instance hasImage_comp_iso [HasImage f] [IsIso g] : HasImage (f ≫ g) :=
       IsImage := { lift := fun F' => image.lift F'.of_comp_iso } }
 #align category_theory.limits.has_image_comp_iso CategoryTheory.Limits.hasImage_comp_iso
 
+#print CategoryTheory.Limits.image.compIso /-
 /-- Postcomposing by an isomorphism induces an isomorphism on the image. -/
 def image.compIso [HasImage f] [IsIso g] : image f ≅ image (f ≫ g)
     where
   Hom := image.lift (Image.monoFactorisation (f ≫ g)).of_comp_iso
   inv := image.lift ((Image.monoFactorisation f).comp_mono g)
 #align category_theory.limits.image.comp_iso CategoryTheory.Limits.image.compIso
+-/
 
+#print CategoryTheory.Limits.image.compIso_hom_comp_image_ι /-
 @[simp, reassoc.1]
 theorem image.compIso_hom_comp_image_ι [HasImage f] [IsIso g] :
     (image.compIso f g).Hom ≫ image.ι (f ≫ g) = image.ι f ≫ g :=
@@ -626,7 +767,9 @@ theorem image.compIso_hom_comp_image_ι [HasImage f] [IsIso g] :
   ext
   simp [image.comp_iso]
 #align category_theory.limits.image.comp_iso_hom_comp_image_ι CategoryTheory.Limits.image.compIso_hom_comp_image_ι
+-/
 
+#print CategoryTheory.Limits.image.compIso_inv_comp_image_ι /-
 @[simp, reassoc.1]
 theorem image.compIso_inv_comp_image_ι [HasImage f] [IsIso g] :
     (image.compIso f g).inv ≫ image.ι f = image.ι (f ≫ g) ≫ inv g :=
@@ -634,6 +777,7 @@ theorem image.compIso_inv_comp_image_ι [HasImage f] [IsIso g] :
   ext
   simp [image.comp_iso]
 #align category_theory.limits.image.comp_iso_inv_comp_image_ι CategoryTheory.Limits.image.compIso_inv_comp_image_ι
+-/
 
 end
 
@@ -652,13 +796,25 @@ end
 
 section HasImageMap
 
+/- warning: category_theory.limits.image_map -> CategoryTheory.Limits.ImageMap is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)], (Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1))) f g) -> Type.{u1}
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)], (Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1))) f g) -> Type.{u1}
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.image_map CategoryTheory.Limits.ImageMapₓ'. -/
 /-- An image map is a morphism `image f → image g` fitting into a commutative square and satisfying
     the obvious commutativity conditions. -/
 structure ImageMap {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g) where
   map : image f.Hom ⟶ image g.Hom
-  map_ι' : map ≫ image.ι g.Hom = image.ι f.Hom ≫ sq.right := by obviously
+  map_ι : map ≫ image.ι g.Hom = image.ι f.Hom ≫ sq.right := by obviously
 #align category_theory.limits.image_map CategoryTheory.Limits.ImageMap
 
+/- warning: category_theory.limits.inhabited_image_map -> CategoryTheory.Limits.inhabitedImageMap is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)], Inhabited.{succ u1} (CategoryTheory.Limits.ImageMap.{u1, u2} C _inst_1 f f _inst_2 _inst_2 (CategoryTheory.CategoryStruct.id.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1)) f))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)], Inhabited.{succ u1} (CategoryTheory.Limits.ImageMap.{u1, u2} C _inst_1 f f _inst_2 _inst_2 (CategoryTheory.CategoryStruct.id.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1)) f))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.inhabited_image_map CategoryTheory.Limits.inhabitedImageMapₓ'. -/
 instance inhabitedImageMap {f : Arrow C} [HasImage f.Hom] : Inhabited (ImageMap (𝟙 f)) :=
   ⟨⟨𝟙 _, by tidy⟩⟩
 #align category_theory.limits.inhabited_image_map CategoryTheory.Limits.inhabitedImageMap
@@ -667,12 +823,24 @@ restate_axiom image_map.map_ι'
 
 attribute [simp, reassoc.1] image_map.map_ι
 
+/- warning: category_theory.limits.image_map.factor_map -> CategoryTheory.Limits.ImageMap.factor_map is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)] (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1))) f g) (m : CategoryTheory.Limits.ImageMap.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Limits.image.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) _inst_3)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Limits.image.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f) _inst_2) (CategoryTheory.Limits.image.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) _inst_3) (CategoryTheory.Limits.factorThruImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f) _inst_2) (CategoryTheory.Limits.ImageMap.map.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq m)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) (CategoryTheory.Limits.image.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) _inst_3) (CategoryTheory.CommaMorphism.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f g sq) (CategoryTheory.Limits.factorThruImage.{u1, u2} C _inst_1 (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) _inst_3))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C 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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.image_map.factor_map CategoryTheory.Limits.ImageMap.factor_mapₓ'. -/
 @[simp, reassoc.1]
 theorem ImageMap.factor_map {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
     (m : ImageMap sq) : factorThruImage f.Hom ≫ m.map = sq.left ≫ factorThruImage g.Hom :=
   (cancel_mono (image.ι g.Hom)).1 <| by simp
 #align category_theory.limits.image_map.factor_map CategoryTheory.Limits.ImageMap.factor_map
 
+/- warning: category_theory.limits.image_map.transport -> CategoryTheory.Limits.ImageMap.transport is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.image_map.transport CategoryTheory.Limits.ImageMap.transportₓ'. -/
 /-- To give an image map for a commutative square with `f` at the top and `g` at the bottom, it
     suffices to give a map between any mono factorisation of `f` and any image factorisation of
     `g`. -/
@@ -681,47 +849,83 @@ def ImageMap.transport {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f
     {map : F.i ⟶ F'.i} (map_ι : map ≫ F'.m = F.m ≫ sq.right) : ImageMap sq
     where
   map := image.lift F ≫ map ≫ hF'.lift (Image.monoFactorisation g.Hom)
-  map_ι' := by simp [map_ι]
+  map_ι := by simp [map_ι]
 #align category_theory.limits.image_map.transport CategoryTheory.Limits.ImageMap.transport
 
+/- warning: category_theory.limits.has_image_map -> CategoryTheory.Limits.HasImageMap is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)], (Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1))) f g) -> Prop
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)], (Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1))) f g) -> Prop
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image_map CategoryTheory.Limits.HasImageMapₓ'. -/
 /-- `has_image_map sq` means that there is an `image_map` for the square `sq`. -/
 class HasImageMap {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g) : Prop where mk' ::
   HasImageMap : Nonempty (ImageMap sq)
 #align category_theory.limits.has_image_map CategoryTheory.Limits.HasImageMap
 
+/- warning: category_theory.limits.has_image_map.mk -> CategoryTheory.Limits.HasImageMap.mk is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image_map.mk CategoryTheory.Limits.HasImageMap.mkₓ'. -/
 theorem HasImageMap.mk {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] {sq : f ⟶ g}
     (m : ImageMap sq) : HasImageMap sq :=
   ⟨Nonempty.intro m⟩
 #align category_theory.limits.has_image_map.mk CategoryTheory.Limits.HasImageMap.mk
 
+/- warning: category_theory.limits.has_image_map.transport -> CategoryTheory.Limits.HasImageMap.transport is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image_map.transport CategoryTheory.Limits.HasImageMap.transportₓ'. -/
 theorem HasImageMap.transport {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
     (F : MonoFactorisation f.Hom) {F' : MonoFactorisation g.Hom} (hF' : IsImage F')
     (map : F.i ⟶ F'.i) (map_ι : map ≫ F'.m = F.m ≫ sq.right) : HasImageMap sq :=
   HasImageMap.mk <| ImageMap.transport sq F hF' map_ι
 #align category_theory.limits.has_image_map.transport CategoryTheory.Limits.HasImageMap.transport
 
