category_theory.quotient ⟷ Mathlib.CategoryTheory.Quotient

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

@@ -136,9 +136,10 @@ def functor : C ⥤ Quotient r where
 #align category_theory.quotient.functor CategoryTheory.Quotient.functor
 -/
 
-noncomputable instance : Full (functor r) where preimage X Y f := Quot.out f
+noncomputable instance : CategoryTheory.Functor.Full (functor r) where preimage X Y f := Quot.out f
 
-instance : EssSurj (functor r) where mem_essImage Y := ⟨Y.as, ⟨eqToIso (by ext; rfl)⟩⟩
+instance : CategoryTheory.Functor.EssSurj (functor r)
+    where mem_essImage Y := ⟨Y.as, ⟨eqToIso (by ext; rfl)⟩⟩
 
 #print CategoryTheory.Quotient.induction /-
 protected theorem induction {P : ∀ {a b : Quotient r}, (a ⟶ b) → Prop}

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 David Wärn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Wärn
 -/
-import CategoryTheory.NaturalIsomorphism
+import CategoryTheory.NatIso
 import CategoryTheory.EqToHom
 
 #align_import category_theory.quotient from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 David Wärn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Wärn
 -/
-import Mathbin.CategoryTheory.NaturalIsomorphism
-import Mathbin.CategoryTheory.EqToHom
+import CategoryTheory.NaturalIsomorphism
+import CategoryTheory.EqToHom
 
 #align_import category_theory.quotient from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 David Wärn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Wärn
-
-! This file was ported from Lean 3 source module category_theory.quotient
-! 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.NaturalIsomorphism
 import Mathbin.CategoryTheory.EqToHom
 
+#align_import category_theory.quotient from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # Quotient category
 

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

@@ -38,8 +38,6 @@ namespace CategoryTheory
 
 variable {C : Type _} [Category C] (r : HomRel C)
 
-include r
-
 #print CategoryTheory.Congruence /-
 /-- A `hom_rel` is a congruence when it's an equivalence on every hom-set, and it can be composed
 from left and right. -/
@@ -115,11 +113,13 @@ def comp ⦃a b c : Quotient r⦄ : Hom r a b → Hom r b c → Hom r a c := fun
 #align category_theory.quotient.comp CategoryTheory.Quotient.comp
 -/
 
+#print CategoryTheory.Quotient.comp_mk /-
 @[simp]
 theorem comp_mk {a b c : Quotient r} (f : a.as ⟶ b.as) (g : b.as ⟶ c.as) :
     comp r (Quot.mk _ f) (Quot.mk _ g) = Quot.mk _ (f ≫ g) :=
   rfl
 #align category_theory.quotient.comp_mk CategoryTheory.Quotient.comp_mk
+-/
 
 #print CategoryTheory.Quotient.category /-
 instance category : Category (Quotient r)
@@ -143,16 +143,21 @@ noncomputable instance : Full (functor r) where preimage X Y f := Quot.out f
 
 instance : EssSurj (functor r) where mem_essImage Y := ⟨Y.as, ⟨eqToIso (by ext; rfl)⟩⟩
 
+#print CategoryTheory.Quotient.induction /-
 protected theorem induction {P : ∀ {a b : Quotient r}, (a ⟶ b) → Prop}
     (h : ∀ {x y : C} (f : x ⟶ y), P ((functor r).map f)) : ∀ {a b : Quotient r} (f : a ⟶ b), P f :=
   by rintro ⟨x⟩ ⟨y⟩ ⟨f⟩; exact h f
 #align category_theory.quotient.induction CategoryTheory.Quotient.induction
+-/
 
+#print CategoryTheory.Quotient.sound /-
 protected theorem sound {a b : C} {f₁ f₂ : a ⟶ b} (h : r f₁ f₂) :
     (functor r).map f₁ = (functor r).map f₂ := by
   simpa using Quot.sound (comp_closure.intro (𝟙 a) f₁ f₂ (𝟙 b) h)
 #align category_theory.quotient.sound CategoryTheory.Quotient.sound
+-/
 
+#print CategoryTheory.Quotient.functor_map_eq_iff /-
 theorem functor_map_eq_iff [Congruence r] {X Y : C} (f f' : X ⟶ Y) :
     (functor r).map f = (functor r).map f' ↔ r f f' :=
   by
@@ -166,12 +171,12 @@ theorem functor_map_eq_iff [Congruence r] {X Y : C} (f f' : X ⟶ Y) :
     · apply trans <;> assumption
   · apply Quotient.sound
 #align category_theory.quotient.functor_map_eq_iff CategoryTheory.Quotient.functor_map_eq_iff
+-/
 
 variable {D : Type _} [Category D] (F : C ⥤ D)
   (H : ∀ (x y : C) (f₁ f₂ : x ⟶ y), r f₁ f₂ → F.map f₁ = F.map f₂)
 
-include H
-
+#print CategoryTheory.Quotient.lift /-
 /-- The induced functor on the quotient category. -/
 @[simps]
 def lift : Quotient r ⥤ D where
@@ -181,14 +186,18 @@ def lift : Quotient r ⥤ D where
   map_id' a := F.map_id a.as
   map_comp' := by rintro a b c ⟨f⟩ ⟨g⟩; exact F.map_comp f g
 #align category_theory.quotient.lift CategoryTheory.Quotient.lift
+-/
 
+#print CategoryTheory.Quotient.lift_spec /-
 theorem lift_spec : functor r ⋙ lift r F H = F :=
   by
   apply Functor.ext; rotate_left
   · rintro X; rfl
   · rintro X Y f; simp
 #align category_theory.quotient.lift_spec CategoryTheory.Quotient.lift_spec
+-/
 
+#print CategoryTheory.Quotient.lift_unique /-
 theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ = lift r F H :=
   by
   subst_vars
@@ -201,26 +210,35 @@ theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ =
     simp only [Quot.liftOn_mk, functor.comp_map]
     congr <;> ext <;> rfl
 #align category_theory.quotient.lift_unique CategoryTheory.Quotient.lift_unique
+-/
 
+#print CategoryTheory.Quotient.lift.isLift /-
 /-- The original functor factors through the induced functor. -/
 def lift.isLift : functor r ⋙ lift r F H ≅ F :=
   NatIso.ofComponents (fun X => Iso.refl _) (by tidy)
 #align category_theory.quotient.lift.is_lift CategoryTheory.Quotient.lift.isLift
+-/
 
+#print CategoryTheory.Quotient.lift.isLift_hom /-
 @[simp]
 theorem lift.isLift_hom (X : C) : (lift.isLift r F H).Hom.app X = 𝟙 (F.obj X) :=
   rfl
 #align category_theory.quotient.lift.is_lift_hom CategoryTheory.Quotient.lift.isLift_hom
+-/
 
+#print CategoryTheory.Quotient.lift.isLift_inv /-
 @[simp]
 theorem lift.isLift_inv (X : C) : (lift.isLift r F H).inv.app X = 𝟙 (F.obj X) :=
   rfl
 #align category_theory.quotient.lift.is_lift_inv CategoryTheory.Quotient.lift.isLift_inv
+-/
 
