category_theory.limits.shapes.terminal

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

239d882c

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

f4758115

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta
 -/
-import CategoryTheory.Pempty
+import CategoryTheory.PEmpty
 import CategoryTheory.Limits.HasLimits
 import CategoryTheory.EpiMono
 import CategoryTheory.Category.Preorder

f4758115

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta
 -/
-import Mathbin.CategoryTheory.Pempty
-import Mathbin.CategoryTheory.Limits.HasLimits
-import Mathbin.CategoryTheory.EpiMono
-import Mathbin.CategoryTheory.Category.Preorder
+import CategoryTheory.Pempty
+import CategoryTheory.Limits.HasLimits
+import CategoryTheory.EpiMono
+import CategoryTheory.Category.Preorder
 
 #align_import category_theory.limits.shapes.terminal from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"

f4758115

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.limits.shapes.terminal
-! 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.Pempty
 import Mathbin.CategoryTheory.Limits.HasLimits
 import Mathbin.CategoryTheory.EpiMono
 import Mathbin.CategoryTheory.Category.Preorder
 
+#align_import category_theory.limits.shapes.terminal from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # Initial and terminal objects in a category.

f4758115

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -68,6 +68,7 @@ abbrev IsInitial (X : C) :=
 #align category_theory.limits.is_initial CategoryTheory.Limits.IsInitial
 -/
 
+#print CategoryTheory.Limits.isTerminalEquivUnique /-
 /-- An object `Y` is terminal iff for every `X` there is a unique morphism `X ⟶ Y`. -/
 def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
     IsLimit (⟨Y, by tidy⟩ : Cone F) ≃ ∀ X : C, Unique (X ⟶ Y)
@@ -81,6 +82,7 @@ def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_terminal_equiv_unique CategoryTheory.Limits.isTerminalEquivUnique
+-/
 
 #print CategoryTheory.Limits.IsTerminal.ofUnique /-
 /-- An object `Y` is terminal if for every `X` there is a unique morphism `X ⟶ Y`
@@ -90,10 +92,12 @@ def IsTerminal.ofUnique (Y : C) [h : ∀ X : C, Unique (X ⟶ Y)] : IsTerminal Y
 #align category_theory.limits.is_terminal.of_unique CategoryTheory.Limits.IsTerminal.ofUnique
 -/
 
+#print CategoryTheory.Limits.isTerminalTop /-
 /-- If `α` is a preorder with top, then `⊤` is a terminal object. -/
 def isTerminalTop {α : Type _} [Preorder α] [OrderTop α] : IsTerminal (⊤ : α) :=
   IsTerminal.ofUnique _
 #align category_theory.limits.is_terminal_top CategoryTheory.Limits.isTerminalTop
+-/
 
 #print CategoryTheory.Limits.IsTerminal.ofIso /-
 /-- Transport a term of type `is_terminal` across an isomorphism. -/
@@ -104,6 +108,7 @@ def IsTerminal.ofIso {Y Z : C} (hY : IsTerminal Y) (i : Y ≅ Z) : IsTerminal Z
 #align category_theory.limits.is_terminal.of_iso CategoryTheory.Limits.IsTerminal.ofIso
 -/
 
+#print CategoryTheory.Limits.isInitialEquivUnique /-
 /-- An object `X` is initial iff for every `Y` there is a unique morphism `X ⟶ Y`. -/
 def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :
     IsColimit (⟨X, by tidy⟩ : Cocone F) ≃ ∀ Y : C, Unique (X ⟶ Y)
@@ -117,6 +122,7 @@ def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_initial_equiv_unique CategoryTheory.Limits.isInitialEquivUnique
+-/
 
 #print CategoryTheory.Limits.IsInitial.ofUnique /-
 /-- An object `X` is initial if for every `Y` there is a unique morphism `X ⟶ Y`
@@ -126,10 +132,12 @@ def IsInitial.ofUnique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : IsInitial X
 #align category_theory.limits.is_initial.of_unique CategoryTheory.Limits.IsInitial.ofUnique
 -/
 
+#print CategoryTheory.Limits.isInitialBot /-
 /-- If `α` is a preorder with bot, then `⊥` is an initial object. -/
 def isInitialBot {α : Type _} [Preorder α] [OrderBot α] : IsInitial (⊥ : α) :=
   IsInitial.ofUnique _
 #align category_theory.limits.is_initial_bot CategoryTheory.Limits.isInitialBot
+-/
 
