category_theory.with_terminal | 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

14b69e9f

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

c2092722

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -109,9 +109,9 @@ def incl : C ⥤ WithTerminal C where
 #align category_theory.with_terminal.incl CategoryTheory.WithTerminal.incl
 -/
 
-instance : Full (incl : C ⥤ _) where preimage X Y f := f
+instance : CategoryTheory.Functor.Full (incl : C ⥤ _) where preimage X Y f := f
 
-instance : Faithful (incl : C ⥤ _) where
+instance : CategoryTheory.Functor.Faithful (incl : C ⥤ _) where
 
 #print CategoryTheory.WithTerminal.map /-
 /-- Map `with_terminal` with respect to a functor `F : C ⥤ D`. -/
@@ -310,9 +310,9 @@ def incl : C ⥤ WithInitial C where
 #align category_theory.with_initial.incl CategoryTheory.WithInitial.incl
 -/
 
-instance : Full (incl : C ⥤ _) where preimage X Y f := f
+instance : CategoryTheory.Functor.Full (incl : C ⥤ _) where preimage X Y f := f
 
-instance : Faithful (incl : C ⥤ _) where
+instance : CategoryTheory.Functor.Faithful (incl : C ⥤ _) where
 
 #print CategoryTheory.WithInitial.map /-
 /-- Map `with_initial` with respect to a functor `F : C ⥤ D`. -/

c2092722

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
-import Mathbin.CategoryTheory.Limits.Shapes.Terminal
+import CategoryTheory.Limits.Shapes.Terminal
 
 #align_import category_theory.with_terminal from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"

c2092722

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.with_terminal
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Limits.Shapes.Terminal
 
+#align_import category_theory.with_terminal from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
 /-!
 
 # `with_initial` and `with_terminal`

c2092722

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -67,6 +67,7 @@ attribute [local tidy] tactic.case_bash
 
 variable {C}
 
+#print CategoryTheory.WithTerminal.Hom /-
 /-- Morphisms for `with_terminal C`. -/
 @[simp, nolint has_nonempty_instance]
 def Hom : WithTerminal C → WithTerminal C → Type v
@@ -74,14 +75,18 @@ def Hom : WithTerminal C → WithTerminal C → Type v
   | star, of X => PEmpty
   | _, star => PUnit
 #align category_theory.with_terminal.hom CategoryTheory.WithTerminal.Hom
+-/
 
+#print CategoryTheory.WithTerminal.id /-
 /-- Identity morphisms for `with_terminal C`. -/
 @[simp]
 def id : ∀ X : WithTerminal C, Hom X X
   | of X => 𝟙 _
   | star => PUnit.unit
 #align category_theory.with_terminal.id CategoryTheory.WithTerminal.id
+-/
 
+#print CategoryTheory.WithTerminal.comp /-
 /-- Composition of morphisms for `with_terminal C`. -/
 @[simp]
 def comp : ∀ {X Y Z : WithTerminal C}, Hom X Y → Hom Y Z → Hom X Z
@@ -91,6 +96,7 @@ def comp : ∀ {X Y Z : WithTerminal C}, Hom X Y → Hom Y Z → Hom X Z
   | _, star, of Y => fun f g => PEmpty.elim g
   | star, star, star => fun _ _ => PUnit.unit
 #align category_theory.with_terminal.comp CategoryTheory.WithTerminal.comp
+-/
 
 instance : Category.{v} (WithTerminal C)
     where
@@ -98,16 +104,19 @@ instance : Category.{v} (WithTerminal C)
   id X := id _
   comp X Y Z f g := comp f g
 
+#print CategoryTheory.WithTerminal.incl /-
 /-- The inclusion from `C` into `with_terminal C`. -/
 def incl : C ⥤ WithTerminal C where
   obj := of
   map X Y f := f
 #align category_theory.with_terminal.incl CategoryTheory.WithTerminal.incl
+-/
 
 instance : Full (incl : C ⥤ _) where preimage X Y f := f
 
 instance : Faithful (incl : C ⥤ _) where
 
+#print CategoryTheory.WithTerminal.map /-
 /-- Map `with_terminal` with respect to a functor `F : C ⥤ D`. -/
 def map {D : Type _} [Category D] (F : C ⥤ D) : WithTerminal C ⥤ WithTerminal D
     where
@@ -121,6 +130,7 @@ def map {D : Type _} [Category D] (F : C ⥤ D) : WithTerminal C ⥤ WithTermina
     | of x, star, PUnit.unit => PUnit.unit
     | star, star, PUnit.unit => PUnit.unit
 #align category_theory.with_terminal.map CategoryTheory.WithTerminal.map
+-/
 
 instance {X : WithTerminal C} : Unique (X ⟶ star)
     where
@@ -130,11 +140,14 @@ instance {X : WithTerminal C} : Unique (X ⟶ star)
     | star => PUnit.unit
   uniq := by tidy
 
+#print CategoryTheory.WithTerminal.starTerminal /-
 /-- `with_terminal.star` is terminal. -/
 def starTerminal : Limits.IsTerminal (star : WithTerminal C) :=
   Limits.IsTerminal.ofUnique _
 #align category_theory.with_terminal.star_terminal CategoryTheory.WithTerminal.starTerminal
+-/
 
+#print CategoryTheory.WithTerminal.lift /-
 /-- Lift a functor `F : C ⥤ D` to `with_term C ⥤ D`. -/
 @[simps]
 def lift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
@@ -150,7 +163,9 @@ def lift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x
     | of x, star, PUnit.unit => M x
     | star, star, PUnit.unit => 𝟙 Z
 #align category_theory.with_terminal.lift CategoryTheory.WithTerminal.lift
+-/
 
+#print CategoryTheory.WithTerminal.inclLift /-
 /-- The isomorphism between `incl ⋙ lift F _ _` with `F`. -/
 @[simps]
 def inclLift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
@@ -159,14 +174,18 @@ def inclLift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.o
   Hom := { app := fun X => 𝟙 _ }
   inv := { app := fun X => 𝟙 _ }
 #align category_theory.with_terminal.incl_lift CategoryTheory.WithTerminal.inclLift
+-/
 
+#print CategoryTheory.WithTerminal.liftStar /-
 /-- The isomorphism between `(lift F _ _).obj with_terminal.star` with `Z`. -/
 @[simps]
 def liftStar {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
     (hM : ∀ (x y : C) (f : x ⟶ y), F.map f ≫ M y = M x) : (lift F M hM).obj star ≅ Z :=
   eqToIso rfl
 #align category_theory.with_terminal.lift_star CategoryTheory.WithTerminal.liftStar
+-/
 
+#print CategoryTheory.WithTerminal.lift_map_liftStar /-
 theorem lift_map_liftStar {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
     (hM : ∀ (x y : C) (f : x ⟶ y), F.map f ≫ M y = M x) (x : C) :
     (lift F M hM).map (starTerminal.from (incl.obj x)) ≫ (liftStar F M hM).Hom =
@@ -175,7 +194,9 @@ theorem lift_map_liftStar {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : 
   erw [category.id_comp, category.comp_id]
   rfl
 #align category_theory.with_terminal.lift_map_lift_star CategoryTheory.WithTerminal.lift_map_liftStar
+-/
 