+#print CategoryTheory.Quotient.lift_map_functor_map /-
 theorem lift_map_functor_map {X Y : C} (f : X ⟶ Y) :
     (lift r F H).map ((functor r).map f) = F.map f := by
   rw [← nat_iso.naturality_1 (lift.is_lift r F H)]; dsimp; simp
 #align category_theory.quotient.lift_map_functor_map CategoryTheory.Quotient.lift_map_functor_map
+-/
 
 end Quotient
 

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

@@ -29,7 +29,8 @@ relation, `functor_map_eq_iff` says that no unnecessary identifications have bee
 #print HomRel /-
 /-- A `hom_rel` on `C` consists of a relation on every hom-set. -/
 def HomRel (C) [Quiver C] :=
-  ∀ ⦃X Y : C⦄, (X ⟶ Y) → (X ⟶ Y) → Prop deriving Inhabited
+  ∀ ⦃X Y : C⦄, (X ⟶ Y) → (X ⟶ Y) → Prop
+deriving Inhabited
 #align hom_rel HomRel
 -/
 
@@ -192,7 +193,7 @@ theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ =
   by
   subst_vars
   apply functor.hext
-  · rintro X; dsimp [lift, Functor]; congr ; ext; rfl
+  · rintro X; dsimp [lift, Functor]; congr; ext; rfl
   · rintro X Y f
     dsimp [lift, Functor]
     apply Quot.inductionOn f

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

@@ -114,12 +114,6 @@ def comp ⦃a b c : Quotient r⦄ : Hom r a b → Hom r b c → Hom r a c := fun
 #align category_theory.quotient.comp CategoryTheory.Quotient.comp
 -/
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.quotient.comp_mk CategoryTheory.Quotient.comp_mkₓ'. -/
 @[simp]
 theorem comp_mk {a b c : Quotient r} (f : a.as ⟶ b.as) (g : b.as ⟶ c.as) :
     comp r (Quot.mk _ f) (Quot.mk _ g) = Quot.mk _ (f ≫ g) :=
@@ -148,34 +142,16 @@ noncomputable instance : Full (functor r) where preimage X Y f := Quot.out f
 
 instance : EssSurj (functor r) where mem_essImage Y := ⟨Y.as, ⟨eqToIso (by ext; rfl)⟩⟩
 
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 protected theorem induction {P : ∀ {a b : Quotient r}, (a ⟶ b) → Prop}
     (h : ∀ {x y : C} (f : x ⟶ y), P ((functor r).map f)) : ∀ {a b : Quotient r} (f : a ⟶ b), P f :=
   by rintro ⟨x⟩ ⟨y⟩ ⟨f⟩; exact h f
 #align category_theory.quotient.induction CategoryTheory.Quotient.induction
 
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 protected theorem sound {a b : C} {f₁ f₂ : a ⟶ b} (h : r f₁ f₂) :
     (functor r).map f₁ = (functor r).map f₂ := by
   simpa using Quot.sound (comp_closure.intro (𝟙 a) f₁ f₂ (𝟙 b) h)
 #align category_theory.quotient.sound CategoryTheory.Quotient.sound
 
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 theorem functor_map_eq_iff [Congruence r] {X Y : C} (f f' : X ⟶ Y) :
     (functor r).map f = (functor r).map f' ↔ r f f' :=
   by
@@ -195,12 +171,6 @@ variable {D : Type _} [Category D] (F : C ⥤ D)
 
 include H
 
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 /-- The induced functor on the quotient category. -/
 @[simps]
 def lift : Quotient r ⥤ D where
@@ -211,12 +181,6 @@ def lift : Quotient r ⥤ D where
   map_comp' := by rintro a b c ⟨f⟩ ⟨g⟩; exact F.map_comp f g
 #align category_theory.quotient.lift CategoryTheory.Quotient.lift
 
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 theorem lift_spec : functor r ⋙ lift r F H = F :=
   by
   apply Functor.ext; rotate_left
@@ -224,12 +188,6 @@ theorem lift_spec : functor r ⋙ lift r F H = F :=
   · rintro X Y f; simp
 #align category_theory.quotient.lift_spec CategoryTheory.Quotient.lift_spec
 
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 theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ = lift r F H :=
   by
   subst_vars
@@ -243,42 +201,21 @@ theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ =
     congr <;> ext <;> rfl
 #align category_theory.quotient.lift_unique CategoryTheory.Quotient.lift_unique
 
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 /-- The original functor factors through the induced functor. -/
 def lift.isLift : functor r ⋙ lift r F H ≅ F :=
   NatIso.ofComponents (fun X => Iso.refl _) (by tidy)
 #align category_theory.quotient.lift.is_lift CategoryTheory.Quotient.lift.isLift
 
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 @[simp]
 theorem lift.isLift_hom (X : C) : (lift.isLift r F H).Hom.app X = 𝟙 (F.obj X) :=
   rfl
 #align category_theory.quotient.lift.is_lift_hom CategoryTheory.Quotient.lift.isLift_hom
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.quotient.lift.is_lift_inv CategoryTheory.Quotient.lift.isLift_invₓ'. -/
 @[simp]
 theorem lift.isLift_inv (X : C) : (lift.isLift r F H).inv.app X = 𝟙 (F.obj X) :=
   rfl
 #align category_theory.quotient.lift.is_lift_inv CategoryTheory.Quotient.lift.isLift_inv
 
-/- warning: category_theory.quotient.lift_map_functor_map -> CategoryTheory.Quotient.lift_map_functor_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.quotient.lift_map_functor_map CategoryTheory.Quotient.lift_map_functor_mapₓ'. -/
 theorem lift_map_functor_map {X Y : C} (f : X ⟶ Y) :
     (lift r F H).map ((functor r).map f) = F.map f := by
   rw [← nat_iso.naturality_1 (lift.is_lift r F H)]; dsimp; simp

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

@@ -146,13 +146,7 @@ def functor : C ⥤ Quotient r where
 
 noncomputable instance : Full (functor r) where preimage X Y f := Quot.out f
 
-instance : EssSurj (functor r)
-    where mem_essImage Y :=
-    ⟨Y.as,
-      ⟨eqToIso
-          (by
-            ext
-            rfl)⟩⟩
+instance : EssSurj (functor r) where mem_essImage Y := ⟨Y.as, ⟨eqToIso (by ext; rfl)⟩⟩
 
 /- warning: category_theory.quotient.induction -> CategoryTheory.Quotient.induction is a dubious translation:
 lean 3 declaration is
@@ -162,9 +156,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.quotient.induction CategoryTheory.Quotient.inductionₓ'. -/
 protected theorem induction {P : ∀ {a b : Quotient r}, (a ⟶ b) → Prop}
     (h : ∀ {x y : C} (f : x ⟶ y), P ((functor r).map f)) : ∀ {a b : Quotient r} (f : a ⟶ b), P f :=
-  by
-  rintro ⟨x⟩ ⟨y⟩ ⟨f⟩
-  exact h f
+  by rintro ⟨x⟩ ⟨y⟩ ⟨f⟩; exact h f
 #align category_theory.quotient.induction CategoryTheory.Quotient.induction
 