 #print CategoryTheory.Limits.IsInitial.ofIso /-
 /-- Transport a term of type `is_initial` across an isomorphism. -/
@@ -374,10 +382,8 @@ abbrev initial [HasInitial C] : C :=
 #align category_theory.limits.initial CategoryTheory.Limits.initial
 -/
 
--- mathport name: «expr⊤_ »
 notation "⊤_ " C:20 => terminal C
 
--- mathport name: «expr⊥_ »
 notation "⊥_ " C:20 => initial C
 
 section
@@ -564,6 +570,7 @@ instance {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C] :
           π := { app := fun _ => terminal.from _ } }
       IsLimit := { lift := fun s => terminal.from _ } }
 
+#print CategoryTheory.Limits.limitConstTerminal /-
 /-- The limit of the constant `⊤_ C` functor is `⊤_ C`. -/
 @[simps Hom]
 def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C] :
@@ -575,7 +582,9 @@ def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasT
       { pt := ⊤_ C
         π := { app := fun j => terminal.from _ } }
 #align category_theory.limits.limit_const_terminal CategoryTheory.Limits.limitConstTerminal
+-/
 
+#print CategoryTheory.Limits.limitConstTerminal_inv_π /-
 @[simp, reassoc]
 theorem limitConstTerminal_inv_π {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C]
     {j : J} :
@@ -583,6 +592,7 @@ theorem limitConstTerminal_inv_π {J : Type _} [Category J] {C : Type _} [Catego
       terminal.from _ :=
   by ext ⟨⟨⟩⟩
 #align category_theory.limits.limit_const_terminal_inv_π CategoryTheory.Limits.limitConstTerminal_inv_π
+-/
 
 instance {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
     HasColimit ((CategoryTheory.Functor.const J).obj (⊥_ C)) :=
@@ -592,6 +602,7 @@ instance {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
           ι := { app := fun _ => initial.to _ } }
       IsColimit := { desc := fun s => initial.to _ } }
 
+#print CategoryTheory.Limits.colimitConstInitial /-
 /-- The colimit of the constant `⊥_ C` functor is `⊥_ C`. -/
 @[simps inv]
 def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
@@ -603,7 +614,9 @@ def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [Has
         ι := { app := fun j => initial.to _ } }
   inv := initial.to _
 #align category_theory.limits.colimit_const_initial CategoryTheory.Limits.colimitConstInitial
+-/
 
+#print CategoryTheory.Limits.ι_colimitConstInitial_hom /-
 @[simp, reassoc]
 theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C]
     {j : J} :
@@ -611,6 +624,7 @@ theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Categ
       initial.to _ :=
   by ext ⟨⟨⟩⟩
 #align category_theory.limits.ι_colimit_const_initial_hom CategoryTheory.Limits.ι_colimitConstInitial_hom
+-/
 
 #print CategoryTheory.Limits.InitialMonoClass /-
 /-- A category is a `initial_mono_class` if the canonical morphism of an initial object is a
@@ -685,6 +699,7 @@ section Comparison
 
 variable {D : Type u₂} [Category.{v₂} D] (G : C ⥤ D)
 
+#print CategoryTheory.Limits.terminalComparison /-
 /-- The comparison morphism from the image of a terminal object to the terminal object in the target
 category.
 This is an isomorphism iff `G` preserves terminal objects, see
@@ -693,7 +708,9 @@ This is an isomorphism iff `G` preserves terminal objects, see
 def terminalComparison [HasTerminal C] [HasTerminal D] : G.obj (⊤_ C) ⟶ ⊤_ D :=
   terminal.from _
 #align category_theory.limits.terminal_comparison CategoryTheory.Limits.terminalComparison
+-/
 
+#print CategoryTheory.Limits.initialComparison /-
 -- TODO: Show this is an isomorphism if and only if `G` preserves initial objects.
 /--
 The comparison morphism from the initial object in the target category to the image of the initial
@@ -702,6 +719,7 @@ object.
 def initialComparison [HasInitial C] [HasInitial D] : ⊥_ D ⟶ G.obj (⊥_ C) :=
   initial.to _
 #align category_theory.limits.initial_comparison CategoryTheory.Limits.initialComparison
+-/
 
 end Comparison
 
@@ -735,6 +753,7 @@ def limitOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) :
 #align category_theory.limits.limit_of_diagram_initial CategoryTheory.Limits.limitOfDiagramInitial
 -/
 