+/- warning: category_theory.limits.has_image_map.image_map -> CategoryTheory.Limits.HasImageMap.imageMap is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)] (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1))) f g) [_inst_4 : CategoryTheory.Limits.HasImageMap.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq], CategoryTheory.Limits.ImageMap.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)] (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1))) f g) [_inst_4 : CategoryTheory.Limits.HasImageMap.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq], CategoryTheory.Limits.ImageMap.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image_map.image_map CategoryTheory.Limits.HasImageMap.imageMapₓ'. -/
 /-- Obtain an `image_map` from a `has_image_map` instance. -/
 def HasImageMap.imageMap {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom] (sq : f ⟶ g)
     [HasImageMap sq] : ImageMap sq :=
   Classical.choice <| @HasImageMap.hasImageMap _ _ _ _ _ _ sq _
 #align category_theory.limits.has_image_map.image_map CategoryTheory.Limits.HasImageMap.imageMap
 
+/- warning: category_theory.limits.has_image_map_of_is_iso -> CategoryTheory.Limits.hasImageMapOfIsIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)] (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1))) f g) [_inst_4 : CategoryTheory.IsIso.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Arrow.category.{u1, u2} C _inst_1) f g sq], CategoryTheory.Limits.HasImageMap.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)] (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1))) f g) [_inst_4 : CategoryTheory.IsIso.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1) f g sq], CategoryTheory.Limits.HasImageMap.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image_map_of_is_iso CategoryTheory.Limits.hasImageMapOfIsIsoₓ'. -/
 -- see Note [lower instance priority]
 instance (priority := 100) hasImageMapOfIsIso {f g : Arrow C} [HasImage f.Hom] [HasImage g.Hom]
     (sq : f ⟶ g) [IsIso sq] : HasImageMap sq :=
   HasImageMap.mk
     { map := image.lift ((Image.monoFactorisation g.Hom).of_arrow_iso (inv sq))
-      map_ι' := by
+      map_ι := by
         erw [← cancel_mono (inv sq).right, category.assoc, ← mono_factorisation.of_arrow_iso_m,
           image.lift_fac, category.assoc, ← comma.comp_right, is_iso.hom_inv_id, comma.id_right,
           category.comp_id] }
 #align category_theory.limits.has_image_map_of_is_iso CategoryTheory.Limits.hasImageMapOfIsIso
 
+/- warning: category_theory.limits.has_image_map.comp -> CategoryTheory.Limits.HasImageMap.comp is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} {h : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C 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g)] [_inst_4 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) h)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 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(CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1))) g h) [_inst_5 : CategoryTheory.Limits.HasImageMap.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq1] [_inst_6 : CategoryTheory.Limits.HasImageMap.{u1, u2} C _inst_1 g h _inst_3 _inst_4 sq2], CategoryTheory.Limits.HasImageMap.{u1, u2} C _inst_1 f h _inst_2 _inst_4 (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1)) f g h sq1 sq2)
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.has_image_map.comp CategoryTheory.Limits.HasImageMap.compₓ'. -/
 instance HasImageMap.comp {f g h : Arrow C} [HasImage f.Hom] [HasImage g.Hom] [HasImage h.Hom]
     (sq1 : f ⟶ g) (sq2 : g ⟶ h) [HasImageMap sq1] [HasImageMap sq2] : HasImageMap (sq1 ≫ sq2) :=
   HasImageMap.mk
     { map := (HasImageMap.imageMap sq1).map ≫ (HasImageMap.imageMap sq2).map
-      map_ι' := by
+      map_ι := by
         simp only [image_map.map_ι, image_map.map_ι_assoc, comma.comp_right, category.assoc] }
 #align category_theory.limits.has_image_map.comp CategoryTheory.Limits.HasImageMap.comp
 
@@ -739,23 +943,43 @@ end
 
 variable [HasImageMap sq]
 
+/- warning: category_theory.limits.image.map -> CategoryTheory.Limits.image.map is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)] (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.instCategoryArrow.{u1, u2} C _inst_1))) f g) [_inst_4 : CategoryTheory.Limits.HasImageMap.{u1, u2} C _inst_1 f g _inst_2 _inst_3 sq], Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Limits.image.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f) _inst_2) (CategoryTheory.Limits.image.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g) _inst_3)
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map CategoryTheory.Limits.image.mapₓ'. -/
 /-- The map on images induced by a commutative square. -/
 abbrev image.map : image f.Hom ⟶ image g.Hom :=
   (HasImageMap.imageMap sq).map
 #align category_theory.limits.image.map CategoryTheory.Limits.image.map
 
+/- warning: category_theory.limits.image.factor_map -> CategoryTheory.Limits.image.factor_map is a dubious translation:
+lean 3 declaration is
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CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) g)] (sq : Quiver.Hom.{succ u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Arrow.{u1, u2} C _inst_1) 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+but is expected to have type
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(CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.right.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)] [_inst_3 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C 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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.factor_map CategoryTheory.Limits.image.factor_mapₓ'. -/
 theorem image.factor_map : factorThruImage f.Hom ≫ image.map sq = sq.left ≫ factorThruImage g.Hom :=
   by simp
 #align category_theory.limits.image.factor_map CategoryTheory.Limits.image.factor_map
 
+/- warning: category_theory.limits.image.map_ι -> CategoryTheory.Limits.image.map_ι is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {f : CategoryTheory.Arrow.{u1, u2} C _inst_1} {g : CategoryTheory.Arrow.{u1, u2} C _inst_1} [_inst_2 : CategoryTheory.Limits.HasImage.{u1, u2} C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1)) (CategoryTheory.Comma.left.{u1, u1, u1, u2, u2, u2} C _inst_1 C _inst_1 C _inst_1 (CategoryTheory.Functor.id.{u1, u2} C _inst_1) (CategoryTheory.Functor.id.{u1, u2} C _inst_1) f)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) C 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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map_ι CategoryTheory.Limits.image.map_ιₓ'. -/
 theorem image.map_ι : image.map sq ≫ image.ι g.Hom = image.ι f.Hom ≫ sq.right := by simp
 #align category_theory.limits.image.map_ι CategoryTheory.Limits.image.map_ι
 
+#print CategoryTheory.Limits.image.map_homMk'_ι /-
 theorem image.map_homMk'_ι {X Y P Q : C} {k : X ⟶ Y} [HasImage k] {l : P ⟶ Q} [HasImage l]
     {m : X ⟶ P} {n : Y ⟶ Q} (w : m ≫ l = k ≫ n) [HasImageMap (Arrow.homMk' w)] :
     image.map (Arrow.homMk' w) ≫ image.ι l = image.ι k ≫ n :=
   image.map_ι _
 #align category_theory.limits.image.map_hom_mk'_ι CategoryTheory.Limits.image.map_homMk'_ι
+-/
 
 section
 
@@ -763,10 +987,22 @@ variable {h : Arrow C} [HasImage h.Hom] (sq' : g ⟶ h)
 
 variable [HasImageMap sq']
 
+/- warning: category_theory.limits.image_map_comp -> CategoryTheory.Limits.imageMapComp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.image_map_comp CategoryTheory.Limits.imageMapCompₓ'. -/
 /-- Image maps for composable commutative squares induce an image map in the composite square. -/
 def imageMapComp : ImageMap (sq ≫ sq') where map := image.map sq ≫ image.map sq'
 #align category_theory.limits.image_map_comp CategoryTheory.Limits.imageMapComp
 
+/- warning: category_theory.limits.image.map_comp -> CategoryTheory.Limits.image.map_comp is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map_comp CategoryTheory.Limits.image.map_compₓ'. -/
 @[simp]
 theorem image.map_comp [HasImageMap (sq ≫ sq')] :
     image.map (sq ≫ sq') = image.map sq ≫ image.map sq' :=
@@ -779,11 +1015,23 @@ section
 
 variable (f)
 
+/- warning: category_theory.limits.image_map_id -> CategoryTheory.Limits.imageMapId is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.image_map_id CategoryTheory.Limits.imageMapIdₓ'. -/
 /-- The identity `image f ⟶ image f` fits into the commutative square represented by the identity
     morphism `𝟙 f` in the arrow category. -/
 def imageMapId : ImageMap (𝟙 f) where map := 𝟙 (image f.Hom)
 #align category_theory.limits.image_map_id CategoryTheory.Limits.imageMapId
 
+/- warning: category_theory.limits.image.map_id -> CategoryTheory.Limits.image.map_id is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.image.map_id CategoryTheory.Limits.image.map_idₓ'. -/
 @[simp]
 theorem image.map_id [HasImageMap (𝟙 f)] : image.map (𝟙 f) = 𝟙 (image f.Hom) :=
   show (HasImageMap.imageMap (𝟙 f)).map = (imageMapId f).map by congr
@@ -797,10 +1045,12 @@ section
 
 variable (C) [HasImages C]
 