+#print CategoryTheory.WithTerminal.liftUnique /-
 /-- The uniqueness of `lift`. -/
 @[simp]
 def liftUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
@@ -197,13 +218,16 @@ def liftUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F
         change G.map (𝟙 _) ≫ hG.hom = hG.hom ≫ 𝟙 _
         simp)
 #align category_theory.with_terminal.lift_unique CategoryTheory.WithTerminal.liftUnique
+-/
 
+#print CategoryTheory.WithTerminal.liftToTerminal /-
 /-- A variant of `lift` with `Z` a terminal object. -/
 @[simps]
 def liftToTerminal {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsTerminal Z) :
     WithTerminal C ⥤ D :=
   lift F (fun x => hZ.from _) fun x y f => hZ.hom_ext _ _
 #align category_theory.with_terminal.lift_to_terminal CategoryTheory.WithTerminal.liftToTerminal
+-/
 
 #print CategoryTheory.WithTerminal.inclLiftToTerminal /-
 /-- A variant of `incl_lift` with `Z` a terminal object. -/
@@ -214,21 +238,27 @@ def inclLiftToTerminal {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Lim
 #align category_theory.with_terminal.incl_lift_to_terminal CategoryTheory.WithTerminal.inclLiftToTerminal
 -/
 
+#print CategoryTheory.WithTerminal.liftToTerminalUnique /-
 /-- A variant of `lift_unique` with `Z` a terminal object. -/
 @[simps]
 def liftToTerminalUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsTerminal Z)
     (G : WithTerminal C ⥤ D) (h : incl ⋙ G ≅ F) (hG : G.obj star ≅ Z) : G ≅ liftToTerminal F hZ :=
   liftUnique F (fun z => hZ.from _) (fun x y f => hZ.hom_ext _ _) G h hG fun x => hZ.hom_ext _ _
 #align category_theory.with_terminal.lift_to_terminal_unique CategoryTheory.WithTerminal.liftToTerminalUnique
+-/
 
+#print CategoryTheory.WithTerminal.homFrom /-
 /-- Constructs a morphism to `star` from `of X`. -/
 @[simp]
 def homFrom (X : C) : incl.obj X ⟶ star :=
   starTerminal.from _
 #align category_theory.with_terminal.hom_from CategoryTheory.WithTerminal.homFrom
+-/
 
+#print CategoryTheory.WithTerminal.isIso_of_from_star /-
 instance isIso_of_from_star {X : WithTerminal C} (f : star ⟶ X) : IsIso f := by tidy
 #align category_theory.with_terminal.is_iso_of_from_star CategoryTheory.WithTerminal.isIso_of_from_star
+-/
 
 end WithTerminal
 
@@ -238,6 +268,7 @@ attribute [local tidy] tactic.case_bash
 
 variable {C}
 
+#print CategoryTheory.WithInitial.Hom /-
 /-- Morphisms for `with_initial C`. -/
 @[simp, nolint has_nonempty_instance]
 def Hom : WithInitial C → WithInitial C → Type v
@@ -245,14 +276,18 @@ def Hom : WithInitial C → WithInitial C → Type v
   | of X, _ => PEmpty
   | star, _ => PUnit
 #align category_theory.with_initial.hom CategoryTheory.WithInitial.Hom
+-/
 
+#print CategoryTheory.WithInitial.id /-
 /-- Identity morphisms for `with_initial C`. -/
 @[simp]
 def id : ∀ X : WithInitial C, Hom X X
   | of X => 𝟙 _
   | star => PUnit.unit
 #align category_theory.with_initial.id CategoryTheory.WithInitial.id
+-/
 
+#print CategoryTheory.WithInitial.comp /-
 /-- Composition of morphisms for `with_initial C`. -/
 @[simp]
 def comp : ∀ {X Y Z : WithInitial C}, Hom X Y → Hom Y Z → Hom X Z
@@ -262,6 +297,7 @@ def comp : ∀ {X Y Z : WithInitial C}, Hom X Y → Hom Y Z → Hom X Z
   | of Y, star, _ => fun f g => PEmpty.elim f
   | star, star, star => fun _ _ => PUnit.unit
 #align category_theory.with_initial.comp CategoryTheory.WithInitial.comp
+-/
 
 instance : Category.{v} (WithInitial C)
     where
@@ -269,16 +305,19 @@ instance : Category.{v} (WithInitial C)
   id X := id _
   comp X Y Z f g := comp f g
 
+#print CategoryTheory.WithInitial.incl /-
 /-- The inclusion of `C` into `with_initial C`. -/
 def incl : C ⥤ WithInitial C where
   obj := of
   map X Y f := f
 #align category_theory.with_initial.incl CategoryTheory.WithInitial.incl
+-/
 
 instance : Full (incl : C ⥤ _) where preimage X Y f := f
 
 instance : Faithful (incl : C ⥤ _) where
 
+#print CategoryTheory.WithInitial.map /-
 /-- Map `with_initial` with respect to a functor `F : C ⥤ D`. -/
 def map {D : Type _} [Category D] (F : C ⥤ D) : WithInitial C ⥤ WithInitial D
     where
@@ -292,6 +331,7 @@ def map {D : Type _} [Category D] (F : C ⥤ D) : WithInitial C ⥤ WithInitial
     | star, of x, PUnit.unit => PUnit.unit
     | star, star, PUnit.unit => PUnit.unit
 #align category_theory.with_initial.map CategoryTheory.WithInitial.map
+-/
 
 instance {X : WithInitial C} : Unique (star ⟶ X)
     where
@@ -301,11 +341,14 @@ instance {X : WithInitial C} : Unique (star ⟶ X)
     | star => PUnit.unit
   uniq := by tidy
 
+#print CategoryTheory.WithInitial.starInitial /-
 /-- `with_initial.star` is initial. -/
 def starInitial : Limits.IsInitial (star : WithInitial C) :=
   Limits.IsInitial.ofUnique _
 #align category_theory.with_initial.star_initial CategoryTheory.WithInitial.starInitial
+-/
 
+#print CategoryTheory.WithInitial.lift /-
 /-- Lift a functor `F : C ⥤ D` to `with_initial C ⥤ D`. -/
 @[simps]
 def lift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
@@ -321,7 +364,9 @@ def lift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F
     | star, of x, PUnit.unit => M _
     | star, star, PUnit.unit => 𝟙 _
 #align category_theory.with_initial.lift CategoryTheory.WithInitial.lift
+-/
 
+#print CategoryTheory.WithInitial.inclLift /-
 /-- The isomorphism between `incl ⋙ lift F _ _` with `F`. -/
 @[simps]
 def inclLift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
@@ -330,14 +375,18 @@ def inclLift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z 
   Hom := { app := fun X => 𝟙 _ }
   inv := { app := fun X => 𝟙 _ }
 #align category_theory.with_initial.incl_lift CategoryTheory.WithInitial.inclLift
+-/
 
+#print CategoryTheory.WithInitial.liftStar /-
 /-- The isomorphism between `(lift F _ _).obj with_term.star` with `Z`. -/
 @[simps]
 def liftStar {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
     (hM : ∀ (x y : C) (f : x ⟶ y), M x ≫ F.map f = M y) : (lift F M hM).obj star ≅ Z :=
   eqToIso rfl
 #align category_theory.with_initial.lift_star CategoryTheory.WithInitial.liftStar
+-/
 