+#print CategoryTheory.Limits.limitOfInitial /-
 -- See note [dsimp, simp]
 -- This is reducible to allow usage of lemmas about `cone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has an initial object then the image of it is isomorphic
@@ -743,7 +762,9 @@ to the limit of `F`. -/
 def limitOfInitial (F : J ⥤ C) [HasInitial J] [HasLimit F] : limit F ≅ F.obj (⊥_ J) :=
   IsLimit.conePointUniqueUpToIso (limit.isLimit _) (limitOfDiagramInitial initialIsInitial F)
 #align category_theory.limits.limit_of_initial CategoryTheory.Limits.limitOfInitial
+-/
 
+#print CategoryTheory.Limits.coneOfDiagramTerminal /-
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J`, construct a cone for `J`,
 provided that the morphisms in the diagram are isomorphisms.
 In `limit_of_diagram_terminal` we show it is a limit cone. -/
@@ -760,14 +781,18 @@ def coneOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
         simp only [is_iso.eq_inv_comp, is_iso.comp_inv_eq, category.id_comp, ← F.map_comp,
           hX.hom_ext (hX.from i) (f ≫ hX.from j)] }
 #align category_theory.limits.cone_of_diagram_terminal CategoryTheory.Limits.coneOfDiagramTerminal
+-/
 
+#print CategoryTheory.Limits.limitOfDiagramTerminal /-
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J` and that the morphisms in the
 diagram are isomorphisms, show the cone `cone_of_diagram_terminal` is a limit. -/
 def limitOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsLimit (coneOfDiagramTerminal hX F)
     where lift S := S.π.app _
 #align category_theory.limits.limit_of_diagram_terminal CategoryTheory.Limits.limitOfDiagramTerminal
+-/
 
+#print CategoryTheory.Limits.limitOfTerminal /-
 -- This is reducible to allow usage of lemmas about `cone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has a terminal object and all the morphisms in the diagram
 are isomorphisms, then the image of the terminal object is isomorphic to the limit of `F`. -/
@@ -776,6 +801,7 @@ def limitOfTerminal (F : J ⥤ C) [HasTerminal J] [HasLimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : limit F ≅ F.obj (⊤_ J) :=
   IsLimit.conePointUniqueUpToIso (limit.isLimit _) (limitOfDiagramTerminal terminalIsTerminal F)
 #align category_theory.limits.limit_of_terminal CategoryTheory.Limits.limitOfTerminal
+-/
 
 #print CategoryTheory.Limits.coconeOfDiagramTerminal /-
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J`, construct a cocone for `J`.
@@ -803,6 +829,7 @@ def colimitOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) :
 #align category_theory.limits.colimit_of_diagram_terminal CategoryTheory.Limits.colimitOfDiagramTerminal
 -/
 
+#print CategoryTheory.Limits.colimitOfTerminal /-
 -- This is reducible to allow usage of lemmas about `cocone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has a terminal object then the image of it is isomorphic
 to the colimit of `F`. -/
@@ -811,7 +838,9 @@ def colimitOfTerminal (F : J ⥤ C) [HasTerminal J] [HasColimit F] : colimit F 
   IsColimit.coconePointUniqueUpToIso (colimit.isColimit _)
     (colimitOfDiagramTerminal terminalIsTerminal F)
 #align category_theory.limits.colimit_of_terminal CategoryTheory.Limits.colimitOfTerminal
+-/
 
+#print CategoryTheory.Limits.coconeOfDiagramInitial /-
 /-- From a functor `F : J ⥤ C`, given an initial object of `J`, construct a cocone for `J`,
 provided that the morphisms in the diagram are isomorphisms.
 In `colimit_of_diagram_initial` we show it is a colimit cocone. -/
@@ -828,14 +857,18 @@ def coconeOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
         simp only [is_iso.eq_inv_comp, is_iso.comp_inv_eq, category.comp_id, ← F.map_comp,
           hX.hom_ext (hX.to i ≫ f) (hX.to j)] }
 #align category_theory.limits.cocone_of_diagram_initial CategoryTheory.Limits.coconeOfDiagramInitial
+-/
 
+#print CategoryTheory.Limits.colimitOfDiagramInitial /-
 /-- From a functor `F : J ⥤ C`, given an initial object of `J` and that the morphisms in the
 diagram are isomorphisms, show the cone `cocone_of_diagram_initial` is a colimit. -/
 def colimitOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsColimit (coconeOfDiagramInitial hX F)
     where desc S := S.ι.app _
 #align category_theory.limits.colimit_of_diagram_initial CategoryTheory.Limits.colimitOfDiagramInitial
+-/
 