+#print CategoryTheory.Limits.HasImageMaps /-
 /-- If a category `has_image_maps`, then all commutative squares induce morphisms on images. -/
 class HasImageMaps where
   HasImageMap : ∀ {f g : Arrow C} (st : f ⟶ g), HasImageMap st
 #align category_theory.limits.has_image_maps CategoryTheory.Limits.HasImageMaps
+-/
 
 attribute [instance] has_image_maps.has_image_map
 
@@ -810,6 +1060,7 @@ section HasImageMaps
 
 variable [HasImages C] [HasImageMaps C]
 
+#print CategoryTheory.Limits.im /-
 /-- The functor from the arrow category of `C` to `C` itself that maps a morphism to its image
     and a commutative square to the induced morphism on images. -/
 @[simps]
@@ -817,25 +1068,31 @@ def im : Arrow C ⥤ C where
   obj f := image f.Hom
   map _ _ st := image.map st
 #align category_theory.limits.im CategoryTheory.Limits.im
+-/
 
 end HasImageMaps
 
 section StrongEpiMonoFactorisation
 
+#print CategoryTheory.Limits.StrongEpiMonoFactorisation /-
 /-- A strong epi-mono factorisation is a decomposition `f = e ≫ m` with `e` a strong epimorphism
     and `m` a monomorphism. -/
 structure StrongEpiMonoFactorisation {X Y : C} (f : X ⟶ Y) extends MonoFactorisation f where
   [e_strongEpi : StrongEpi e]
 #align category_theory.limits.strong_epi_mono_factorisation CategoryTheory.Limits.StrongEpiMonoFactorisation
+-/
 
 attribute [instance] strong_epi_mono_factorisation.e_strong_epi
 
+#print CategoryTheory.Limits.strongEpiMonoFactorisationInhabited /-
 /-- Satisfying the inhabited linter -/
 instance strongEpiMonoFactorisationInhabited {X Y : C} (f : X ⟶ Y) [StrongEpi f] :
     Inhabited (StrongEpiMonoFactorisation f) :=
   ⟨⟨⟨Y, 𝟙 Y, f, by simp⟩⟩⟩
 #align category_theory.limits.strong_epi_mono_factorisation_inhabited CategoryTheory.Limits.strongEpiMonoFactorisationInhabited
+-/
 
+#print CategoryTheory.Limits.StrongEpiMonoFactorisation.toMonoIsImage /-
 /-- A mono factorisation coming from a strong epi-mono factorisation always has the universal
     property of the image. -/
 def StrongEpiMonoFactorisation.toMonoIsImage {X Y : C} {f : X ⟶ Y}
@@ -843,23 +1100,29 @@ def StrongEpiMonoFactorisation.toMonoIsImage {X Y : C} {f : X ⟶ Y}
     where lift G :=
     (CommSq.mk (show G.e ≫ G.m = F.e ≫ F.m by rw [F.to_mono_factorisation.fac, G.fac])).lift
 #align category_theory.limits.strong_epi_mono_factorisation.to_mono_is_image CategoryTheory.Limits.StrongEpiMonoFactorisation.toMonoIsImage
+-/
 
 variable (C)
 
+#print CategoryTheory.Limits.HasStrongEpiMonoFactorisations /-
 /-- A category has strong epi-mono factorisations if every morphism admits a strong epi-mono
     factorisation. -/
 class HasStrongEpiMonoFactorisations : Prop where mk' ::
   has_fac : ∀ {X Y : C} (f : X ⟶ Y), Nonempty (StrongEpiMonoFactorisation f)
 #align category_theory.limits.has_strong_epi_mono_factorisations CategoryTheory.Limits.HasStrongEpiMonoFactorisations
+-/
 
 variable {C}
 
+#print CategoryTheory.Limits.HasStrongEpiMonoFactorisations.mk /-
 theorem HasStrongEpiMonoFactorisations.mk
     (d : ∀ {X Y : C} (f : X ⟶ Y), StrongEpiMonoFactorisation f) :
     HasStrongEpiMonoFactorisations C :=
   ⟨fun X Y f => Nonempty.intro <| d f⟩
 #align category_theory.limits.has_strong_epi_mono_factorisations.mk CategoryTheory.Limits.HasStrongEpiMonoFactorisations.mk
+-/
 
+#print CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations /-
 instance (priority := 100) hasImages_of_hasStrongEpiMonoFactorisations
     [HasStrongEpiMonoFactorisations C] : HasImages C
     where HasImage X Y f :=
@@ -868,6 +1131,7 @@ instance (priority := 100) hasImages_of_hasStrongEpiMonoFactorisations
       { f := F'.toMonoFactorisation
         IsImage := F'.toMonoIsImage }
 #align category_theory.limits.has_images_of_has_strong_epi_mono_factorisations CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations
+-/
 
 end StrongEpiMonoFactorisation
 
@@ -875,11 +1139,13 @@ section HasStrongEpiImages
 
 variable (C) [HasImages C]
 
+#print CategoryTheory.Limits.HasStrongEpiImages /-
 /-- A category has strong epi images if it has all images and `factor_thru_image f` is a strong
     epimorphism for all `f`. -/
 class HasStrongEpiImages : Prop where
   strong_factorThruImage : ∀ {X Y : C} (f : X ⟶ Y), StrongEpi (factorThruImage f)
 #align category_theory.limits.has_strong_epi_images CategoryTheory.Limits.HasStrongEpiImages
+-/
 
 attribute [instance] has_strong_epi_images.strong_factor_thru_image
 
@@ -887,6 +1153,7 @@ end HasStrongEpiImages
 
 section HasStrongEpiImages
 
+#print CategoryTheory.Limits.strongEpi_of_strongEpiMonoFactorisation /-
 /-- If there is a single strong epi-mono factorisation of `f`, then every image factorisation is a
     strong epi-mono factorisation. -/
 theorem strongEpi_of_strongEpiMonoFactorisation {X Y : C} {f : X ⟶ Y}
@@ -895,12 +1162,16 @@ theorem strongEpi_of_strongEpiMonoFactorisation {X Y : C} {f : X ⟶ Y}
   rw [← is_image.e_iso_ext_hom F.to_mono_is_image hF']
   apply strong_epi_comp
 #align category_theory.limits.strong_epi_of_strong_epi_mono_factorisation CategoryTheory.Limits.strongEpi_of_strongEpiMonoFactorisation
+-/
 
+#print CategoryTheory.Limits.strongEpi_factorThruImage_of_strongEpiMonoFactorisation /-
 theorem strongEpi_factorThruImage_of_strongEpiMonoFactorisation {X Y : C} {f : X ⟶ Y} [HasImage f]
     (F : StrongEpiMonoFactorisation f) : StrongEpi (factorThruImage f) :=
   strongEpi_of_strongEpiMonoFactorisation F <| Image.isImage f
 #align category_theory.limits.strong_epi_factor_thru_image_of_strong_epi_mono_factorisation CategoryTheory.Limits.strongEpi_factorThruImage_of_strongEpiMonoFactorisation
+-/
 
+#print CategoryTheory.Limits.hasStrongEpiImages_of_hasStrongEpiMonoFactorisations /-
 /-- If we constructed our images from strong epi-mono factorisations, then these images are
     strong epi images. -/
 instance (priority := 100) hasStrongEpiImages_of_hasStrongEpiMonoFactorisations
@@ -909,6 +1180,7 @@ instance (priority := 100) hasStrongEpiImages_of_hasStrongEpiMonoFactorisations
     strongEpi_factorThruImage_of_strongEpiMonoFactorisation <|
       Classical.choice <| HasStrongEpiMonoFactorisations.has_fac f
 #align category_theory.limits.has_strong_epi_images_of_has_strong_epi_mono_factorisations CategoryTheory.Limits.hasStrongEpiImages_of_hasStrongEpiMonoFactorisations
+-/
 
 end HasStrongEpiImages
 
@@ -916,6 +1188,7 @@ section HasStrongEpiImages
 
 variable [HasImages C]
 