+#print CategoryTheory.WithInitial.liftStar_lift_map /-
 theorem liftStar_lift_map {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
     (hM : ∀ (x y : C) (f : x ⟶ y), M x ≫ F.map f = M y) (x : C) :
     (liftStar F M hM).Hom ≫ (lift F M hM).map (starInitial.to (incl.obj x)) =
@@ -346,7 +395,9 @@ theorem liftStar_lift_map {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : 
   erw [category.id_comp, category.comp_id]
   rfl
 #align category_theory.with_initial.lift_star_lift_map CategoryTheory.WithInitial.liftStar_lift_map
+-/
 
+#print CategoryTheory.WithInitial.liftUnique /-
 /-- The uniqueness of `lift`. -/
 @[simp]
 def liftUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
@@ -372,13 +423,16 @@ def liftUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z
         change G.map (𝟙 _) ≫ hG.hom = hG.hom ≫ 𝟙 _
         simp)
 #align category_theory.with_initial.lift_unique CategoryTheory.WithInitial.liftUnique
+-/
 
+#print CategoryTheory.WithInitial.liftToInitial /-
 /-- A variant of `lift` with `Z` an initial object. -/
 @[simps]
 def liftToInitial {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsInitial Z) :
     WithInitial C ⥤ D :=
   lift F (fun x => hZ.to _) fun x y f => hZ.hom_ext _ _
 #align category_theory.with_initial.lift_to_initial CategoryTheory.WithInitial.liftToInitial
+-/
 
 #print CategoryTheory.WithInitial.inclLiftToInitial /-
 /-- A variant of `incl_lift` with `Z` an initial object. -/
@@ -389,21 +443,27 @@ def inclLiftToInitial {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limi
 #align category_theory.with_initial.incl_lift_to_initial CategoryTheory.WithInitial.inclLiftToInitial
 -/
 
+#print CategoryTheory.WithInitial.liftToInitialUnique /-
 /-- A variant of `lift_unique` with `Z` an initial object. -/
 @[simps]
 def liftToInitialUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsInitial Z)
     (G : WithInitial C ⥤ D) (h : incl ⋙ G ≅ F) (hG : G.obj star ≅ Z) : G ≅ liftToInitial F hZ :=
   liftUnique F (fun z => hZ.to _) (fun x y f => hZ.hom_ext _ _) G h hG fun x => hZ.hom_ext _ _
 #align category_theory.with_initial.lift_to_initial_unique CategoryTheory.WithInitial.liftToInitialUnique
+-/
 
+#print CategoryTheory.WithInitial.homTo /-
 /-- Constructs a morphism from `star` to `of X`. -/
 @[simp]
 def homTo (X : C) : star ⟶ incl.obj X :=
   starInitial.to _
 #align category_theory.with_initial.hom_to CategoryTheory.WithInitial.homTo
+-/
 
+#print CategoryTheory.WithInitial.isIso_of_to_star /-
 instance isIso_of_to_star {X : WithInitial C} (f : X ⟶ star) : IsIso f := by tidy
 #align category_theory.with_initial.is_iso_of_to_star CategoryTheory.WithInitial.isIso_of_to_star
+-/
 
 end WithInitial

c2092722

bump to nightly-2023-06-08-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

8f04dc2b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 
 ! This file was ported from Lean 3 source module category_theory.with_terminal
-! leanprover-community/mathlib commit 14b69e9f3c16630440a2cbd46f1ddad0d561dee7
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
 ! 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.Limits.Shapes.Terminal
 
 # `with_initial` and `with_terminal`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a category `C`, this file constructs two objects:
 1. `with_terminal C`, the category built from `C` by formally adjoining a terminal object.
 2. `with_initial C`, the category built from `C` by formally adjoining an initial object.

14b69e9f

bump to nightly-2023-06-06-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

152a172d

Diff

@@ -49,14 +49,14 @@ inductive WithTerminal : Type u
   | of : C → with_terminal
   | star : with_terminal
   deriving Inhabited
-#align category_theory.with_terminal CategoryTheory.WithTerminal
+#align category_theory.with_terminal CategoryTheory.WithTerminalₓ
 
 /-- Formally adjoin an initial object to a category. -/
 inductive WithInitial : Type u
   | of : C → with_initial
   | star : with_initial
   deriving Inhabited
-#align category_theory.with_initial CategoryTheory.WithInitial
+#align category_theory.with_initial CategoryTheory.WithInitialₓ
 
 namespace WithTerminal
 
@@ -202,12 +202,14 @@ def liftToTerminal {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.
   lift F (fun x => hZ.from _) fun x y f => hZ.hom_ext _ _
 #align category_theory.with_terminal.lift_to_terminal CategoryTheory.WithTerminal.liftToTerminal
 
+#print CategoryTheory.WithTerminal.inclLiftToTerminal /-
 /-- A variant of `incl_lift` with `Z` a terminal object. -/
 @[simps]
 def inclLiftToTerminal {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsTerminal Z) :
     incl ⋙ liftToTerminal F hZ ≅ F :=
   inclLift _ _ _
 #align category_theory.with_terminal.incl_lift_to_terminal CategoryTheory.WithTerminal.inclLiftToTerminal
+-/
 
 /-- A variant of `lift_unique` with `Z` a terminal object. -/
 @[simps]
@@ -375,12 +377,14 @@ def liftToInitial {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.I
   lift F (fun x => hZ.to _) fun x y f => hZ.hom_ext _ _
 #align category_theory.with_initial.lift_to_initial CategoryTheory.WithInitial.liftToInitial
 
+#print CategoryTheory.WithInitial.inclLiftToInitial /-
 /-- A variant of `incl_lift` with `Z` an initial object. -/
 @[simps]
 def inclLiftToInitial {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsInitial Z) :
     incl ⋙ liftToInitial F hZ ≅ F :=
   inclLift _ _ _
 #align category_theory.with_initial.incl_lift_to_initial CategoryTheory.WithInitial.inclLiftToInitial
+-/
 
 /-- A variant of `lift_unique` with `Z` an initial object. -/
 @[simps]

14b69e9f

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -64,12 +64,6 @@ attribute [local tidy] tactic.case_bash
 
 variable {C}
 
-/- warning: category_theory.with_terminal.hom -> CategoryTheory.WithTerminal.Hom is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C], (CategoryTheory.WithTerminal.{u1, u2} C _inst_1) -> (CategoryTheory.WithTerminal.{u1, u2} C _inst_1) -> Type.{u1}
-but is expected to have type
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C], (CategoryTheory.WithTerminal.{u2, u1} C _inst_1) -> (CategoryTheory.WithTerminal.{u2, u1} C _inst_1) -> Type.{u2}
-Case conversion may be inaccurate. Consider using '#align category_theory.with_terminal.hom CategoryTheory.WithTerminal.Homₓ'. -/
 /-- Morphisms for `with_terminal C`. -/
 @[simp, nolint has_nonempty_instance]
 def Hom : WithTerminal C → WithTerminal C → Type v
@@ -78,12 +72,6 @@ def Hom : WithTerminal C → WithTerminal C → Type v
   | _, star => PUnit
 #align category_theory.with_terminal.hom CategoryTheory.WithTerminal.Hom
 