+#print CategoryTheory.Limits.colimitOfInitial /-
 -- This is reducible to allow usage of lemmas about `cocone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has an initial object and all the morphisms in the diagram
 are isomorphisms, then the image of the initial object is isomorphic to the colimit of `F`. -/
@@ -845,48 +878,65 @@ def colimitOfInitial (F : J ⥤ C) [HasInitial J] [HasColimit F]
   IsColimit.coconePointUniqueUpToIso (colimit.isColimit _)
     (colimitOfDiagramInitial initialIsInitial _)
 #align category_theory.limits.colimit_of_initial CategoryTheory.Limits.colimitOfInitial
+-/
 
+#print CategoryTheory.Limits.isIso_π_of_isInitial /-
 /-- If `j` is initial in the index category, then the map `limit.π F j` is an isomorphism.
 -/
 theorem isIso_π_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasLimit F] :
     IsIso (limit.π F j) :=
   ⟨⟨limit.lift _ (coneOfDiagramInitial I F), ⟨by ext; simp, by simp⟩⟩⟩
 #align category_theory.limits.is_iso_π_of_is_initial CategoryTheory.Limits.isIso_π_of_isInitial
+-/
 
+#print CategoryTheory.Limits.isIso_π_initial /-
 instance isIso_π_initial [HasInitial J] (F : J ⥤ C) [HasLimit F] : IsIso (limit.π F (⊥_ J)) :=
   isIso_π_of_isInitial initialIsInitial F
 #align category_theory.limits.is_iso_π_initial CategoryTheory.Limits.isIso_π_initial
+-/
 
+#print CategoryTheory.Limits.isIso_π_of_isTerminal /-
 theorem isIso_π_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasLimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (limit.π F j) :=
   ⟨⟨limit.lift _ (coneOfDiagramTerminal I F), by ext; simp, by simp⟩⟩
 #align category_theory.limits.is_iso_π_of_is_terminal CategoryTheory.Limits.isIso_π_of_isTerminal
+-/
 
+#print CategoryTheory.Limits.isIso_π_terminal /-
 instance isIso_π_terminal [HasTerminal J] (F : J ⥤ C) [HasLimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (limit.π F (⊤_ J)) :=
   isIso_π_of_isTerminal terminalIsTerminal F
 #align category_theory.limits.is_iso_π_terminal CategoryTheory.Limits.isIso_π_terminal
+-/
 
+#print CategoryTheory.Limits.isIso_ι_of_isTerminal /-
 /-- If `j` is terminal in the index category, then the map `colimit.ι F j` is an isomorphism.
 -/
 theorem isIso_ι_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasColimit F] :
     IsIso (colimit.ι F j) :=
   ⟨⟨colimit.desc _ (coconeOfDiagramTerminal I F), ⟨by simp, by ext; simp⟩⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_terminal CategoryTheory.Limits.isIso_ι_of_isTerminal
+-/
 
+#print CategoryTheory.Limits.isIso_ι_terminal /-
 instance isIso_ι_terminal [HasTerminal J] (F : J ⥤ C) [HasColimit F] : IsIso (colimit.ι F (⊤_ J)) :=
   isIso_ι_of_isTerminal terminalIsTerminal F
 #align category_theory.limits.is_iso_ι_terminal CategoryTheory.Limits.isIso_ι_terminal
+-/
 
+#print CategoryTheory.Limits.isIso_ι_of_isInitial /-
 theorem isIso_ι_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasColimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (colimit.ι F j) :=
   ⟨⟨colimit.desc _ (coconeOfDiagramInitial I F), ⟨by tidy, by ext; simp⟩⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_initial CategoryTheory.Limits.isIso_ι_of_isInitial
+-/
 
+#print CategoryTheory.Limits.isIso_ι_initial /-
 instance isIso_ι_initial [HasInitial J] (F : J ⥤ C) [HasColimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (colimit.ι F (⊥_ J)) :=
   isIso_ι_of_isInitial initialIsInitial F
 #align category_theory.limits.is_iso_ι_initial CategoryTheory.Limits.isIso_ι_initial
+-/
 
 end

f4758115

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -68,9 +68,6 @@ abbrev IsInitial (X : C) :=
 #align category_theory.limits.is_initial CategoryTheory.Limits.IsInitial
 -/
 