 /- warning: category_theory.quotient.sound -> CategoryTheory.Quotient.sound is a dubious translation:
@@ -191,13 +183,9 @@ theorem functor_map_eq_iff [Congruence r] {X Y : C} (f f' : X ⟶ Y) :
   · erw [Quot.eq]
     intro h
     induction' h with m m' hm
-    · cases hm
-      apply congruence.comp_left
-      apply congruence.comp_right
-      assumption
+    · cases hm; apply congruence.comp_left; apply congruence.comp_right; assumption
     · apply refl
-    · apply symm
-      assumption
+    · apply symm; assumption
     · apply trans <;> assumption
   · apply Quotient.sound
 #align category_theory.quotient.functor_map_eq_iff CategoryTheory.Quotient.functor_map_eq_iff
@@ -218,14 +206,9 @@ Case conversion may be inaccurate. Consider using '#align category_theory.quotie
 def lift : Quotient r ⥤ D where
   obj a := F.obj a.as
   map a b hf :=
-    Quot.liftOn hf (fun f => F.map f)
-      (by
-        rintro _ _ ⟨_, _, _, _, h⟩
-        simp [H _ _ _ _ h])
+    Quot.liftOn hf (fun f => F.map f) (by rintro _ _ ⟨_, _, _, _, h⟩; simp [H _ _ _ _ h])
   map_id' a := F.map_id a.as
-  map_comp' := by
-    rintro a b c ⟨f⟩ ⟨g⟩
-    exact F.map_comp f g
+  map_comp' := by rintro a b c ⟨f⟩ ⟨g⟩; exact F.map_comp f g
 #align category_theory.quotient.lift CategoryTheory.Quotient.lift
 
 /- warning: category_theory.quotient.lift_spec -> CategoryTheory.Quotient.lift_spec is a dubious translation:
@@ -237,10 +220,8 @@ Case conversion may be inaccurate. Consider using '#align category_theory.quotie
 theorem lift_spec : functor r ⋙ lift r F H = F :=
   by
   apply Functor.ext; rotate_left
-  · rintro X
-    rfl
-  · rintro X Y f
-    simp
+  · rintro X; rfl
+  · rintro X Y f; simp
 #align category_theory.quotient.lift_spec CategoryTheory.Quotient.lift_spec
 
 /- warning: category_theory.quotient.lift_unique -> CategoryTheory.Quotient.lift_unique is a dubious translation:
@@ -253,11 +234,7 @@ theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ =
   by
   subst_vars
   apply functor.hext
-  · rintro X
-    dsimp [lift, Functor]
-    congr
-    ext
-    rfl
+  · rintro X; dsimp [lift, Functor]; congr ; ext; rfl
   · rintro X Y f
     dsimp [lift, Functor]
     apply Quot.inductionOn f
@@ -303,11 +280,8 @@ theorem lift.isLift_inv (X : C) : (lift.isLift r F H).inv.app X = 𝟙 (F.obj X)
 <too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.quotient.lift_map_functor_map CategoryTheory.Quotient.lift_map_functor_mapₓ'. -/
 theorem lift_map_functor_map {X Y : C} (f : X ⟶ Y) :
-    (lift r F H).map ((functor r).map f) = F.map f :=
-  by
-  rw [← nat_iso.naturality_1 (lift.is_lift r F H)]
-  dsimp
-  simp
+    (lift r F H).map ((functor r).map f) = F.map f := by
+  rw [← nat_iso.naturality_1 (lift.is_lift r F H)]; dsimp; simp
 #align category_theory.quotient.lift_map_functor_map CategoryTheory.Quotient.lift_map_functor_map
 
 end Quotient

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

@@ -300,10 +300,7 @@ theorem lift.isLift_inv (X : C) : (lift.isLift r F H).inv.app X = 𝟙 (F.obj X)
 #align category_theory.quotient.lift.is_lift_inv CategoryTheory.Quotient.lift.isLift_inv
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.quotient.lift_map_functor_map CategoryTheory.Quotient.lift_map_functor_mapₓ'. -/
 theorem lift_map_functor_map {X Y : C} (f : X ⟶ Y) :
     (lift r F H).map ((functor r).map f) = F.map f :=

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Wärn
 
 ! This file was ported from Lean 3 source module category_theory.quotient
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.EqToHom
 /-!
 # Quotient category
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Constructs the quotient of a category by an arbitrary family of relations on its hom-sets,
 by introducing a type synonym for the objects, and identifying homs as necessary.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -23,10 +23,12 @@ relation, `functor_map_eq_iff` says that no unnecessary identifications have bee
 -/
 
 
+#print HomRel /-
 /-- A `hom_rel` on `C` consists of a relation on every hom-set. -/
 def HomRel (C) [Quiver C] :=
   ∀ ⦃X Y : C⦄, (X ⟶ Y) → (X ⟶ Y) → Prop deriving Inhabited
 #align hom_rel HomRel
+-/
 
 namespace CategoryTheory
 
@@ -34,6 +36,7 @@ variable {C : Type _} [Category C] (r : HomRel C)
 
 include r
 
+#print CategoryTheory.Congruence /-
 /-- A `hom_rel` is a congruence when it's an equivalence on every hom-set, and it can be composed
 from left and right. -/
 class Congruence : Prop where
@@ -41,49 +44,63 @@ class Congruence : Prop where
   compLeft : ∀ {X Y Z} (f : X ⟶ Y) {g g' : Y ⟶ Z}, r g g' → r (f ≫ g) (f ≫ g')
   compRight : ∀ {X Y Z} {f f' : X ⟶ Y} (g : Y ⟶ Z), r f f' → r (f ≫ g) (f' ≫ g)
 #align category_theory.congruence CategoryTheory.Congruence
+-/
 
 attribute [instance] congruence.is_equiv
 
+#print CategoryTheory.Quotient /-
 /-- A type synonym for `C`, thought of as the objects of the quotient category. -/
 @[ext]
 structure Quotient where
   as : C
 #align category_theory.quotient CategoryTheory.Quotient
+-/
 
 instance [Inhabited C] : Inhabited (Quotient r) :=
   ⟨{ as := default }⟩
 
 namespace Quotient
 
+#print CategoryTheory.Quotient.CompClosure /-
 /-- Generates the closure of a family of relations w.r.t. composition from left and right. -/
 inductive CompClosure ⦃s t : C⦄ : (s ⟶ t) → (s ⟶ t) → Prop
   |
   intro {a b} (f : s ⟶ a) (m₁ m₂ : a ⟶ b) (g : b ⟶ t) (h : r m₁ m₂) :
     comp_closure (f ≫ m₁ ≫ g) (f ≫ m₂ ≫ g)
 #align category_theory.quotient.comp_closure CategoryTheory.Quotient.CompClosure
+-/
 
+#print CategoryTheory.Quotient.CompClosure.of /-
 theorem CompClosure.of {a b} (m₁ m₂ : a ⟶ b) (h : r m₁ m₂) : CompClosure r m₁ m₂ := by
   simpa using comp_closure.intro (𝟙 _) m₁ m₂ (𝟙 _) h
 #align category_theory.quotient.comp_closure.of CategoryTheory.Quotient.CompClosure.of
+-/
 