-/- warning: category_theory.with_terminal.id -> CategoryTheory.WithTerminal.id is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.WithTerminal.{u1, u2} C _inst_1), CategoryTheory.WithTerminal.Hom.{u1, u2} C _inst_1 X X
-but is expected to have type
-  PUnit.{max (succ (succ u1)) (succ (succ u2))}
-Case conversion may be inaccurate. Consider using '#align category_theory.with_terminal.id CategoryTheory.WithTerminal.idₓ'. -/
 /-- Identity morphisms for `with_terminal C`. -/
 @[simp]
 def id : ∀ X : WithTerminal C, Hom X X
@@ -91,12 +79,6 @@ def id : ∀ X : WithTerminal C, Hom X X
   | star => PUnit.unit
 #align category_theory.with_terminal.id CategoryTheory.WithTerminal.id
 
-/- warning: category_theory.with_terminal.comp -> CategoryTheory.WithTerminal.comp is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : CategoryTheory.WithTerminal.{u1, u2} C _inst_1} {Y : CategoryTheory.WithTerminal.{u1, u2} C _inst_1} {Z : CategoryTheory.WithTerminal.{u1, u2} C _inst_1}, (CategoryTheory.WithTerminal.Hom.{u1, u2} C _inst_1 X Y) -> (CategoryTheory.WithTerminal.Hom.{u1, u2} C _inst_1 Y Z) -> (CategoryTheory.WithTerminal.Hom.{u1, u2} C _inst_1 X Z)
-but is expected to have type
-  PUnit.{max (succ (succ u1)) (succ (succ u2))}
-Case conversion may be inaccurate. Consider using '#align category_theory.with_terminal.comp CategoryTheory.WithTerminal.compₓ'. -/
 /-- Composition of morphisms for `with_terminal C`. -/
 @[simp]
 def comp : ∀ {X Y Z : WithTerminal C}, Hom X Y → Hom Y Z → Hom X Z
@@ -251,12 +233,6 @@ attribute [local tidy] tactic.case_bash
 
 variable {C}
 
-/- warning: category_theory.with_initial.hom -> CategoryTheory.WithInitial.Hom is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C], (CategoryTheory.WithInitial.{u1, u2} C _inst_1) -> (CategoryTheory.WithInitial.{u1, u2} C _inst_1) -> Type.{u1}
-but is expected to have type
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C], (CategoryTheory.WithInitial.{u2, u1} C _inst_1) -> (CategoryTheory.WithInitial.{u2, u1} C _inst_1) -> Type.{u2}
-Case conversion may be inaccurate. Consider using '#align category_theory.with_initial.hom CategoryTheory.WithInitial.Homₓ'. -/
 /-- Morphisms for `with_initial C`. -/
 @[simp, nolint has_nonempty_instance]
 def Hom : WithInitial C → WithInitial C → Type v
@@ -265,12 +241,6 @@ def Hom : WithInitial C → WithInitial C → Type v
   | star, _ => PUnit
 #align category_theory.with_initial.hom CategoryTheory.WithInitial.Hom
 
-/- warning: category_theory.with_initial.id -> CategoryTheory.WithInitial.id is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (X : CategoryTheory.WithInitial.{u1, u2} C _inst_1), CategoryTheory.WithInitial.Hom.{u1, u2} C _inst_1 X X
-but is expected to have type
-  PUnit.{max (succ (succ u1)) (succ (succ u2))}
-Case conversion may be inaccurate. Consider using '#align category_theory.with_initial.id CategoryTheory.WithInitial.idₓ'. -/
 /-- Identity morphisms for `with_initial C`. -/
 @[simp]
 def id : ∀ X : WithInitial C, Hom X X
@@ -278,12 +248,6 @@ def id : ∀ X : WithInitial C, Hom X X
   | star => PUnit.unit
 #align category_theory.with_initial.id CategoryTheory.WithInitial.id
 
-/- warning: category_theory.with_initial.comp -> CategoryTheory.WithInitial.comp is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : CategoryTheory.WithInitial.{u1, u2} C _inst_1} {Y : CategoryTheory.WithInitial.{u1, u2} C _inst_1} {Z : CategoryTheory.WithInitial.{u1, u2} C _inst_1}, (CategoryTheory.WithInitial.Hom.{u1, u2} C _inst_1 X Y) -> (CategoryTheory.WithInitial.Hom.{u1, u2} C _inst_1 Y Z) -> (CategoryTheory.WithInitial.Hom.{u1, u2} C _inst_1 X Z)
-but is expected to have type
-  PUnit.{max (succ (succ u1)) (succ (succ u2))}
-Case conversion may be inaccurate. Consider using '#align category_theory.with_initial.comp CategoryTheory.WithInitial.compₓ'. -/
 /-- Composition of morphisms for `with_initial C`. -/
 @[simp]
 def comp : ∀ {X Y Z : WithInitial C}, Hom X Y → Hom Y Z → Hom X Z

14b69e9f

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -206,8 +206,7 @@ def liftUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F
     (by
       rintro (X | X) (Y | Y) f
       · apply h.hom.naturality
-      · cases f
-        exact hh _
+      · cases f; exact hh _
       · cases f
       · cases f
         change G.map (𝟙 _) ≫ hG.hom = hG.hom ≫ 𝟙 _

14b69e9f

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

14b69e9f

chore(CategoryTheory): make Functor.Full a Prop (#12449)

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

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

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

ce289a0e

Diff

@@ -124,7 +124,7 @@ def incl : C ⥤ WithTerminal C where
 #align category_theory.with_terminal.incl CategoryTheory.WithTerminal.incl
 
 instance : (incl : C ⥤ _).Full where
-  preimage f := f
+  map_surjective f := ⟨f, rfl⟩
 
 instance : (incl : C ⥤ _).Faithful where
 
@@ -422,7 +422,7 @@ def incl : C ⥤ WithInitial C where
 #align category_theory.with_initial.incl CategoryTheory.WithInitial.incl
 
 instance : (incl : C ⥤ _).Full where
-  preimage f := f
+  map_surjective f := ⟨f, rfl⟩
 
 instance : (incl : C ⥤ _).Faithful where

14b69e9f

chore: classify porting notes referring to missing linters (#12098)

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

c5b5490c

Diff

@@ -67,7 +67,7 @@ namespace WithTerminal
 variable {C}
 
 /-- Morphisms for `WithTerminal C`. -/
--- Porting note: unsupported `nolint has_nonempty_instance`
+-- Porting note(#5171): removed `nolint has_nonempty_instance`
 @[simp]
 def Hom : WithTerminal C → WithTerminal C → Type v
   | of X, of Y => X ⟶ Y
@@ -367,7 +367,7 @@ namespace WithInitial
 variable {C}
 
 /-- Morphisms for `WithInitial C`. -/
--- Porting note: unsupported `nolint has_nonempty_instance`
+-- Porting note(#5171): removed `nolint has_nonempty_instance`
 @[simp]
 def Hom : WithInitial C → WithInitial C → Type v
   | of X, of Y => X ⟶ Y