+#print CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages /-
 /-- A category with strong epi images has image maps. -/
 instance (priority := 100) hasImageMapsOfHasStrongEpiImages [HasStrongEpiImages C] : HasImageMaps C
     where HasImageMap f g st :=
@@ -928,7 +1201,9 @@ instance (priority := 100) hasImageMapsOfHasStrongEpiImages [HasStrongEpiImages
                   factorThruImage f.Hom ≫ image.ι f.Hom ≫ st.right
                 by simp)).lift }
 #align category_theory.limits.has_image_maps_of_has_strong_epi_images CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages
+-/
 
+#print CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers /-
 /-- If a category has images, equalizers and pullbacks, then images are automatically strong epi
     images. -/
 instance (priority := 100) hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers [HasPullbacks C]
@@ -948,6 +1223,7 @@ instance (priority := 100) hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers [
             ext
             simp only [sq.w, category.assoc, image.fac_lift_assoc, pullback.lift_fst_assoc] }
 #align category_theory.limits.has_strong_epi_images_of_has_pullbacks_of_has_equalizers CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers
+-/
 
 end HasStrongEpiImages
 
@@ -955,6 +1231,7 @@ variable [HasStrongEpiMonoFactorisations C]
 
 variable {X Y : C} {f : X ⟶ Y}
 
+#print CategoryTheory.Limits.image.isoStrongEpiMono /-
 /--
 If `C` has strong epi mono factorisations, then the image is unique up to isomorphism, in that if
 `f` factors as a strong epi followed by a mono, this factorisation is essentially the image
@@ -968,18 +1245,23 @@ def image.isoStrongEpiMono {I' : C} (e : X ⟶ I') (m : I' ⟶ Y) (comm : e ≫
           e }.toMonoIsImage <|
     Image.isImage f
 #align category_theory.limits.image.iso_strong_epi_mono CategoryTheory.Limits.image.isoStrongEpiMono
+-/
 
+#print CategoryTheory.Limits.image.isoStrongEpiMono_hom_comp_ι /-
 @[simp]
 theorem image.isoStrongEpiMono_hom_comp_ι {I' : C} (e : X ⟶ I') (m : I' ⟶ Y) (comm : e ≫ m = f)
     [StrongEpi e] [Mono m] : (image.isoStrongEpiMono e m comm).Hom ≫ image.ι f = m :=
   IsImage.lift_fac _ _
 #align category_theory.limits.image.iso_strong_epi_mono_hom_comp_ι CategoryTheory.Limits.image.isoStrongEpiMono_hom_comp_ι
+-/
 
+#print CategoryTheory.Limits.image.isoStrongEpiMono_inv_comp_mono /-
 @[simp]
 theorem image.isoStrongEpiMono_inv_comp_mono {I' : C} (e : X ⟶ I') (m : I' ⟶ Y) (comm : e ≫ m = f)
     [StrongEpi e] [Mono m] : (image.isoStrongEpiMono e m comm).inv ≫ m = image.ι f :=
   image.lift_fac _
 #align category_theory.limits.image.iso_strong_epi_mono_inv_comp_mono CategoryTheory.Limits.image.isoStrongEpiMono_inv_comp_mono
+-/
 
 end CategoryTheory.Limits
 
@@ -989,6 +1271,12 @@ open CategoryTheory.Limits
 
 variable {C D : Type _} [Category C] [Category D]
 
+/- warning: category_theory.functor.has_strong_epi_mono_factorisations_imp_of_is_equivalence -> CategoryTheory.Functor.hasStrongEpiMonoFactorisations_imp_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) [_inst_3 : CategoryTheory.IsEquivalence.{u3, u4, u1, u2} C _inst_1 D _inst_2 F] [h : CategoryTheory.Limits.HasStrongEpiMonoFactorisations.{u3, u1} C _inst_1], CategoryTheory.Limits.HasStrongEpiMonoFactorisations.{u4, u2} D _inst_2
+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) [_inst_3 : CategoryTheory.IsEquivalence.{u4, u3, u2, u1} C _inst_1 D _inst_2 F] [h : CategoryTheory.Limits.HasStrongEpiMonoFactorisations.{u4, u2} C _inst_1], CategoryTheory.Limits.HasStrongEpiMonoFactorisations.{u3, u1} D _inst_2
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.has_strong_epi_mono_factorisations_imp_of_is_equivalence CategoryTheory.Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalenceₓ'. -/
 theorem hasStrongEpiMonoFactorisations_imp_of_isEquivalence (F : C ⥤ D) [IsEquivalence F]
     [h : HasStrongEpiMonoFactorisations C] : HasStrongEpiMonoFactorisations D :=
   ⟨fun X Y f =>

563aed34

bump to nightly-2023-02-27-08

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

91d8c210

Diff

@@ -77,7 +77,7 @@ structure MonoFactorisation (f : X ⟶ Y) where
   m : I ⟶ Y
   [m_mono : Mono m]
   e : X ⟶ I
-  fac' : e ≫ m = f := by obviously
+  fac : e ≫ m = f := by obviously
 #align category_theory.limits.mono_factorisation CategoryTheory.Limits.MonoFactorisation
 
 restate_axiom mono_factorisation.fac'
@@ -169,7 +169,7 @@ def ofArrowIso {f g : Arrow C} (F : MonoFactorisation f.Hom) (sq : f ⟶ g) [IsI
   m := F.m ≫ sq.right
   e := inv sq.left ≫ F.e
   m_mono := mono_comp _ _
-  fac' := by simp only [fac_assoc, arrow.w, is_iso.inv_comp_eq, category.assoc]
+  fac := by simp only [fac_assoc, arrow.w, is_iso.inv_comp_eq, category.assoc]
 #align category_theory.limits.mono_factorisation.of_arrow_iso CategoryTheory.Limits.MonoFactorisation.ofArrowIso
 
 end MonoFactorisation
@@ -334,7 +334,7 @@ theorem as_factorThruImage : (Image.monoFactorisation f).e = factorThruImage f :
 
 @[simp, reassoc.1]
 theorem image.fac : factorThruImage f ≫ image.ι f = f :=
-  (Image.monoFactorisation f).fac'
+  (Image.monoFactorisation f).fac
 #align category_theory.limits.image.fac CategoryTheory.Limits.image.fac
 
 variable {f}
@@ -1002,7 +1002,7 @@ theorem hasStrongEpiMonoFactorisations_imp_of_isEquivalence (F : C ⥤ D) [IsEqu
         { i := F.obj em.I
           e := F.as_equivalence.counit_iso.inv.app X ≫ F.map em.e
           m := F.map em.m ≫ F.as_equivalence.counit_iso.hom.app Y
-          fac' := by
+          fac := by
             simpa only [category.assoc, ← F.map_comp_assoc, em.fac', is_equivalence.fun_inv_map,
               iso.inv_hom_id_app, iso.inv_hom_id_app_assoc] using category.comp_id _ }⟩
 #align category_theory.functor.has_strong_epi_mono_factorisations_imp_of_is_equivalence CategoryTheory.Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalence

563aed34

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

563aed34

chore: remove unnecessary cdots (#12417)

These · are scoping when there is a single active goal.

These were found using a modification of the linter at #12339.

5450e922

Diff

@@ -110,8 +110,8 @@ theorem ext {F F' : MonoFactorisation f} (hI : F.I = F'.I)
   cases' hI
   simp? at hm says simp only [eqToHom_refl, Category.id_comp] at hm
   congr
-  · apply (cancel_mono Fm).1
-    rw [Ffac, hm, Ffac']
+  apply (cancel_mono Fm).1
+  rw [Ffac, hm, Ffac']
 #align category_theory.limits.mono_factorisation.ext CategoryTheory.Limits.MonoFactorisation.ext
 
 /-- Any mono factorisation of `f` gives a mono factorisation of `f ≫ g` when `g` is a mono. -/

563aed34

style: add missing spaces between a tactic name and its arguments (#11714)

After the (d)simp and rw tactics - hints to find further occurrences welcome.