+#print CategoryTheory.Quotient.comp_left /-
 theorem comp_left {a b c : C} (f : a ⟶ b) :
     ∀ (g₁ g₂ : b ⟶ c) (h : CompClosure r g₁ g₂), CompClosure r (f ≫ g₁) (f ≫ g₂)
   | _, _, ⟨x, m₁, m₂, y, h⟩ => by simpa using comp_closure.intro (f ≫ x) m₁ m₂ y h
 #align category_theory.quotient.comp_left CategoryTheory.Quotient.comp_left
+-/
 
+#print CategoryTheory.Quotient.comp_right /-
 theorem comp_right {a b c : C} (g : b ⟶ c) :
     ∀ (f₁ f₂ : a ⟶ b) (h : CompClosure r f₁ f₂), CompClosure r (f₁ ≫ g) (f₂ ≫ g)
   | _, _, ⟨x, m₁, m₂, y, h⟩ => by simpa using comp_closure.intro x m₁ m₂ (y ≫ g) h
 #align category_theory.quotient.comp_right CategoryTheory.Quotient.comp_right
+-/
 
+#print CategoryTheory.Quotient.Hom /-
 /-- Hom-sets of the quotient category. -/
 def Hom (s t : Quotient r) :=
   Quot <| @CompClosure C _ r s.as t.as
 #align category_theory.quotient.hom CategoryTheory.Quotient.Hom
+-/
 
 instance (a : Quotient r) : Inhabited (Hom r a a) :=
   ⟨Quot.mk _ (𝟙 a.as)⟩
 
+#print CategoryTheory.Quotient.comp /-
 /-- Composition in the quotient category. -/
 def comp ⦃a b c : Quotient r⦄ : Hom r a b → Hom r b c → Hom r a c := fun hf hg =>
   Quot.liftOn hf
@@ -92,26 +109,37 @@ def comp ⦃a b c : Quotient r⦄ : Hom r a b → Hom r b c → Hom r a c := fun
         Quot.sound <| comp_left r f g₁ g₂ h)
     fun f₁ f₂ h => Quot.inductionOn hg fun g => Quot.sound <| comp_right r g f₁ f₂ h
 #align category_theory.quotient.comp CategoryTheory.Quotient.comp
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.quotient.comp_mk CategoryTheory.Quotient.comp_mkₓ'. -/
 @[simp]
 theorem comp_mk {a b c : Quotient r} (f : a.as ⟶ b.as) (g : b.as ⟶ c.as) :
     comp r (Quot.mk _ f) (Quot.mk _ g) = Quot.mk _ (f ≫ g) :=
   rfl
 #align category_theory.quotient.comp_mk CategoryTheory.Quotient.comp_mk
 
+#print CategoryTheory.Quotient.category /-
 instance category : Category (Quotient r)
     where
   Hom := Hom r
   id a := Quot.mk _ (𝟙 a.as)
   comp := comp r
 #align category_theory.quotient.category CategoryTheory.Quotient.category
+-/
 
+#print CategoryTheory.Quotient.functor /-
 /-- The functor from a category to its quotient. -/
 @[simps]
 def functor : C ⥤ Quotient r where
   obj a := { as := a }
   map _ _ f := Quot.mk _ f
 #align category_theory.quotient.functor CategoryTheory.Quotient.functor
+-/
 
 noncomputable instance : Full (functor r) where preimage X Y f := Quot.out f
 
@@ -123,6 +151,12 @@ instance : EssSurj (functor r)
             ext
             rfl)⟩⟩
 
+/- warning: category_theory.quotient.induction -> CategoryTheory.Quotient.induction is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] (r : HomRel.{u1, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1))) {P : forall {a : CategoryTheory.Quotient.{u1, u2} C _inst_1 r} {b : CategoryTheory.Quotient.{u1, u2} C _inst_1 r}, (Quiver.Hom.{succ u2, u1} (CategoryTheory.Quotient.{u1, u2} C _inst_1 r) (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} (CategoryTheory.Quotient.{u1, u2} C _inst_1 r) (CategoryTheory.Category.toCategoryStruct.{u2, u1} (CategoryTheory.Quotient.{u1, u2} C _inst_1 r) (CategoryTheory.Quotient.category.{u1, u2} C _inst_1 r))) a b) -> Prop}, (forall {x : C} {y : C} (f : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) x y), P (CategoryTheory.Functor.obj.{u2, u2, u1, u1} C _inst_1 (CategoryTheory.Quotient.{u1, u2} C _inst_1 r) (CategoryTheory.Quotient.category.{u1, u2} C _inst_1 r) (CategoryTheory.Quotient.functor.{u1, u2} C _inst_1 r) x) (CategoryTheory.Functor.obj.{u2, u2, u1, u1} C _inst_1 (CategoryTheory.Quotient.{u1, u2} C _inst_1 r) (CategoryTheory.Quotient.category.{u1, u2} C _inst_1 r) (CategoryTheory.Quotient.functor.{u1, u2} C _inst_1 r) y) (CategoryTheory.Functor.map.{u2, u2, u1, u1} C _inst_1 (CategoryTheory.Quotient.{u1, u2} C _inst_1 r) (CategoryTheory.Quotient.category.{u1, u2} C _inst_1 r) (CategoryTheory.Quotient.functor.{u1, u2} C _inst_1 r) x y f)) -> (forall {a : CategoryTheory.Quotient.{u1, u2} C _inst_1 r} {b : CategoryTheory.Quotient.{u1, u2} C _inst_1 r} (f : Quiver.Hom.{succ u2, u1} (CategoryTheory.Quotient.{u1, u2} C _inst_1 r) (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} (CategoryTheory.Quotient.{u1, u2} C _inst_1 r) (CategoryTheory.Category.toCategoryStruct.{u2, u1} (CategoryTheory.Quotient.{u1, u2} C _inst_1 r) (CategoryTheory.Quotient.category.{u1, u2} C _inst_1 r))) a b), P a b f)
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+Case conversion may be inaccurate. Consider using '#align category_theory.quotient.induction CategoryTheory.Quotient.inductionₓ'. -/
 protected theorem induction {P : ∀ {a b : Quotient r}, (a ⟶ b) → Prop}
     (h : ∀ {x y : C} (f : x ⟶ y), P ((functor r).map f)) : ∀ {a b : Quotient r} (f : a ⟶ b), P f :=
   by
@@ -130,11 +164,23 @@ protected theorem induction {P : ∀ {a b : Quotient r}, (a ⟶ b) → Prop}
   exact h f
 #align category_theory.quotient.induction CategoryTheory.Quotient.induction
 
+/- warning: category_theory.quotient.sound -> CategoryTheory.Quotient.sound is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.quotient.sound CategoryTheory.Quotient.soundₓ'. -/
 protected theorem sound {a b : C} {f₁ f₂ : a ⟶ b} (h : r f₁ f₂) :
     (functor r).map f₁ = (functor r).map f₂ := by
   simpa using Quot.sound (comp_closure.intro (𝟙 a) f₁ f₂ (𝟙 b) h)
 #align category_theory.quotient.sound CategoryTheory.Quotient.sound
 