14b69e9f

chore(CategoryTheory): move Full, Faithful, EssSurj, IsEquivalence and ReflectsIsomorphisms to the Functor namespace (#11985)

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

65b7affc

Diff

@@ -123,10 +123,10 @@ def incl : C ⥤ WithTerminal C where
   map f := f
 #align category_theory.with_terminal.incl CategoryTheory.WithTerminal.incl
 
-instance : Full (incl : C ⥤ _) where
+instance : (incl : C ⥤ _).Full where
   preimage f := f
 
-instance : Faithful (incl : C ⥤ _) where
+instance : (incl : C ⥤ _).Faithful where
 
 /-- Map `WithTerminal` with respect to a functor `F : C ⥤ D`. -/
 @[simps]
@@ -421,10 +421,10 @@ def incl : C ⥤ WithInitial C where
   map f := f
 #align category_theory.with_initial.incl CategoryTheory.WithInitial.incl
 
-instance : Full (incl : C ⥤ _) where
+instance : (incl : C ⥤ _).Full where
   preimage f := f
 
-instance : Faithful (incl : C ⥤ _) where
+instance : (incl : C ⥤ _).Faithful where
 
 /-- Map `WithInitial` with respect to a functor `F : C ⥤ D`. -/
 @[simps]

14b69e9f

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -67,7 +67,7 @@ namespace WithTerminal
 variable {C}
 
 /-- Morphisms for `WithTerminal C`. -/
--- porting note: unsupported `nolint has_nonempty_instance`
+-- Porting note: unsupported `nolint has_nonempty_instance`
 @[simp]
 def Hom : WithTerminal C → WithTerminal C → Type v
   | of X, of Y => X ⟶ Y
@@ -367,7 +367,7 @@ namespace WithInitial
 variable {C}
 
 /-- Morphisms for `WithInitial C`. -/
--- porting note: unsupported `nolint has_nonempty_instance`
+-- Porting note: unsupported `nolint has_nonempty_instance`
 @[simp]
 def Hom : WithInitial C → WithInitial C → Type v
   | of X, of Y => X ⟶ Y

14b69e9f

chore: bump aesop; update syntax (#10955)

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

46974e92

Diff

@@ -51,7 +51,7 @@ inductive WithTerminal : Type u
   deriving Inhabited
 #align category_theory.with_terminal CategoryTheory.WithTerminal
 
-attribute [local aesop safe cases (rule_sets [CategoryTheory])] WithTerminal
+attribute [local aesop safe cases (rule_sets := [CategoryTheory])] WithTerminal
 
 /-- Formally adjoin an initial object to a category. -/
 inductive WithInitial : Type u
@@ -60,7 +60,7 @@ inductive WithInitial : Type u
   deriving Inhabited
 #align category_theory.with_initial CategoryTheory.WithInitial
 
-attribute [local aesop safe cases (rule_sets [CategoryTheory])] WithInitial
+attribute [local aesop safe cases (rule_sets := [CategoryTheory])] WithInitial
 
 namespace WithTerminal
 
@@ -114,7 +114,7 @@ def down {X Y : C} (f : of X ⟶ of Y) : X ⟶ Y := f
     down (f ≫ g) = down f ≫ down g :=
   rfl
 
-@[aesop safe destruct (rule_sets [CategoryTheory])]
+@[aesop safe destruct (rule_sets := [CategoryTheory])]
 lemma false_of_from_star {X : C} (f : star ⟶ of X) : False := (f : PEmpty).elim
 
 /-- The inclusion from `C` into `WithTerminal C`. -/
@@ -412,7 +412,7 @@ def down {X Y : C} (f : of X ⟶ of Y) : X ⟶ Y := f
     down (f ≫ g) = down f ≫ down g :=
   rfl
 
-@[aesop safe destruct (rule_sets [CategoryTheory])]
+@[aesop safe destruct (rule_sets := [CategoryTheory])]
 lemma false_of_to_star {X : C} (f : of X ⟶ star) : False := (f : PEmpty).elim
 
 /-- The inclusion of `C` into `WithInitial C`. -/

14b69e9f

style: reduce spacing variation in "porting note" comments (#10886)

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

86b84c52

Diff

@@ -655,7 +655,7 @@ def homTo (X : C) : star ⟶ incl.obj X :=
   starInitial.to _
 #align category_theory.with_initial.hom_to CategoryTheory.WithInitial.homTo
 
--- Porting note : need to do cases analysis
+-- Porting note: need to do cases analysis
 instance isIso_of_to_star {X : WithInitial C} (f : X ⟶ star) : IsIso f :=
   match X with
   | of _X => f.elim

14b69e9f

feat(CategoryTheory/WithTerminal): Add pseudofunctors (#10533)

Defined the pseudofunctors from Cat to Cat induced by WithTerminal and WithInitial.

55a538bd

Diff

@@ -1,10 +1,10 @@
 /-
 Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Adam Topaz
+Authors: Joseph Tooby-Smith, Adam Topaz
 -/
 import Mathlib.CategoryTheory.Limits.Shapes.Terminal
-
+import Mathlib.CategoryTheory.Bicategory.Functor
 #align_import category_theory.with_terminal from "leanprover-community/mathlib"@"14b69e9f3c16630440a2cbd46f1ddad0d561dee7"
 
 /-!
@@ -19,7 +19,7 @@ The terminal resp. initial object is `WithTerminal.star` resp. `WithInitial.star
 the proofs that these are terminal resp. initial are in `WithTerminal.star_terminal`
 and `WithInitial.star_initial`.
 
-The inclusion from `C` intro `WithTerminal C` resp. `WithInitial C` is denoted
+The inclusion from `C` into `WithTerminal C` resp. `WithInitial C` is denoted
 `WithTerminal.incl` resp. `WithInitial.incl`.
 
 The relevant constructions needed for the universal properties of these constructions are:
@@ -32,6 +32,9 @@ The relevant constructions needed for the universal properties of these construc
 In addition to this, we provide `WithTerminal.map` and `WithInitial.map` providing the
 functoriality of these constructions with respect to functors on the base categories.
 
+We define corresponding pseudofunctors `WithTerminal.pseudofunctor` and `WithInitial.pseudofunctor`
+from `Cat` to `Cat`.
+
 -/
 
 
@@ -126,6 +129,7 @@ instance : Full (incl : C ⥤ _) where
 instance : Faithful (incl : C ⥤ _) where
 
 /-- Map `WithTerminal` with respect to a functor `F : C ⥤ D`. -/
+@[simps]
 def map {D : Type*} [Category D] (F : C ⥤ D) : WithTerminal C ⥤ WithTerminal D where
   obj X :=
     match X with
@@ -138,6 +142,116 @@ def map {D : Type*} [Category D] (F : C ⥤ D) : WithTerminal C ⥤ WithTerminal
     | star, star, _ => PUnit.unit
 #align category_theory.with_terminal.map CategoryTheory.WithTerminal.map
 