zulip discussion

Co-authored-by: @sven-manthe

7151d90b

Diff

@@ -493,7 +493,7 @@ def image.eqToHom (h : f = f') : image f ⟶ image f' :=
 instance (h : f = f') : IsIso (image.eqToHom h) :=
   ⟨⟨image.eqToHom h.symm,
       ⟨(cancel_mono (image.ι f)).1 (by
-          -- Porting note: added let's for used to be a simp[image.eqToHom]
+          -- Porting note: added let's for used to be a simp [image.eqToHom]
           let F : MonoFactorisation f' :=
             ⟨image f, image.ι f, factorThruImage f, (by aesop_cat)⟩
           dsimp [image.eqToHom]
@@ -502,7 +502,7 @@ instance (h : f = f') : IsIso (image.eqToHom h) :=
             ⟨image f', image.ι f', factorThruImage f', (by aesop_cat)⟩
           rw [image.lift_fac F'] ),
         (cancel_mono (image.ι f')).1 (by
-          -- Porting note: added let's for used to be a simp[image.eqToHom]
+          -- Porting note: added let's for used to be a simp [image.eqToHom]
           let F' : MonoFactorisation f :=
             ⟨image f', image.ι f', factorThruImage f', (by aesop_cat)⟩
           dsimp [image.eqToHom]

563aed34

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -65,7 +65,6 @@ open CategoryTheory.Limits.WalkingParallelPair
 namespace CategoryTheory.Limits
 
 variable {C : Type u} [Category.{v} C]
-
 variable {X Y : C} (f : X ⟶ Y)
 
 /-- A factorisation of a morphism `f = e ≫ m`, with `m` monic. -/
@@ -807,7 +806,6 @@ theorem image.map_homMk'_ι {X Y P Q : C} {k : X ⟶ Y} [HasImage k] {l : P ⟶
 section
 
 variable {h : Arrow C} [HasImage h.hom] (sq' : g ⟶ h)
-
 variable [HasImageMap sq']
 
 /-- Image maps for composable commutative squares induce an image map in the composite square. -/
@@ -1006,7 +1004,6 @@ instance (priority := 100) hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers [
 end HasStrongEpiImages
 
 variable [HasStrongEpiMonoFactorisations C]
-
 variable {X Y : C} {f : X ⟶ Y}
 
 /--

563aed34

chore: remove useless tactics (#11333)

The removal of some pointless tactics flagged by #11308.

ee18bf38

Diff

@@ -465,7 +465,6 @@ instance [HasImage f] [∀ {Z : C} (g h : image f ⟶ Z), HasLimit (parallelPair
 
 theorem epi_image_of_epi {X Y : C} (f : X ⟶ Y) [HasImage f] [E : Epi f] : Epi (image.ι f) := by
   rw [← image.fac f] at E
-  skip
   exact epi_of_epi (factorThruImage f) (image.ι f)
 #align category_theory.limits.epi_image_of_epi CategoryTheory.Limits.epi_image_of_epi

563aed34

chore: Remove nonterminal simp at (#7795)

Removes nonterminal uses of simp at. Replaces most of these with instances of simp? ... says.

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

4160b2aa

Diff

@@ -109,7 +109,7 @@ theorem ext {F F' : MonoFactorisation f} (hI : F.I = F'.I)
     (hm : F.m = eqToHom hI ≫ F'.m) : F = F' := by
   cases' F with _ Fm _ _ Ffac; cases' F' with _ Fm' _ _ Ffac'
   cases' hI
-  simp at hm
+  simp? at hm says simp only [eqToHom_refl, Category.id_comp] at hm
   congr
   · apply (cancel_mono Fm).1
     rw [Ffac, hm, Ffac']

563aed34

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -595,7 +595,7 @@ instance hasImage_iso_comp [IsIso f] [HasImage g] : HasImage (f ≫ g) :=
                    lift_fac := fun F' => by
                     dsimp
                     have : (MonoFactorisation.ofIsoComp f F').m = F'.m := rfl
-                    rw [←this,image.lift_fac (MonoFactorisation.ofIsoComp f F')] } }
+                    rw [← this,image.lift_fac (MonoFactorisation.ofIsoComp f F')] } }
 #align category_theory.limits.has_image_iso_comp CategoryTheory.Limits.hasImage_iso_comp
 
 /-- `image.preComp f g` is an isomorphism when `f` is an isomorphism
@@ -622,7 +622,7 @@ instance hasImage_comp_iso [HasImage f] [IsIso g] : HasImage (f ≫ g) :=
       { lift := fun F' => image.lift F'.ofCompIso
         lift_fac := fun F' => by
           rw [← Category.comp_id (image.lift (MonoFactorisation.ofCompIso F') ≫ F'.m),
-            ←IsIso.inv_hom_id g,← Category.assoc]
+            ← IsIso.inv_hom_id g,← Category.assoc]
           refine congrArg (· ≫ g) ?_
           have : (image.lift (MonoFactorisation.ofCompIso F') ≫ F'.m) ≫ inv g =
             image.lift (MonoFactorisation.ofCompIso F') ≫

563aed34

chore: exactly 4 spaces in theorems (#7328)

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

d3263b23

Diff

@@ -106,7 +106,7 @@ variable {f}
 determined. -/
 @[ext]
 theorem ext {F F' : MonoFactorisation f} (hI : F.I = F'.I)
-  (hm : F.m = eqToHom hI ≫ F'.m) : F = F' := by
+    (hm : F.m = eqToHom hI ≫ F'.m) : F = F' := by
   cases' F with _ Fm _ _ Ffac; cases' F' with _ Fm' _ _ Ffac'
   cases' hI
   simp at hm

563aed34

chore: remove unused simps (#6632)

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

916c75c1

Diff

@@ -110,7 +110,6 @@ theorem ext {F F' : MonoFactorisation f} (hI : F.I = F'.I)
   cases' F with _ Fm _ _ Ffac; cases' F' with _ Fm' _ _ Ffac'
   cases' hI
   simp at hm
-  dsimp at Ffac Ffac'
   congr
   · apply (cancel_mono Fm).1
     rw [Ffac, hm, Ffac']

563aed34

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -1041,7 +1041,7 @@ namespace CategoryTheory.Functor
 
 open CategoryTheory.Limits
 
-variable {C D : Type _} [Category C] [Category D]
+variable {C D : Type*} [Category C] [Category D]
 
 theorem hasStrongEpiMonoFactorisations_imp_of_isEquivalence (F : C ⥤ D) [IsEquivalence F]
     [h : HasStrongEpiMonoFactorisations C] : HasStrongEpiMonoFactorisations D :=

563aed34

feat: Linter that checks that Prop classes are Props (#6148)

930dd29d

Diff

@@ -849,7 +849,7 @@ section
 variable (C) [Category.{v} C] [HasImages C]
 
 /-- If a category `has_image_maps`, then all commutative squares induce morphisms on images. -/
-class HasImageMaps where
+class HasImageMaps : Prop where
   has_image_map : ∀ {f g : Arrow C} (st : f ⟶ g), HasImageMap st
 #align category_theory.limits.has_image_maps CategoryTheory.Limits.HasImageMaps

563aed34

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.limits.shapes.images
-! leanprover-community/mathlib commit 563aed347eb59dc4181cb732cda0d124d736eaa3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
 import Mathlib.CategoryTheory.Limits.Shapes.Pullbacks
 import Mathlib.CategoryTheory.Limits.Shapes.StrongEpi
 
+#align_import category_theory.limits.shapes.images from "leanprover-community/mathlib"@"563aed347eb59dc4181cb732cda0d124d736eaa3"
+
 /-!
 # Categorical images

563aed34

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

12343aa5

Diff

@@ -598,7 +598,7 @@ instance hasImage_iso_comp [IsIso f] [HasImage g] : HasImage (f ≫ g) :=
       isImage := { lift := fun F' => image.lift (F'.ofIsoComp f)
                    lift_fac := fun F' => by
                     dsimp
-                    have : (MonoFactorisation.ofIsoComp f F').m  = F'.m := rfl
+                    have : (MonoFactorisation.ofIsoComp f F').m = F'.m := rfl
                     rw [←this,image.lift_fac (MonoFactorisation.ofIsoComp f F')] } }
 #align category_theory.limits.has_image_iso_comp CategoryTheory.Limits.hasImage_iso_comp
 