+/- warning: category_theory.quotient.functor_map_eq_iff -> CategoryTheory.Quotient.functor_map_eq_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.quotient.functor_map_eq_iff CategoryTheory.Quotient.functor_map_eq_iffₓ'. -/
 theorem functor_map_eq_iff [Congruence r] {X Y : C} (f f' : X ⟶ Y) :
     (functor r).map f = (functor r).map f' ↔ r f f' :=
   by
@@ -158,6 +204,12 @@ variable {D : Type _} [Category D] (F : C ⥤ D)
 
 include H
 
+/- warning: category_theory.quotient.lift -> CategoryTheory.Quotient.lift is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.quotient.lift CategoryTheory.Quotient.liftₓ'. -/
 /-- The induced functor on the quotient category. -/
 @[simps]
 def lift : Quotient r ⥤ D where
@@ -173,6 +225,12 @@ def lift : Quotient r ⥤ D where
     exact F.map_comp f g
 #align category_theory.quotient.lift CategoryTheory.Quotient.lift
 
+/- warning: category_theory.quotient.lift_spec -> CategoryTheory.Quotient.lift_spec is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.quotient.lift_spec CategoryTheory.Quotient.lift_specₓ'. -/
 theorem lift_spec : functor r ⋙ lift r F H = F :=
   by
   apply Functor.ext; rotate_left
@@ -182,6 +240,12 @@ theorem lift_spec : functor r ⋙ lift r F H = F :=
     simp
 #align category_theory.quotient.lift_spec CategoryTheory.Quotient.lift_spec
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.quotient.lift_unique CategoryTheory.Quotient.lift_uniqueₓ'. -/
 theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ = lift r F H :=
   by
   subst_vars
@@ -199,21 +263,45 @@ theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ =
     congr <;> ext <;> rfl
 #align category_theory.quotient.lift_unique CategoryTheory.Quotient.lift_unique
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.quotient.lift.is_lift CategoryTheory.Quotient.lift.isLiftₓ'. -/
 /-- The original functor factors through the induced functor. -/
 def lift.isLift : functor r ⋙ lift r F H ≅ F :=
   NatIso.ofComponents (fun X => Iso.refl _) (by tidy)
 #align category_theory.quotient.lift.is_lift CategoryTheory.Quotient.lift.isLift
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.quotient.lift.is_lift_hom CategoryTheory.Quotient.lift.isLift_homₓ'. -/
 @[simp]
 theorem lift.isLift_hom (X : C) : (lift.isLift r F H).Hom.app X = 𝟙 (F.obj X) :=
   rfl
 #align category_theory.quotient.lift.is_lift_hom CategoryTheory.Quotient.lift.isLift_hom
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.quotient.lift.is_lift_inv CategoryTheory.Quotient.lift.isLift_invₓ'. -/
 @[simp]
 theorem lift.isLift_inv (X : C) : (lift.isLift r F H).inv.app X = 𝟙 (F.obj X) :=
   rfl
 #align category_theory.quotient.lift.is_lift_inv CategoryTheory.Quotient.lift.isLift_inv
 
+/- warning: category_theory.quotient.lift_map_functor_map -> CategoryTheory.Quotient.lift_map_functor_map 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.quotient.lift_map_functor_map CategoryTheory.Quotient.lift_map_functor_mapₓ'. -/
 theorem lift_map_functor_map {X Y : C} (f : X ⟶ Y) :
     (lift r F H).map ((functor r).map f) = F.map f :=
   by

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

Before this PR, Functor.Full contained the data of the preimage of maps by a full functor F. This PR makes Functor.Full a proposition. This is to prevent any diamond to appear.

The lemma Functor.image_preimage is also renamed Functor.map_preimage.

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

@@ -115,11 +115,8 @@ def functor : C ⥤ Quotient r where
   map := @fun _ _ f ↦ Quot.mk _ f
 #align category_theory.quotient.functor CategoryTheory.Quotient.functor
 
-noncomputable instance fullFunctor : (functor r).Full where
-  preimage := @fun X Y f ↦ Quot.out f
-  witness f := by
-    dsimp [functor]
-    simp
+instance full_functor : (functor r).Full where
+  map_surjective f:= ⟨Quot.out f, by simp [functor]⟩
 
 instance essSurj_functor : (functor r).EssSurj where
   mem_essImage Y :=
@@ -276,7 +273,7 @@ variable (D)
 
 instance full_whiskeringLeft_functor :
     ((whiskeringLeft C _ D).obj (functor r)).Full where
-  preimage := natTransLift r
+  map_surjective f := ⟨natTransLift r f, by aesop_cat⟩
 
 instance faithful_whiskeringLeft_functor :
     ((whiskeringLeft C _ D).obj (functor r)).Faithful := ⟨by apply natTrans_ext⟩

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

@@ -115,13 +115,13 @@ def functor : C ⥤ Quotient r where
   map := @fun _ _ f ↦ Quot.mk _ f
 #align category_theory.quotient.functor CategoryTheory.Quotient.functor
 
-noncomputable instance fullFunctor : Full (functor r) where
+noncomputable instance fullFunctor : (functor r).Full where
   preimage := @fun X Y f ↦ Quot.out f
   witness f := by
     dsimp [functor]
     simp
 
-instance essSurj_functor : EssSurj (functor r) where
+instance essSurj_functor : (functor r).EssSurj where
   mem_essImage Y :=
     ⟨Y.as, ⟨eqToIso (by
             ext
@@ -275,11 +275,11 @@ def natIsoLift {F G : Quotient r ⥤ D} (τ : Quotient.functor r ⋙ F ≅ Quoti
 variable (D)
 
 instance full_whiskeringLeft_functor :
-    Full ((whiskeringLeft C _ D).obj (functor r)) where
+    ((whiskeringLeft C _ D).obj (functor r)).Full where
   preimage := natTransLift r
 
 instance faithful_whiskeringLeft_functor :
-    Faithful ((whiskeringLeft C _ D).obj (functor r)) := ⟨by apply natTrans_ext⟩
+    ((whiskeringLeft C _ D).obj (functor r)).Faithful := ⟨by apply natTrans_ext⟩
 
 end Quotient
 

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -99,7 +99,7 @@ theorem comp_mk {a b c : Quotient r} (f : a.as ⟶ b.as) (g : b.as ⟶ c.as) :
   rfl
 #align category_theory.quotient.comp_mk CategoryTheory.Quotient.comp_mk
 
--- porting note: Had to manually add the proofs of `comp_id` `id_comp` and `assoc`
+-- Porting note: Had to manually add the proofs of `comp_id` `id_comp` and `assoc`
 instance category : Category (Quotient r) where
   Hom := Hom r
   id a := Quot.mk _ (𝟙 a.as)
@@ -194,7 +194,7 @@ theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ =
     congr
   · rintro _ _ f
     dsimp [lift, Functor]
-    refine Quot.inductionOn f (fun _ ↦ ?_) -- porting note: this line was originally an `apply`
+    refine Quot.inductionOn f (fun _ ↦ ?_) -- Porting note: this line was originally an `apply`
     simp only [Quot.liftOn_mk, Functor.comp_map]
     congr
 #align category_theory.quotient.lift_unique CategoryTheory.Quotient.lift_unique

This PR introduces the class of quasi-isomorphisms in the homotopy category of homological complexes.