+/-- A natural isomorphism between the functor `map (𝟭 C)` and `𝟭 (WithTerminal C)`. -/
+@[simps!]
+def mapId (C : Type*) [Category C] : map (𝟭 C) ≅ 𝟭 (WithTerminal C) :=
+  NatIso.ofComponents (fun X => match X with
+    | of x => Iso.refl _
+    | star => Iso.refl _) (by aesop_cat)
+
+/-- A natural isomorphism between the functor `map (F ⋙ G) ` and `map F ⋙ map G `. -/
+@[simps!]
+def mapComp {D E : Type*} [Category D] [Category E] (F : C ⥤ D) (G : D ⥤ E) :
+    map (F ⋙ G) ≅ map F ⋙ map G :=
+  NatIso.ofComponents (fun X => match X with
+    | of x => Iso.refl _
+    | star => Iso.refl _) (by aesop_cat)
+
+/-- From a natural transformation of functors `C ⥤ D`, the induced natural transformation
+of functors `WithTerminal C ⥤ WithTerminal D`. -/
+@[simps]
+def map₂ {D : Type*} [Category D] {F G : C ⥤ D} (η : F ⟶ G) : map F ⟶ map G where
+  app := fun X => match X with
+    | of x => η.app x
+    | star => 𝟙 star
+  naturality := by
+    intro X Y f
+    match X, Y, f with
+    | of x, of y, f => exact η.naturality f
+    | of x, star, _ => rfl
+    | star, star, _ => rfl
+
+/-- The pseudofunctor from `Cat` to `Cat` defined with `WithTerminal`. -/
+@[simps]
+def pseudofunctor : Pseudofunctor Cat Cat where
+  obj C := Cat.of (WithTerminal C)
+  map := map
+  map₂ := map₂
+  mapId C := mapId C
+  mapComp := mapComp
+  map₂_id := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X <;> rfl
+  map₂_comp := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X <;> rfl
+  map₂_whisker_left := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X
+    · rw [NatTrans.comp_app, NatTrans.comp_app]
+      simp only [map, Cat.comp_obj, Cat.comp_map, map₂, mapComp_hom_app, Iso.refl_hom,
+        mapComp_inv_app, Iso.refl_inv, Category.comp_id, Category.id_comp]
+      rfl
+    · rfl
+  map₂_whisker_right := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X
+    · rw [NatTrans.comp_app, NatTrans.comp_app]
+      simp only [map, Cat.comp_obj, Cat.comp_map, map₂, mapComp_hom_app, Iso.refl_hom,
+        mapComp_inv_app, Iso.refl_inv, Category.comp_id, Category.id_comp]
+      rfl
+    · rfl
+  map₂_associator := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X
+    · rw [NatTrans.comp_app,NatTrans.comp_app,NatTrans.comp_app,NatTrans.comp_app]
+      simp only [map, Cat.comp_obj, Cat.comp_map, map₂, Bicategory.Strict.associator_eqToIso,
+        eqToIso_refl, Iso.refl_hom, mapComp_hom_app, mapComp_inv_app, Iso.refl_inv,
+        Category.comp_id, Category.id_comp]
+      rw [NatTrans.id_app, NatTrans.id_app]
+      simp only [Cat.comp_obj, Bicategory.whiskerRight, whiskerRight_app, mapComp_hom_app,
+        Iso.refl_hom, down_id, Functor.map_id, Bicategory.whiskerLeft, whiskerLeft_app,
+        mapComp_inv_app, Iso.refl_inv, Category.comp_id]
+    · rfl
+  map₂_left_unitor := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X
+    · rw [NatTrans.comp_app, NatTrans.comp_app]
+      simp only [map, Cat.comp_obj, Cat.comp_map, Cat.id_map, map₂,
+        Bicategory.Strict.leftUnitor_eqToIso, eqToIso_refl, Iso.refl_hom, mapComp_hom_app,
+        Bicategory.whiskerRight, whiskerRight_app, mapId_hom_app, Category.id_comp]
+      rw [NatTrans.id_app, NatTrans.id_app]
+      simp only [Cat.comp_obj, Category.comp_id]
+      rw [← Functor.map_id]
+      rfl
+    · rfl
+  map₂_right_unitor := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X
+    · rw [NatTrans.comp_app, NatTrans.comp_app]
+      simp only [map, Cat.comp_obj, Cat.comp_map, Cat.id_map, map₂,
+        Bicategory.Strict.rightUnitor_eqToIso, eqToIso_refl, Iso.refl_hom, mapComp_hom_app,
+        Bicategory.whiskerLeft, whiskerLeft_app, mapId_hom_app, Category.id_comp]
+      rw [NatTrans.id_app, NatTrans.id_app]
+      simp only [Cat.comp_obj, Category.comp_id]
+      rw [← Functor.map_id]
+      rfl
+    · rfl
+
 instance {X : WithTerminal C} : Unique (X ⟶ star) where
   default :=
     match X with
@@ -313,6 +427,7 @@ instance : Full (incl : C ⥤ _) where
 instance : Faithful (incl : C ⥤ _) where
 
 /-- Map `WithInitial` with respect to a functor `F : C ⥤ D`. -/
+@[simps]
 def map {D : Type*} [Category D] (F : C ⥤ D) : WithInitial C ⥤ WithInitial D where
   obj X :=
     match X with
@@ -326,6 +441,116 @@ def map {D : Type*} [Category D] (F : C ⥤ D) : WithInitial C ⥤ WithInitial D
 