@@ -761,7 +761,7 @@ attribute [local ext] ImageMap
 
 /- Porting note: ImageMap.mk.injEq has LHS simplify to True due to the next instance
 We make a replacement -/
-theorem ImageMap.map_uniq_aux {f g : Arrow C} [HasImage f.hom]  [HasImage g.hom] {sq : f ⟶ g}
+theorem ImageMap.map_uniq_aux {f g : Arrow C} [HasImage f.hom] [HasImage g.hom] {sq : f ⟶ g}
     (map : image f.hom ⟶ image g.hom)
     (map_ι : map ≫ image.ι g.hom = image.ι f.hom ≫ sq.right := by aesop_cat)
     (map' : image f.hom ⟶ image g.hom)
@@ -770,12 +770,12 @@ theorem ImageMap.map_uniq_aux {f g : Arrow C} [HasImage f.hom]  [HasImage g.hom]
   apply (cancel_mono (image.ι g.hom)).1 this
 
 -- Porting note: added to get variant on ImageMap.mk.injEq below
-theorem ImageMap.map_uniq {f g : Arrow C} [HasImage f.hom]  [HasImage g.hom]
+theorem ImageMap.map_uniq {f g : Arrow C} [HasImage f.hom] [HasImage g.hom]
     {sq : f ⟶ g} (F G : ImageMap sq) : F.map = G.map := by
   apply ImageMap.map_uniq_aux _ F.map_ι _ G.map_ι
 
 @[simp]
-theorem ImageMap.mk.injEq' {f g : Arrow C} [HasImage f.hom]  [HasImage g.hom] {sq : f ⟶ g}
+theorem ImageMap.mk.injEq' {f g : Arrow C} [HasImage f.hom] [HasImage g.hom] {sq : f ⟶ g}
     (map : image f.hom ⟶ image g.hom)
     (map_ι : map ≫ image.ι g.hom = image.ι f.hom ≫ sq.right := by aesop_cat)
     (map' : image f.hom ⟶ image g.hom)

563aed34

chore: remove occurrences of semicolon after space (#5713)

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

c795bd35

Diff

@@ -110,7 +110,7 @@ determined. -/
 @[ext]
 theorem ext {F F' : MonoFactorisation f} (hI : F.I = F'.I)
   (hm : F.m = eqToHom hI ≫ F'.m) : F = F' := by
-  cases' F with _ Fm _ _ Ffac ; cases' F' with _ Fm' _ _ Ffac'
+  cases' F with _ Fm _ _ Ffac; cases' F' with _ Fm' _ _ Ffac'
   cases' hI
   simp at hm
   dsimp at Ffac Ffac'

563aed34

chore: formatting issues (#4947)

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

5068808d

Diff

@@ -1021,7 +1021,7 @@ factorisation.
 -/
 def image.isoStrongEpiMono {I' : C} (e : X ⟶ I') (m : I' ⟶ Y) (comm : e ≫ m = f) [StrongEpi e]
     [Mono m] : I' ≅ image f :=
-  let F : StrongEpiMonoFactorisation f := { I := I', m := m, e:=e}
+  let F : StrongEpiMonoFactorisation f := { I := I', m := m, e := e}
   IsImage.isoExt F.toMonoIsImage <| Image.isImage f
 #align category_theory.limits.image.iso_strong_epi_mono CategoryTheory.Limits.image.isoStrongEpiMono

563aed34

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

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

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

14167e48

Diff

@@ -1048,8 +1048,7 @@ variable {C D : Type _} [Category C] [Category D]
 
 theorem hasStrongEpiMonoFactorisations_imp_of_isEquivalence (F : C ⥤ D) [IsEquivalence F]
     [h : HasStrongEpiMonoFactorisations C] : HasStrongEpiMonoFactorisations D :=
-  ⟨fun {X} {Y} f =>
-    by
+  ⟨fun {X} {Y} f => by
     let em : StrongEpiMonoFactorisation (F.inv.map f) :=
       (HasStrongEpiMonoFactorisations.has_fac (F.inv.map f)).some
     haveI : Mono (F.map em.m ≫ F.asEquivalence.counitIso.hom.app Y) := mono_comp _ _

563aed34

chore: fix #align lines (#3640)

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.)

2b42dc7c

Diff

@@ -530,7 +530,6 @@ theorem image.eq_fac [HasEqualizers C] (h : f = f') :
   apply image.ext
   dsimp [asIso,image.eqToIso, image.eqToHom]
   rw [image.lift_fac] -- Porting note: simp did not fire with this it seems
-
 #align category_theory.limits.image.eq_fac CategoryTheory.Limits.image.eq_fac
 
 end

563aed34

chore: port missing instance priorities (#3613)

See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/mathport.20drops.20priorities.20in.20.60attribute.20.5Binstance.5D.60. mathport has been dropping the priorities on instances when using the attribute command.

This PR adds back all the priorities, except for local attribute, and instances involving coercions, which I didn't want to mess with.

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

b0c1460c

Diff

@@ -410,7 +410,7 @@ class HasImages : Prop where
 
 attribute [inherit_doc HasImages] HasImages.has_image
 
-attribute [instance] HasImages.has_image
+attribute [instance 100] HasImages.has_image
 
 end
 
@@ -857,7 +857,7 @@ class HasImageMaps where
   has_image_map : ∀ {f g : Arrow C} (st : f ⟶ g), HasImageMap st
 #align category_theory.limits.has_image_maps CategoryTheory.Limits.HasImageMaps
 
-attribute [instance] HasImageMaps.has_image_map
+attribute [instance 100] HasImageMaps.has_image_map
 
 end

563aed34

feat: port CategoryTheory.Limits.Types (#2712)

89751ebf

Diff

@@ -81,7 +81,7 @@ structure MonoFactorisation (f : X ⟶ Y) where
 #align category_theory.limits.mono_factorisation CategoryTheory.Limits.MonoFactorisation
 #align category_theory.limits.mono_factorisation.fac' CategoryTheory.Limits.MonoFactorisation.fac
 
-attribute [inherit_doc MonoFactorisation] MonoFactorisation.I MonoFactorisation.m 
+attribute [inherit_doc MonoFactorisation] MonoFactorisation.I MonoFactorisation.m
   MonoFactorisation.m_mono MonoFactorisation.e MonoFactorisation.fac
 
 attribute [reassoc (attr := simp)] MonoFactorisation.fac
@@ -108,11 +108,11 @@ variable {f}
 /-- The morphism `m` in a factorisation `f = e ≫ m` through a monomorphism is uniquely
 determined. -/
 @[ext]
-theorem ext {F F' : MonoFactorisation f} (hI : F.I = F'.I) 
+theorem ext {F F' : MonoFactorisation f} (hI : F.I = F'.I)
   (hm : F.m = eqToHom hI ≫ F'.m) : F = F' := by
   cases' F with _ Fm _ _ Ffac ; cases' F' with _ Fm' _ _ Ffac'
   cases' hI
-  simp at hm 
+  simp at hm
   dsimp at Ffac Ffac'
   congr
   · apply (cancel_mono Fm).1
@@ -210,7 +210,7 @@ variable {f}
 /-- Two factorisations through monomorphisms satisfying the universal property
 must factor through isomorphic objects. -/
 @[simps]
-def isoExt {F F' : MonoFactorisation f} (hF : IsImage F) (hF' : IsImage F') : 
+def isoExt {F F' : MonoFactorisation f} (hF : IsImage F) (hF' : IsImage F') :
     F.I ≅ F'.I where
   hom := hF.lift F'
   inv := hF'.lift F
@@ -250,7 +250,7 @@ variable (f)
 /-- Data exhibiting that a morphism `f` has an image. -/
 structure ImageFactorisation (f : X ⟶ Y) where
   F : MonoFactorisation f -- Porting note: another violation of the naming convention
-  isImage : IsImage F 
+  isImage : IsImage F
 #align category_theory.limits.image_factorisation CategoryTheory.Limits.ImageFactorisation
 #align category_theory.limits.image_factorisation.is_image CategoryTheory.Limits.ImageFactorisation.isImage
 
@@ -385,7 +385,7 @@ theorem HasImage.uniq (F' : MonoFactorisation f) (l : image f ⟶ F'.I) (w : l 
 #align category_theory.limits.has_image.uniq CategoryTheory.Limits.HasImage.uniq
 