@@ -199,6 +199,15 @@ theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ =
     congr
 #align category_theory.quotient.lift_unique CategoryTheory.Quotient.lift_unique
 
+lemma lift_unique' (F₁ F₂ : Quotient r ⥤ D) (h : functor r ⋙ F₁ = functor r ⋙ F₂) :
+    F₁ = F₂ := by
+  rw [lift_unique r (functor r ⋙ F₂) _ F₂ rfl]; swap
+  · rintro X Y f g h
+    dsimp
+    rw [Quotient.sound r h]
+  apply lift_unique
+  rw [h]
+
 /-- The original functor factors through the induced functor. -/
 def lift.isLift : functor r ⋙ lift r F H ≅ F :=
   NatIso.ofComponents fun X ↦ Iso.refl _

See Zulip thread for the discussion.

@@ -104,9 +104,9 @@ instance category : Category (Quotient r) where
   Hom := Hom r
   id a := Quot.mk _ (𝟙 a.as)
   comp := @comp _ _ r
-  comp_id f := Quot.inductionOn f $ by simp
-  id_comp f := Quot.inductionOn f $ by simp
-  assoc f g h := Quot.inductionOn f $ Quot.inductionOn g $ Quot.inductionOn h $ by simp
+  comp_id f := Quot.inductionOn f <| by simp
+  id_comp f := Quot.inductionOn f <| by simp
+  assoc f g h := Quot.inductionOn f <| Quot.inductionOn g <| Quot.inductionOn h <| by simp
 #align category_theory.quotient.category CategoryTheory.Quotient.category
 
 /-- The functor from a category to its quotient. -/

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

@@ -121,7 +121,7 @@ noncomputable instance fullFunctor : Full (functor r) where
     dsimp [functor]
     simp
 
-instance : EssSurj (functor r) where
+instance essSurj_functor : EssSurj (functor r) where
   mem_essImage Y :=
     ⟨Y.as, ⟨eqToIso (by
             ext

It is shown in this PR that when an equivalence relation on morphisms in a preadditive category is compatible with the addition, then the quotient category is preadditive.

@@ -37,15 +37,13 @@ variable {C : Type _} [Category C] (r : HomRel C)
 from left and right. -/
 class Congruence : Prop where
   /-- `r` is an equivalence on every hom-set. -/
-  isEquiv : ∀ {X Y}, IsEquiv _ (@r X Y)
+  equivalence : ∀ {X Y}, _root_.Equivalence (@r X Y)
   /-- Precomposition with an arrow respects `r`. -/
   compLeft : ∀ {X Y Z} (f : X ⟶ Y) {g g' : Y ⟶ Z}, r g g' → r (f ≫ g) (f ≫ g')
   /-- Postcomposition with an arrow respects `r`. -/
   compRight : ∀ {X Y Z} {f f' : X ⟶ Y} (g : Y ⟶ Z), r f f' → r (f ≫ g) (f' ≫ g)
 #align category_theory.congruence CategoryTheory.Congruence
 
-attribute [instance] Congruence.isEquiv
-
 /-- A type synonym for `C`, thought of as the objects of the quotient category. -/
 @[ext]
 structure Quotient (r : HomRel C) where
@@ -112,13 +110,16 @@ instance category : Category (Quotient r) where
 #align category_theory.quotient.category CategoryTheory.Quotient.category
 
 /-- The functor from a category to its quotient. -/
-@[simps]
 def functor : C ⥤ Quotient r where
   obj a := { as := a }
   map := @fun _ _ f ↦ Quot.mk _ f
 #align category_theory.quotient.functor CategoryTheory.Quotient.functor
 
-noncomputable instance fullFunctor : Full (functor r) where preimage := @fun X Y f ↦ Quot.out f
+noncomputable instance fullFunctor : Full (functor r) where
+  preimage := @fun X Y f ↦ Quot.out f
+  witness f := by
+    dsimp [functor]
+    simp
 
 instance : EssSurj (functor r) where
   mem_essImage Y :=
@@ -138,30 +139,31 @@ protected theorem sound {a b : C} {f₁ f₂ : a ⟶ b} (h : r f₁ f₂) :
   simpa using Quot.sound (CompClosure.intro (𝟙 a) f₁ f₂ (𝟙 b) h)
 #align category_theory.quotient.sound CategoryTheory.Quotient.sound
 
+lemma compClosure_iff_self [h : Congruence r] {X Y : C} (f g : X ⟶ Y) :
+    CompClosure r f g ↔ r f g := by
+  constructor
+  · intro hfg
+    induction' hfg with m m' hm
+    exact Congruence.compLeft _ (Congruence.compRight _ (by assumption))
+  · exact CompClosure.of _ _ _
+
+@[simp]
+theorem compClosure_eq_self [h : Congruence r] :
+    CompClosure r = r := by
+  ext
+  simp only [compClosure_iff_self]
+
 theorem functor_map_eq_iff [h : Congruence r] {X Y : C} (f f' : X ⟶ Y) :
     (functor r).map f = (functor r).map f' ↔ r f f' := by
-  constructor
-  · erw [Quot.eq]
-    intro h
-    induction' h with m m' hm
-    · cases hm
-      apply Congruence.compLeft
-      apply Congruence.compRight
-      assumption
-    · haveI := (h.isEquiv : IsEquiv _ (@r X Y))
-      -- porting note: had to add this line for `refl` (and name the `Congruence` argument)
-      apply refl
-    · apply symm
-      assumption
-    · apply _root_.trans <;> assumption
-  · apply Quotient.sound
+  dsimp [functor]
+  rw [Equivalence.quot_mk_eq_iff, compClosure_eq_self r]
+  simpa only [compClosure_eq_self r] using h.equivalence
 #align category_theory.quotient.functor_map_eq_iff CategoryTheory.Quotient.functor_map_eq_iff
 
 variable {D : Type _} [Category D] (F : C ⥤ D)
   (H : ∀ (x y : C) (f₁ f₂ : x ⟶ y), r f₁ f₂ → F.map f₁ = F.map f₂)
 
 /-- The induced functor on the quotient category. -/
-@[simps]
 def lift : Quotient r ⥤ D where
   obj a := F.obj a.as
   map := @fun a b hf ↦
@@ -180,6 +182,7 @@ theorem lift_spec : functor r ⋙ lift r F H = F := by
   · rintro X
     rfl
   · rintro X Y f
+    dsimp [lift, functor]
     simp
 #align category_theory.quotient.lift_spec CategoryTheory.Quotient.lift_spec
 
@@ -214,7 +217,7 @@ theorem lift.isLift_inv (X : C) : (lift.isLift r F H).inv.app X = 𝟙 (F.obj X)
 theorem lift_map_functor_map {X Y : C} (f : X ⟶ Y) :
     (lift r F H).map ((functor r).map f) = F.map f := by
   rw [← NatIso.naturality_1 (lift.isLift r F H)]
-  dsimp
+  dsimp [lift, functor]
   simp
 #align category_theory.quotient.lift_map_functor_map CategoryTheory.Quotient.lift_map_functor_map
 

@@ -120,8 +120,8 @@ def functor : C ⥤ Quotient r where
 
 noncomputable instance fullFunctor : Full (functor r) where preimage := @fun X Y f ↦ Quot.out f
 
-instance : EssSurj (functor r)
-    where mem_essImage Y :=
+instance : EssSurj (functor r) where
+  mem_essImage Y :=
     ⟨Y.as, ⟨eqToIso (by
             ext
             rfl)⟩⟩

This PR constructs the shift on a quotient category.