 #align category_theory.with_initial.map CategoryTheory.WithInitial.map
 
+/-- A natural isomorphism between the functor `map (𝟭 C)` and `𝟭 (WithInitial C)`. -/
+@[simps!]
+def mapId (C : Type*) [Category C] : map (𝟭 C) ≅ 𝟭 (WithInitial C) :=
+  NatIso.ofComponents (fun X => match X with
+    | of x => Iso.refl _
+    | star => Iso.refl _) (by aesop_cat)
+
+/-- A natural isomorphism between the functor `map (F ⋙ G) ` and `map F ⋙ map G `. -/
+@[simps!]
+def mapComp {D E : Type*} [Category D] [Category E] (F : C ⥤ D) (G : D ⥤ E) :
+    map (F ⋙ G) ≅ map F ⋙ map G :=
+  NatIso.ofComponents (fun X => match X with
+    | of x => Iso.refl _
+    | star => Iso.refl _) (by aesop_cat)
+
+/-- From a natrual transformation of functors `C ⥤ D`, the induced natural transformation
+of functors `WithInitial C ⥤ WithInitial D`. -/
+@[simps]
+def map₂ {D : Type*} [Category D] {F G : C ⥤ D} (η : F ⟶ G) : map F ⟶ map G where
+  app := fun X => match X with
+    | of x => η.app x
+    | star => 𝟙 star
+  naturality := by
+    intro X Y f
+    match X, Y, f with
+    | of x, of y, f => exact η.naturality f
+    | star, of x, _ => rfl
+    | star, star, _ => rfl
+
+/-- The pseudofunctor from `Cat` to `Cat` defined with `WithInitial`. -/
+@[simps]
+def pseudofunctor : Pseudofunctor Cat Cat where
+  obj C := Cat.of (WithInitial C)
+  map := map
+  map₂ := map₂
+  mapId C := mapId C
+  mapComp := mapComp
+  map₂_id := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X <;> rfl
+  map₂_comp := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X <;> rfl
+  map₂_whisker_left := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X
+    · rw [NatTrans.comp_app, NatTrans.comp_app]
+      simp only [map, Cat.comp_obj, Cat.comp_map, map₂, mapComp_hom_app, Iso.refl_hom,
+        mapComp_inv_app, Iso.refl_inv, Category.comp_id, Category.id_comp]
+      rfl
+    · rfl
+  map₂_whisker_right := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X
+    · rw [NatTrans.comp_app, NatTrans.comp_app]
+      simp only [map, Cat.comp_obj, Cat.comp_map, map₂, mapComp_hom_app, Iso.refl_hom,
+        mapComp_inv_app, Iso.refl_inv, Category.comp_id, Category.id_comp]
+      rfl
+    · rfl
+  map₂_associator := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X
+    · rw [NatTrans.comp_app,NatTrans.comp_app,NatTrans.comp_app,NatTrans.comp_app]
+      simp only [map, Cat.comp_obj, Cat.comp_map, map₂, Bicategory.Strict.associator_eqToIso,
+        eqToIso_refl, Iso.refl_hom, mapComp_hom_app, mapComp_inv_app, Iso.refl_inv,
+        Category.comp_id, Category.id_comp]
+      rw [NatTrans.id_app, NatTrans.id_app]
+      simp only [Cat.comp_obj, Bicategory.whiskerRight, whiskerRight_app, mapComp_hom_app,
+        Iso.refl_hom, down_id, Functor.map_id, Bicategory.whiskerLeft, whiskerLeft_app,
+        mapComp_inv_app, Iso.refl_inv, Category.comp_id]
+    · rfl
+  map₂_left_unitor := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X
+    · rw [NatTrans.comp_app, NatTrans.comp_app]
+      simp only [map, Cat.comp_obj, Cat.comp_map, Cat.id_map, map₂,
+        Bicategory.Strict.leftUnitor_eqToIso, eqToIso_refl, Iso.refl_hom, mapComp_hom_app,
+        Bicategory.whiskerRight, whiskerRight_app, mapId_hom_app, Category.id_comp]
+      rw [NatTrans.id_app, NatTrans.id_app]
+      simp only [Cat.comp_obj, Category.comp_id]
+      rw [← Functor.map_id]
+      rfl
+    · rfl
+  map₂_right_unitor := by
+    intros
+    apply NatTrans.ext
+    funext X
+    cases X
+    · rw [NatTrans.comp_app, NatTrans.comp_app]
+      simp only [map, Cat.comp_obj, Cat.comp_map, Cat.id_map, map₂,
+        Bicategory.Strict.rightUnitor_eqToIso, eqToIso_refl, Iso.refl_hom, mapComp_hom_app,
+        Bicategory.whiskerLeft, whiskerLeft_app, mapId_hom_app, Category.id_comp]
+      rw [NatTrans.id_app, NatTrans.id_app]
+      simp only [Cat.comp_obj, Category.comp_id]
+      rw [← Functor.map_id]
+      rfl
+    · rfl
+
 instance {X : WithInitial C} : Unique (star ⟶ X) where
   default :=
     match X with

14b69e9f

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -126,7 +126,7 @@ instance : Full (incl : C ⥤ _) where
 instance : Faithful (incl : C ⥤ _) where
 
 /-- Map `WithTerminal` with respect to a functor `F : C ⥤ D`. -/
-def map {D : Type _} [Category D] (F : C ⥤ D) : WithTerminal C ⥤ WithTerminal D where
+def map {D : Type*} [Category D] (F : C ⥤ D) : WithTerminal C ⥤ WithTerminal D where
   obj X :=
     match X with
     | of x => of <| F.obj x
@@ -152,7 +152,7 @@ def starTerminal : Limits.IsTerminal (star : WithTerminal C) :=
 
 /-- Lift a functor `F : C ⥤ D` to `WithTerminal C ⥤ D`. -/
 @[simps]
-def lift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
+def lift {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
     (hM : ∀ (x y : C) (f : x ⟶ y), F.map f ≫ M y = M x) : WithTerminal C ⥤ D where
   obj X :=
     match X with
@@ -167,7 +167,7 @@ def lift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x
 
 /-- The isomorphism between `incl ⋙ lift F _ _` with `F`. -/
 @[simps!]
-def inclLift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
+def inclLift {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
     (hM : ∀ (x y : C) (f : x ⟶ y), F.map f ≫ M y = M x) : incl ⋙ lift F M hM ≅ F where
   hom := { app := fun X => 𝟙 _ }
   inv := { app := fun X => 𝟙 _ }
@@ -175,12 +175,12 @@ def inclLift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.o
 
 /-- The isomorphism between `(lift F _ _).obj WithTerminal.star` with `Z`. -/
 @[simps!]
-def liftStar {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
+def liftStar {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
     (hM : ∀ (x y : C) (f : x ⟶ y), F.map f ≫ M y = M x) : (lift F M hM).obj star ≅ Z :=
   eqToIso rfl
 #align category_theory.with_terminal.lift_star CategoryTheory.WithTerminal.liftStar
 
-theorem lift_map_liftStar {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
+theorem lift_map_liftStar {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
     (hM : ∀ (x y : C) (f : x ⟶ y), F.map f ≫ M y = M x) (x : C) :
     (lift F M hM).map (starTerminal.from (incl.obj x)) ≫ (liftStar F M hM).hom =
       (inclLift F M hM).hom.app x ≫ M x := by
@@ -190,7 +190,7 @@ theorem lift_map_liftStar {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : 
 
 /-- The uniqueness of `lift`. -/
 @[simp]
-def liftUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
+def liftUnique {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F.obj x ⟶ Z)
     (hM : ∀ (x y : C) (f : x ⟶ y), F.map f ≫ M y = M x)
     (G : WithTerminal C ⥤ D) (h : incl ⋙ G ≅ F)
     (hG : G.obj star ≅ Z)
@@ -214,21 +214,21 @@ def liftUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, F
 
 /-- A variant of `lift` with `Z` a terminal object. -/
 @[simps!]
-def liftToTerminal {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsTerminal Z) :
+def liftToTerminal {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsTerminal Z) :
     WithTerminal C ⥤ D :=
   lift F (fun _x => hZ.from _) fun _x _y _f => hZ.hom_ext _ _
 #align category_theory.with_terminal.lift_to_terminal CategoryTheory.WithTerminal.liftToTerminal
 
 /-- A variant of `incl_lift` with `Z` a terminal object. -/
 @[simps!]
-def inclLiftToTerminal {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsTerminal Z) :
+def inclLiftToTerminal {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsTerminal Z) :
     incl ⋙ liftToTerminal F hZ ≅ F :=
   inclLift _ _ _
 #align category_theory.with_terminal.incl_lift_to_terminal CategoryTheory.WithTerminal.inclLiftToTerminal
 
 /-- A variant of `lift_unique` with `Z` a terminal object. -/
 @[simps!]
-def liftToTerminalUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsTerminal Z)
+def liftToTerminalUnique {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsTerminal Z)
     (G : WithTerminal C ⥤ D) (h : incl ⋙ G ≅ F) (hG : G.obj star ≅ Z) : G ≅ liftToTerminal F hZ :=
   liftUnique F (fun _z => hZ.from _) (fun _x _y _f => hZ.hom_ext _ _) G h hG fun _x =>
     hZ.hom_ext _ _
@@ -313,7 +313,7 @@ instance : Full (incl : C ⥤ _) where
 instance : Faithful (incl : C ⥤ _) where
 