 /-- If `has_image g`, then `has_image (f ≫ g)` when `f` is an isomorphism. -/
-instance {X Y Z : C} (f : X ⟶ Y) [IsIso f] (g : Y ⟶ Z) [HasImage g] : HasImage (f ≫ g) where 
+instance {X Y Z : C} (f : X ⟶ Y) [IsIso f] (g : Y ⟶ Z) [HasImage g] : HasImage (f ≫ g) where
   exists_image :=
     ⟨{  F :=
           { I := image g
@@ -498,23 +498,23 @@ def image.eqToHom (h : f = f') : image f ⟶ image f' :=
 
 instance (h : f = f') : IsIso (image.eqToHom h) :=
   ⟨⟨image.eqToHom h.symm,
-      ⟨(cancel_mono (image.ι f)).1 (by 
+      ⟨(cancel_mono (image.ι f)).1 (by
           -- Porting note: added let's for used to be a simp[image.eqToHom]
-          let F : MonoFactorisation f' :=  
-            ⟨image f, image.ι f, factorThruImage f, (by aesop_cat)⟩ 
+          let F : MonoFactorisation f' :=
+            ⟨image f, image.ι f, factorThruImage f, (by aesop_cat)⟩
           dsimp [image.eqToHom]
           rw [Category.id_comp,Category.assoc,image.lift_fac F]
-          let F' : MonoFactorisation f :=  
-            ⟨image f', image.ι f', factorThruImage f', (by aesop_cat)⟩ 
-          rw [image.lift_fac F'] ), 
+          let F' : MonoFactorisation f :=
+            ⟨image f', image.ι f', factorThruImage f', (by aesop_cat)⟩
+          rw [image.lift_fac F'] ),
         (cancel_mono (image.ι f')).1 (by
           -- Porting note: added let's for used to be a simp[image.eqToHom]
-          let F' : MonoFactorisation f :=  
-            ⟨image f', image.ι f', factorThruImage f', (by aesop_cat)⟩ 
+          let F' : MonoFactorisation f :=
+            ⟨image f', image.ι f', factorThruImage f', (by aesop_cat)⟩
           dsimp [image.eqToHom]
           rw [Category.id_comp,Category.assoc,image.lift_fac F']
-          let F : MonoFactorisation f' :=  
-            ⟨image f, image.ι f, factorThruImage f, (by aesop_cat)⟩ 
+          let F : MonoFactorisation f' :=
+            ⟨image f, image.ι f, factorThruImage f, (by aesop_cat)⟩
           rw [image.lift_fac F])⟩⟩⟩
 
 /-- An equation between morphisms gives an isomorphism between the images. -/
@@ -549,7 +549,7 @@ def image.preComp [HasImage g] [HasImage (f ≫ g)] : image (f ≫ g) ⟶ image
 
 @[reassoc (attr := simp)]
 theorem image.preComp_ι [HasImage g] [HasImage (f ≫ g)] :
-    image.preComp f g ≫ image.ι g = image.ι (f ≫ g) := by 
+    image.preComp f g ≫ image.ι g = image.ι (f ≫ g) := by
       dsimp [image.preComp]
       rw [image.lift_fac] -- Porting note: also here, see image.eq_fac
 #align category_theory.limits.image.pre_comp_ι CategoryTheory.Limits.image.preComp_ι
@@ -596,10 +596,10 @@ instance image.preComp_epi_of_epi [HasImage g] [HasImage (f ≫ g)] [Epi f] :
 instance hasImage_iso_comp [IsIso f] [HasImage g] : HasImage (f ≫ g) :=
   HasImage.mk
     { F := (Image.monoFactorisation g).isoComp f
-      isImage := { lift := fun F' => image.lift (F'.ofIsoComp f) 
-                   lift_fac := fun F' => by 
-                    dsimp  
-                    have : (MonoFactorisation.ofIsoComp f F').m  = F'.m := rfl 
+      isImage := { lift := fun F' => image.lift (F'.ofIsoComp f)
+                   lift_fac := fun F' => by
+                    dsimp
+                    have : (MonoFactorisation.ofIsoComp f F').m  = F'.m := rfl
                     rw [←this,image.lift_fac (MonoFactorisation.ofIsoComp f F')] } }
 #align category_theory.limits.has_image_iso_comp CategoryTheory.Limits.hasImage_iso_comp
 
@@ -623,17 +623,17 @@ instance image.isIso_precomp_iso (f : X ⟶ Y) [IsIso f] [HasImage g] : IsIso (i
 instance hasImage_comp_iso [HasImage f] [IsIso g] : HasImage (f ≫ g) :=
   HasImage.mk
     { F := (Image.monoFactorisation f).compMono g
-      isImage := 
-      { lift := fun F' => image.lift F'.ofCompIso 
-        lift_fac := fun F' => by 
-          rw [← Category.comp_id (image.lift (MonoFactorisation.ofCompIso F') ≫ F'.m), 
+      isImage :=
+      { lift := fun F' => image.lift F'.ofCompIso
+        lift_fac := fun F' => by
+          rw [← Category.comp_id (image.lift (MonoFactorisation.ofCompIso F') ≫ F'.m),
             ←IsIso.inv_hom_id g,← Category.assoc]
           refine congrArg (· ≫ g) ?_
-          have : (image.lift (MonoFactorisation.ofCompIso F') ≫ F'.m) ≫ inv g = 
-            image.lift (MonoFactorisation.ofCompIso F') ≫ 
-            ((MonoFactorisation.ofCompIso F').m) := by 
-              simp only [MonoFactorisation.ofCompIso_I, Category.assoc, 
-                MonoFactorisation.ofCompIso_m] 
+          have : (image.lift (MonoFactorisation.ofCompIso F') ≫ F'.m) ≫ inv g =
+            image.lift (MonoFactorisation.ofCompIso F') ≫
+            ((MonoFactorisation.ofCompIso F').m) := by
+              simp only [MonoFactorisation.ofCompIso_I, Category.assoc,
+                MonoFactorisation.ofCompIso_m]
           rw [this, image.lift_fac (MonoFactorisation.ofCompIso F'),image.as_ι] }}
 #align category_theory.limits.has_image_comp_iso CategoryTheory.Limits.hasImage_comp_iso
 
@@ -683,7 +683,7 @@ structure ImageMap {f g : Arrow C} [HasImage f.hom] [HasImage g.hom] (sq : f ⟶
 #align category_theory.limits.image_map CategoryTheory.Limits.ImageMap
 #align category_theory.limits.image_map.map_ι' CategoryTheory.Limits.ImageMap.map_ι
 
-attribute [inherit_doc ImageMap] ImageMap.map ImageMap.map_ι 
+attribute [inherit_doc ImageMap] ImageMap.map ImageMap.map_ι
 
 -- Porting note: LHS of this simplifies, simpNF still complains after blacklisting
 attribute [-simp, nolint simpNF] ImageMap.mk.injEq
@@ -711,7 +711,7 @@ def ImageMap.transport {f g : Arrow C} [HasImage f.hom] [HasImage g.hom] (sq : f
 #align category_theory.limits.image_map.transport CategoryTheory.Limits.ImageMap.transport
 
 /-- `HasImageMap sq` means that there is an `ImageMap` for the square `sq`. -/
-class HasImageMap {f g : Arrow C} [HasImage f.hom] [HasImage g.hom] (sq : f ⟶ g) : Prop where 
+class HasImageMap {f g : Arrow C} [HasImage f.hom] [HasImage g.hom] (sq : f ⟶ g) : Prop where
 mk' ::
   has_image_map : Nonempty (ImageMap sq)
 #align category_theory.limits.has_image_map CategoryTheory.Limits.HasImageMap
@@ -760,34 +760,34 @@ section
 
 attribute [local ext] ImageMap
 
-/- Porting note: ImageMap.mk.injEq has LHS simplify to True due to the next instance 
+/- Porting note: ImageMap.mk.injEq has LHS simplify to True due to the next instance
 We make a replacement -/
-theorem ImageMap.map_uniq_aux {f g : Arrow C} [HasImage f.hom]  [HasImage g.hom] {sq : f ⟶ g} 
+theorem ImageMap.map_uniq_aux {f g : Arrow C} [HasImage f.hom]  [HasImage g.hom] {sq : f ⟶ g}
     (map : image f.hom ⟶ image g.hom)
-    (map_ι : map ≫ image.ι g.hom = image.ι f.hom ≫ sq.right := by aesop_cat) 
+    (map_ι : map ≫ image.ι g.hom = image.ι f.hom ≫ sq.right := by aesop_cat)
     (map' : image f.hom ⟶ image g.hom)
-    (map_ι' : map' ≫ image.ι g.hom = image.ι f.hom ≫ sq.right) : (map = map') := by 
+    (map_ι' : map' ≫ image.ι g.hom = image.ι f.hom ≫ sq.right) : (map = map') := by
   have : map ≫ image.ι g.hom = map' ≫ image.ι g.hom := by rw [map_ι,map_ι']
   apply (cancel_mono (image.ι g.hom)).1 this
 