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

@@ -218,6 +218,57 @@ theorem lift_map_functor_map {X Y : C} (f : X ⟶ Y) :
   simp
 #align category_theory.quotient.lift_map_functor_map CategoryTheory.Quotient.lift_map_functor_map
 
+variable {r}
+
+lemma natTrans_ext {F G : Quotient r ⥤ D} (τ₁ τ₂ : F ⟶ G)
+    (h : whiskerLeft (Quotient.functor r) τ₁ = whiskerLeft (Quotient.functor r) τ₂) : τ₁ = τ₂ :=
+  NatTrans.ext _ _ (by ext1 ⟨X⟩; exact NatTrans.congr_app h X)
+
+variable (r)
+
+/-- In order to define a natural transformation `F ⟶ G` with `F G : Quotient r ⥤ D`, it suffices
+to do so after precomposing with `Quotient.functor r`. -/
+def natTransLift {F G : Quotient r ⥤ D} (τ : Quotient.functor r ⋙ F ⟶ Quotient.functor r ⋙ G) :
+    F ⟶ G where
+  app := fun ⟨X⟩ => τ.app X
+  naturality := fun ⟨X⟩ ⟨Y⟩ => by
+    rintro ⟨f⟩
+    exact τ.naturality f
+
+@[simp]
+lemma natTransLift_app (F G : Quotient r ⥤ D)
+    (τ : Quotient.functor r ⋙ F ⟶ Quotient.functor r ⋙ G) (X : C) :
+  (natTransLift r τ).app ((Quotient.functor r).obj X) = τ.app X := rfl
+
+@[reassoc]
+lemma comp_natTransLift {F G H : Quotient r ⥤ D}
+    (τ : Quotient.functor r ⋙ F ⟶ Quotient.functor r ⋙ G)
+    (τ' : Quotient.functor r ⋙ G ⟶ Quotient.functor r ⋙ H) :
+    natTransLift r τ ≫ natTransLift r τ' =  natTransLift r (τ ≫ τ') := by aesop_cat
+
+@[simp]
+lemma natTransLift_id (F : Quotient r ⥤ D) :
+    natTransLift r (𝟙 (Quotient.functor r ⋙ F)) = 𝟙 _ := by aesop_cat
+
+/-- In order to define a natural isomorphism `F ≅ G` with `F G : Quotient r ⥤ D`, it suffices
+to do so after precomposing with `Quotient.functor r`. -/
+@[simps]
+def natIsoLift {F G : Quotient r ⥤ D} (τ : Quotient.functor r ⋙ F ≅ Quotient.functor r ⋙ G) :
+    F ≅ G where
+  hom := natTransLift _ τ.hom
+  inv := natTransLift _ τ.inv
+  hom_inv_id := by rw [comp_natTransLift, τ.hom_inv_id, natTransLift_id]
+  inv_hom_id := by rw [comp_natTransLift, τ.inv_hom_id, natTransLift_id]
+
+variable (D)
+
+instance full_whiskeringLeft_functor :
+    Full ((whiskeringLeft C _ D).obj (functor r)) where
+  preimage := natTransLift r
+
+instance faithful_whiskeringLeft_functor :
+    Faithful ((whiskeringLeft C _ D).obj (functor r)) := ⟨by apply natTrans_ext⟩
+
 end Quotient
 
 end CategoryTheory

@@ -218,57 +218,6 @@ theorem lift_map_functor_map {X Y : C} (f : X ⟶ Y) :
   simp
 #align category_theory.quotient.lift_map_functor_map CategoryTheory.Quotient.lift_map_functor_map
 
-variable {r}
-
-lemma natTrans_ext {F G : Quotient r ⥤ D} (τ₁ τ₂ : F ⟶ G)
-    (h : whiskerLeft (Quotient.functor r) τ₁ = whiskerLeft (Quotient.functor r) τ₂) : τ₁ = τ₂ :=
-  NatTrans.ext _ _ (by ext1 ⟨X⟩ ; exact NatTrans.congr_app h X)
-
-variable (r)
-
-/-- In order to define a natural transformation `F ⟶ G` with `F G : Quotient r ⥤ D`, it suffices
-to do so after precomposing with `Quotient.functor r`. -/
-def natTransLift {F G : Quotient r ⥤ D} (τ : Quotient.functor r ⋙ F ⟶ Quotient.functor r ⋙ G) :
-    F ⟶ G where
-  app := fun ⟨X⟩ => τ.app X
-  naturality := fun ⟨X⟩ ⟨Y⟩ => by
-    rintro ⟨f⟩
-    exact τ.naturality f
-
-@[simp]
-lemma natTransLift_app (F G : Quotient r ⥤ D)
-    (τ : Quotient.functor r ⋙ F ⟶ Quotient.functor r ⋙ G) (X : C) :
-  (natTransLift r τ).app ((Quotient.functor r).obj X) = τ.app X := rfl
-
-@[reassoc]
-lemma comp_natTransLift {F G H : Quotient r ⥤ D}
-    (τ : Quotient.functor r ⋙ F ⟶ Quotient.functor r ⋙ G)
-    (τ' : Quotient.functor r ⋙ G ⟶ Quotient.functor r ⋙ H) :
-    natTransLift r τ ≫ natTransLift r τ' =  natTransLift r (τ ≫ τ') := by aesop_cat
-
-@[simp]
-lemma natTransLift_id (F : Quotient r ⥤ D) :
-    natTransLift r (𝟙 (Quotient.functor r ⋙ F)) = 𝟙 _ := by aesop_cat
-
-/-- In order to define a natural isomorphism `F ≅ G` with `F G : Quotient r ⥤ D`, it suffices
-to do so after precomposing with `Quotient.functor r`. -/
-@[simps]
-def natIsoLift {F G : Quotient r ⥤ D} (τ : Quotient.functor r ⋙ F ≅ Quotient.functor r ⋙ G) :
-    F ≅ G where
-  hom := natTransLift _ τ.hom
-  inv := natTransLift _ τ.inv
-  hom_inv_id := by rw [comp_natTransLift, τ.hom_inv_id, natTransLift_id]
-  inv_hom_id := by rw [comp_natTransLift, τ.inv_hom_id, natTransLift_id]
-
-variable (D)
-
-instance full_whiskeringLeft_functor :
-    Full ((whiskeringLeft C _ D).obj (functor r)) where
-  preimage := natTransLift r
-
-instance faithful_whiskeringLeft_functor :
-    Faithful ((whiskeringLeft C _ D).obj (functor r)) := ⟨by apply natTrans_ext⟩
-
 end Quotient
 
 end CategoryTheory

@@ -218,6 +218,57 @@ theorem lift_map_functor_map {X Y : C} (f : X ⟶ Y) :
   simp
 #align category_theory.quotient.lift_map_functor_map CategoryTheory.Quotient.lift_map_functor_map
 