 /-- Map `WithInitial` with respect to a functor `F : C ⥤ D`. -/
-def map {D : Type _} [Category D] (F : C ⥤ D) : WithInitial C ⥤ WithInitial D where
+def map {D : Type*} [Category D] (F : C ⥤ D) : WithInitial C ⥤ WithInitial D where
   obj X :=
     match X with
     | of x => of <| F.obj x
@@ -340,7 +340,7 @@ def starInitial : Limits.IsInitial (star : WithInitial C) :=
 
 /-- Lift a functor `F : C ⥤ D` to `WithInitial C ⥤ D`. -/
 @[simps]
-def lift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
+def lift {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
     (hM : ∀ (x y : C) (f : x ⟶ y), M x ≫ F.map f = M y) : WithInitial C ⥤ D where
   obj X :=
     match X with
@@ -355,7 +355,7 @@ def lift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F
 
 /-- The isomorphism between `incl ⋙ lift F _ _` with `F`. -/
 @[simps!]
-def inclLift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
+def inclLift {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
     (hM : ∀ (x y : C) (f : x ⟶ y), M x ≫ F.map f = M y) : incl ⋙ lift F M hM ≅ F where
   hom := { app := fun X => 𝟙 _ }
   inv := { app := fun X => 𝟙 _ }
@@ -363,12 +363,12 @@ def inclLift {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z 
 
 /-- The isomorphism between `(lift F _ _).obj WithInitial.star` with `Z`. -/
 @[simps!]
-def liftStar {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
+def liftStar {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
     (hM : ∀ (x y : C) (f : x ⟶ y), M x ≫ F.map f = M y) : (lift F M hM).obj star ≅ Z :=
   eqToIso rfl
 #align category_theory.with_initial.lift_star CategoryTheory.WithInitial.liftStar
 
-theorem liftStar_lift_map {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
+theorem liftStar_lift_map {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
     (hM : ∀ (x y : C) (f : x ⟶ y), M x ≫ F.map f = M y) (x : C) :
     (liftStar F M hM).hom ≫ (lift F M hM).map (starInitial.to (incl.obj x)) =
       M x ≫ (inclLift F M hM).hom.app x := by
@@ -378,7 +378,7 @@ theorem liftStar_lift_map {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : 
 
 /-- The uniqueness of `lift`. -/
 @[simp]
-def liftUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
+def liftUnique {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z ⟶ F.obj x)
     (hM : ∀ (x y : C) (f : x ⟶ y), M x ≫ F.map f = M y)
     (G : WithInitial C ⥤ D) (h : incl ⋙ G ≅ F)
     (hG : G.obj star ≅ Z)
@@ -405,21 +405,21 @@ def liftUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (M : ∀ x : C, Z
 
 /-- A variant of `lift` with `Z` an initial object. -/
 @[simps!]
-def liftToInitial {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsInitial Z) :
+def liftToInitial {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsInitial Z) :
     WithInitial C ⥤ D :=
   lift F (fun _x => hZ.to _) fun _x _y _f => hZ.hom_ext _ _
 #align category_theory.with_initial.lift_to_initial CategoryTheory.WithInitial.liftToInitial
 
 /-- A variant of `incl_lift` with `Z` an initial object. -/
 @[simps!]
-def inclLiftToInitial {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsInitial Z) :
+def inclLiftToInitial {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsInitial Z) :
     incl ⋙ liftToInitial F hZ ≅ F :=
   inclLift _ _ _
 #align category_theory.with_initial.incl_lift_to_initial CategoryTheory.WithInitial.inclLiftToInitial
 
 /-- A variant of `lift_unique` with `Z` an initial object. -/
 @[simps!]
-def liftToInitialUnique {D : Type _} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsInitial Z)
+def liftToInitialUnique {D : Type*} [Category D] {Z : D} (F : C ⥤ D) (hZ : Limits.IsInitial Z)
     (G : WithInitial C ⥤ D) (h : incl ⋙ G ≅ F) (hG : G.obj star ≅ Z) : G ≅ liftToInitial F hZ :=
   liftUnique F (fun _z => hZ.to _) (fun _x _y _f => hZ.hom_ext _ _) G h hG fun _x => hZ.hom_ext _ _
 #align category_theory.with_initial.lift_to_initial_unique CategoryTheory.WithInitial.liftToInitialUnique

14b69e9f

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.with_terminal
-! leanprover-community/mathlib commit 14b69e9f3c16630440a2cbd46f1ddad0d561dee7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Limits.Shapes.Terminal
 
+#align_import category_theory.with_terminal from "leanprover-community/mathlib"@"14b69e9f3c16630440a2cbd46f1ddad0d561dee7"
+
 /-!
 
 # `WithInitial` and `WithTerminal`

14b69e9f

chore: fix focusing dots (#5708)

This PR is the result of running

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

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

cb02d09e

Diff

@@ -102,9 +102,9 @@ instance : Category.{v} (WithTerminal C) where
     -- so the `false_of_from_star` destruct rule below can be used here.
     -- That works, but causes mysterious failures of `aesop_cat` in `map`.
     cases a <;> cases b <;> cases c <;> cases d <;> try aesop_cat
-    . exact (h : PEmpty).elim
-    . exact (g : PEmpty).elim
-    . exact (h : PEmpty).elim
+    · exact (h : PEmpty).elim
+    · exact (g : PEmpty).elim
+    · exact (h : PEmpty).elim
 
 /-- Helper function for typechecking. -/
 def down {X Y : C} (f : of X ⟶ of Y) : X ⟶ Y := f
@@ -289,9 +289,9 @@ instance : Category.{v} (WithInitial C) where
     -- Porting note: it would be nice to automate this away as well.
     -- See the note on `Category (WithTerminal C)`
     cases a <;> cases b <;> cases c <;> cases d <;> try aesop_cat
-    . exact (g : PEmpty).elim
-    . exact (f : PEmpty).elim
-    . exact (f : PEmpty).elim
+    · exact (g : PEmpty).elim
+    · exact (f : PEmpty).elim
+    · exact (f : PEmpty).elim
 
 /-- Helper function for typechecking. -/
 def down {X Y : C} (f : of X ⟶ of Y) : X ⟶ Y := f

14b69e9f

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -32,7 +32,7 @@ The relevant constructions needed for the universal properties of these construc
   functor which was lifted.
 3. `liftUnique` provides the uniqueness property of `lift`.
 
-In addition to this, we provide `WithTerminal.map` and `WithInitinal.map` providing the
+In addition to this, we provide `WithTerminal.map` and `WithInitial.map` providing the
 functoriality of these constructions with respect to functors on the base categories.
 
 -/

14b69e9f

feat: port CategoryTheory.WithTerminal (#2630)

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

9aaa5995

`category_theory.with_terminal` ⟷ `Mathlib.CategoryTheory.WithTerminal`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 83

category_theory.with_terminal ⟷ Mathlib.CategoryTheory.WithTerminal

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 83

`category_theory.with_terminal` ⟷ `Mathlib.CategoryTheory.WithTerminal`