 -- Porting note: added to get variant on ImageMap.mk.injEq below
-theorem ImageMap.map_uniq {f g : Arrow C} [HasImage f.hom]  [HasImage g.hom] 
-    {sq : f ⟶ g} (F G : ImageMap sq) : F.map = G.map := by 
-  apply ImageMap.map_uniq_aux _ F.map_ι _ G.map_ι    
+theorem ImageMap.map_uniq {f g : Arrow C} [HasImage f.hom]  [HasImage g.hom]
+    {sq : f ⟶ g} (F G : ImageMap sq) : F.map = G.map := by
+  apply ImageMap.map_uniq_aux _ F.map_ι _ G.map_ι
 
 @[simp]
-theorem ImageMap.mk.injEq' {f g : Arrow C} [HasImage f.hom]  [HasImage g.hom] {sq : f ⟶ g} 
+theorem ImageMap.mk.injEq' {f g : Arrow C} [HasImage f.hom]  [HasImage g.hom] {sq : f ⟶ g}
     (map : image f.hom ⟶ image g.hom)
-    (map_ι : map ≫ image.ι g.hom = image.ι f.hom ≫ sq.right := by aesop_cat) 
+    (map_ι : map ≫ image.ι g.hom = image.ι f.hom ≫ sq.right := by aesop_cat)
     (map' : image f.hom ⟶ image g.hom)
-    (map_ι' : map' ≫ image.ι g.hom = image.ι f.hom ≫ sq.right) : (map = map') = True := by 
-  simp only [Functor.id_obj, eq_iff_iff, iff_true] 
+    (map_ι' : map' ≫ image.ι g.hom = image.ι f.hom ≫ sq.right) : (map = map') = True := by
+  simp only [Functor.id_obj, eq_iff_iff, iff_true]
   apply ImageMap.map_uniq_aux _ map_ι _ map_ι'
 
 instance : Subsingleton (ImageMap sq) :=
   Subsingleton.intro fun a b =>
     ImageMap.ext a b <| ImageMap.map_uniq a b
-    
+
 end
 
 variable [HasImageMap sq]
@@ -823,7 +823,7 @@ def imageMapComp : ImageMap (sq ≫ sq') where map := image.map sq ≫ image.map
 @[simp]
 theorem image.map_comp [HasImageMap (sq ≫ sq')] :
     image.map (sq ≫ sq') = image.map sq ≫ image.map sq' :=
-  show (HasImageMap.imageMap (sq ≫ sq')).map = (imageMapComp sq sq').map by 
+  show (HasImageMap.imageMap (sq ≫ sq')).map = (imageMapComp sq sq').map by
     congr; simp only [eq_iff_true_of_subsingleton]
 #align category_theory.limits.image.map_comp CategoryTheory.Limits.image.map_comp
 
@@ -896,7 +896,7 @@ instance strongEpiMonoFactorisationInhabited {X Y : C} (f : X ⟶ Y) [StrongEpi
 /-- A mono factorisation coming from a strong epi-mono factorisation always has the universal
     property of the image. -/
 def StrongEpiMonoFactorisation.toMonoIsImage {X Y : C} {f : X ⟶ Y}
-    (F : StrongEpiMonoFactorisation f) : IsImage F.toMonoFactorisation where 
+    (F : StrongEpiMonoFactorisation f) : IsImage F.toMonoFactorisation where
   lift G :=
     (CommSq.mk (show G.e ≫ G.m = F.e ≫ F.m by rw [F.toMonoFactorisation.fac, G.fac])).lift
 #align category_theory.limits.strong_epi_mono_factorisation.to_mono_is_image CategoryTheory.Limits.StrongEpiMonoFactorisation.toMonoIsImage
@@ -920,7 +920,7 @@ theorem HasStrongEpiMonoFactorisations.mk
 #align category_theory.limits.has_strong_epi_mono_factorisations.mk CategoryTheory.Limits.HasStrongEpiMonoFactorisations.mk
 
 instance (priority := 100) hasImages_of_hasStrongEpiMonoFactorisations
-    [HasStrongEpiMonoFactorisations C] : HasImages C where 
+    [HasStrongEpiMonoFactorisations C] : HasImages C where
   has_image f :=
     let F' := Classical.choice (HasStrongEpiMonoFactorisations.has_fac f)
     HasImage.mk
@@ -964,7 +964,7 @@ theorem strongEpi_factorThruImage_of_strongEpiMonoFactorisation {X Y : C} {f : X
 /-- If we constructed our images from strong epi-mono factorisations, then these images are
     strong epi images. -/
 instance (priority := 100) hasStrongEpiImages_of_hasStrongEpiMonoFactorisations
-    [HasStrongEpiMonoFactorisations C] : HasStrongEpiImages C where 
+    [HasStrongEpiMonoFactorisations C] : HasStrongEpiImages C where
   strong_factorThruImage f :=
     strongEpi_factorThruImage_of_strongEpiMonoFactorisation <|
       Classical.choice <| HasStrongEpiMonoFactorisations.has_fac f
@@ -992,7 +992,7 @@ instance (priority := 100) hasImageMapsOfHasStrongEpiImages [HasStrongEpiImages
 /-- If a category has images, equalizers and pullbacks, then images are automatically strong epi
     images. -/
 instance (priority := 100) hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers [HasPullbacks C]
-    [HasEqualizers C] : HasStrongEpiImages C where 
+    [HasEqualizers C] : HasStrongEpiImages C where
   strong_factorThruImage f :=
     StrongEpi.mk' fun {A} {B} h h_mono x y sq =>
       CommSq.HasLift.mk'
@@ -1028,9 +1028,9 @@ def image.isoStrongEpiMono {I' : C} (e : X ⟶ I') (m : I' ⟶ Y) (comm : e ≫
 
 @[simp]
 theorem image.isoStrongEpiMono_hom_comp_ι {I' : C} (e : X ⟶ I') (m : I' ⟶ Y) (comm : e ≫ m = f)
-    [StrongEpi e] [Mono m] : (image.isoStrongEpiMono e m comm).hom ≫ image.ι f = m := by 
+    [StrongEpi e] [Mono m] : (image.isoStrongEpiMono e m comm).hom ≫ image.ι f = m := by
   dsimp [isoStrongEpiMono]
-  apply IsImage.lift_fac 
+  apply IsImage.lift_fac
 #align category_theory.limits.image.iso_strong_epi_mono_hom_comp_ι CategoryTheory.Limits.image.isoStrongEpiMono_hom_comp_ι
 
 @[simp]
@@ -1060,10 +1060,9 @@ theorem hasStrongEpiMonoFactorisations_imp_of_isEquivalence (F : C ⥤ D) [IsEqu
         { I := F.obj em.I
           e := F.asEquivalence.counitIso.inv.app X ≫ F.map em.e
           m := F.map em.m ≫ F.asEquivalence.counitIso.hom.app Y
-          fac := by 
+          fac := by
             simpa only [Category.assoc, ← F.map_comp_assoc, em.fac, IsEquivalence.fun_inv_map,
               Iso.inv_hom_id_app, Iso.inv_hom_id_app_assoc] using Category.comp_id _ }⟩
 #align category_theory.functor.has_strong_epi_mono_factorisations_imp_of_is_equivalence CategoryTheory.Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalence
 
 end CategoryTheory.Functor
-

563aed34

feat: port CategoryTheory.Limits.Shapes.Images (#2615)

Co-authored-by: Matthew Robert Ballard <100034030+mattrobball@users.noreply.github.com>

367e5e69

`category_theory.limits.shapes.images` ⟷ `Mathlib.CategoryTheory.Limits.Shapes.Images`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 111

category_theory.limits.shapes.images ⟷ Mathlib.CategoryTheory.Limits.Shapes.Images

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 111

`category_theory.limits.shapes.images` ⟷ `Mathlib.CategoryTheory.Limits.Shapes.Images`