+variable {r}
+
+lemma natTrans_ext {F G : Quotient r ⥤ D} (τ₁ τ₂ : F ⟶ G)
+    (h : whiskerLeft (Quotient.functor r) τ₁ = whiskerLeft (Quotient.functor r) τ₂) : τ₁ = τ₂ :=
+  NatTrans.ext _ _ (by ext1 ⟨X⟩ ; exact NatTrans.congr_app h X)
+
+variable (r)
+
+/-- In order to define a natural transformation `F ⟶ G` with `F G : Quotient r ⥤ D`, it suffices
+to do so after precomposing with `Quotient.functor r`. -/
+def natTransLift {F G : Quotient r ⥤ D} (τ : Quotient.functor r ⋙ F ⟶ Quotient.functor r ⋙ G) :
+    F ⟶ G where
+  app := fun ⟨X⟩ => τ.app X
+  naturality := fun ⟨X⟩ ⟨Y⟩ => by
+    rintro ⟨f⟩
+    exact τ.naturality f
+
+@[simp]
+lemma natTransLift_app (F G : Quotient r ⥤ D)
+    (τ : Quotient.functor r ⋙ F ⟶ Quotient.functor r ⋙ G) (X : C) :
+  (natTransLift r τ).app ((Quotient.functor r).obj X) = τ.app X := rfl
+
+@[reassoc]
+lemma comp_natTransLift {F G H : Quotient r ⥤ D}
+    (τ : Quotient.functor r ⋙ F ⟶ Quotient.functor r ⋙ G)
+    (τ' : Quotient.functor r ⋙ G ⟶ Quotient.functor r ⋙ H) :
+    natTransLift r τ ≫ natTransLift r τ' =  natTransLift r (τ ≫ τ') := by aesop_cat
+
+@[simp]
+lemma natTransLift_id (F : Quotient r ⥤ D) :
+    natTransLift r (𝟙 (Quotient.functor r ⋙ F)) = 𝟙 _ := by aesop_cat
+
+/-- In order to define a natural isomorphism `F ≅ G` with `F G : Quotient r ⥤ D`, it suffices
+to do so after precomposing with `Quotient.functor r`. -/
+@[simps]
+def natIsoLift {F G : Quotient r ⥤ D} (τ : Quotient.functor r ⋙ F ≅ Quotient.functor r ⋙ G) :
+    F ≅ G where
+  hom := natTransLift _ τ.hom
+  inv := natTransLift _ τ.inv
+  hom_inv_id := by rw [comp_natTransLift, τ.hom_inv_id, natTransLift_id]
+  inv_hom_id := by rw [comp_natTransLift, τ.inv_hom_id, natTransLift_id]
+
+variable (D)
+
+instance full_whiskeringLeft_functor :
+    Full ((whiskeringLeft C _ D).obj (functor r)) where
+  preimage := natTransLift r
+
+instance faithful_whiskeringLeft_functor :
+    Faithful ((whiskeringLeft C _ D).obj (functor r)) := ⟨by apply natTrans_ext⟩
+
 end Quotient
 
 end CategoryTheory

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 David Wärn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Wärn
-
-! This file was ported from Lean 3 source module category_theory.quotient
-! leanprover-community/mathlib commit 740acc0e6f9adf4423f92a485d0456fc271482da
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.NatIso
 import Mathlib.CategoryTheory.EqToHom
 
+#align_import category_theory.quotient from "leanprover-community/mathlib"@"740acc0e6f9adf4423f92a485d0456fc271482da"
+
 /-!
 # Quotient category
 

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

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

@@ -201,7 +201,7 @@ theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ =
 
 /-- The original functor factors through the induced functor. -/
 def lift.isLift : functor r ⋙ lift r F H ≅ F :=
-  NatIso.ofComponents (fun X ↦ Iso.refl _) (by aesop_cat)
+  NatIso.ofComponents fun X ↦ Iso.refl _
 #align category_theory.quotient.lift.is_lift CategoryTheory.Quotient.lift.isLift
 
 @[simp]

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".

@@ -131,8 +131,7 @@ instance : EssSurj (functor r)
 
 protected theorem induction {P : ∀ {a b : Quotient r}, (a ⟶ b) → Prop}
     (h : ∀ {x y : C} (f : x ⟶ y), P ((functor r).map f)) :
-    ∀ {a b : Quotient r} (f : a ⟶ b), P f :=
-  by
+    ∀ {a b : Quotient r} (f : a ⟶ b), P f := by
   rintro ⟨x⟩ ⟨y⟩ ⟨f⟩
   exact h f
 #align category_theory.quotient.induction CategoryTheory.Quotient.induction
@@ -143,8 +142,7 @@ protected theorem sound {a b : C} {f₁ f₂ : a ⟶ b} (h : r f₁ f₂) :
 #align category_theory.quotient.sound CategoryTheory.Quotient.sound
 
 theorem functor_map_eq_iff [h : Congruence r] {X Y : C} (f f' : X ⟶ Y) :
-    (functor r).map f = (functor r).map f' ↔ r f f' :=
-  by
+    (functor r).map f = (functor r).map f' ↔ r f f' := by
   constructor
   · erw [Quot.eq]
     intro h
@@ -180,8 +178,7 @@ def lift : Quotient r ⥤ D where
     exact F.map_comp f g
 #align category_theory.quotient.lift CategoryTheory.Quotient.lift
 
-theorem lift_spec : functor r ⋙ lift r F H = F :=
-  by
+theorem lift_spec : functor r ⋙ lift r F H = F := by
   apply Functor.ext; rotate_left
   · rintro X
     rfl
@@ -189,8 +186,7 @@ theorem lift_spec : functor r ⋙ lift r F H = F :=
     simp
 #align category_theory.quotient.lift_spec CategoryTheory.Quotient.lift_spec
 
-theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ = lift r F H :=
-  by
+theorem lift_unique (Φ : Quotient r ⥤ D) (hΦ : functor r ⋙ Φ = F) : Φ = lift r F H := by
   subst_vars
   fapply Functor.hext
   · rintro X
@@ -219,8 +215,7 @@ theorem lift.isLift_inv (X : C) : (lift.isLift r F H).inv.app X = 𝟙 (F.obj X)
 #align category_theory.quotient.lift.is_lift_inv CategoryTheory.Quotient.lift.isLift_inv
 
 theorem lift_map_functor_map {X Y : C} (f : X ⟶ Y) :
-    (lift r F H).map ((functor r).map f) = F.map f :=
-  by
+    (lift r F H).map ((functor r).map f) = F.map f := by
   rw [← NatIso.naturality_1 (lift.isLift r F H)]
   dsimp
   simp

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>

@@ -121,7 +121,7 @@ def functor : C ⥤ Quotient r where
   map := @fun _ _ f ↦ Quot.mk _ f
 #align category_theory.quotient.functor CategoryTheory.Quotient.functor
 
-noncomputable instance : Full (functor r) where preimage := @fun X Y f ↦ Quot.out f
+noncomputable instance fullFunctor : Full (functor r) where preimage := @fun X Y f ↦ Quot.out f
 
 instance : EssSurj (functor r)
     where mem_essImage Y :=

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Rémi Bottinelli <remi.bottinelli@bluewin.ch>