-/- warning: category_theory.limits.is_terminal_equiv_unique -> CategoryTheory.Limits.isTerminalEquivUnique is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_terminal_equiv_unique CategoryTheory.Limits.isTerminalEquivUniqueₓ'. -/
 /-- An object `Y` is terminal iff for every `X` there is a unique morphism `X ⟶ Y`. -/
 def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
     IsLimit (⟨Y, by tidy⟩ : Cone F) ≃ ∀ X : C, Unique (X ⟶ Y)
@@ -93,12 +90,6 @@ def IsTerminal.ofUnique (Y : C) [h : ∀ X : C, Unique (X ⟶ Y)] : IsTerminal Y
 #align category_theory.limits.is_terminal.of_unique CategoryTheory.Limits.IsTerminal.ofUnique
 -/
 
-/- warning: category_theory.limits.is_terminal_top -> CategoryTheory.Limits.isTerminalTop is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_2)], CategoryTheory.Limits.IsTerminal.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_2) _inst_3))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_2)], CategoryTheory.Limits.IsTerminal.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_terminal_top CategoryTheory.Limits.isTerminalTopₓ'. -/
 /-- If `α` is a preorder with top, then `⊤` is a terminal object. -/
 def isTerminalTop {α : Type _} [Preorder α] [OrderTop α] : IsTerminal (⊤ : α) :=
   IsTerminal.ofUnique _
@@ -113,9 +104,6 @@ def IsTerminal.ofIso {Y Z : C} (hY : IsTerminal Y) (i : Y ≅ Z) : IsTerminal Z
 #align category_theory.limits.is_terminal.of_iso CategoryTheory.Limits.IsTerminal.ofIso
 -/
 
-/- warning: category_theory.limits.is_initial_equiv_unique -> CategoryTheory.Limits.isInitialEquivUnique is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_initial_equiv_unique CategoryTheory.Limits.isInitialEquivUniqueₓ'. -/
 /-- An object `X` is initial iff for every `Y` there is a unique morphism `X ⟶ Y`. -/
 def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :
     IsColimit (⟨X, by tidy⟩ : Cocone F) ≃ ∀ Y : C, Unique (X ⟶ Y)
@@ -138,12 +126,6 @@ def IsInitial.ofUnique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : IsInitial X
 #align category_theory.limits.is_initial.of_unique CategoryTheory.Limits.IsInitial.ofUnique
 -/
 
-/- warning: category_theory.limits.is_initial_bot -> CategoryTheory.Limits.isInitialBot is a dubious translation:
-lean 3 declaration is
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 /-- If `α` is a preorder with bot, then `⊥` is an initial object. -/
 def isInitialBot {α : Type _} [Preorder α] [OrderBot α] : IsInitial (⊥ : α) :=
   IsInitial.ofUnique _
@@ -582,12 +564,6 @@ instance {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C] :
           π := { app := fun _ => terminal.from _ } }
       IsLimit := { lift := fun s => terminal.from _ } }
 
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 /-- The limit of the constant `⊤_ C` functor is `⊤_ C`. -/
 @[simps Hom]
 def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C] :
@@ -600,9 +576,6 @@ def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasT
         π := { app := fun j => terminal.from _ } }
 #align category_theory.limits.limit_const_terminal CategoryTheory.Limits.limitConstTerminal
 
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 @[simp, reassoc]
 theorem limitConstTerminal_inv_π {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C]
     {j : J} :
@@ -619,12 +592,6 @@ instance {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
           ι := { app := fun _ => initial.to _ } }
       IsColimit := { desc := fun s => initial.to _ } }
 
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 /-- The colimit of the constant `⊥_ C` functor is `⊥_ C`. -/
 @[simps inv]
 def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
@@ -637,9 +604,6 @@ def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [Has
   inv := initial.to _
 #align category_theory.limits.colimit_const_initial CategoryTheory.Limits.colimitConstInitial
 
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 @[simp, reassoc]
 theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C]
     {j : J} :
@@ -721,12 +685,6 @@ section Comparison
 
 variable {D : Type u₂} [Category.{v₂} D] (G : C ⥤ D)
 
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 /-- The comparison morphism from the image of a terminal object to the terminal object in the target
 category.
 This is an isomorphism iff `G` preserves terminal objects, see
@@ -736,12 +694,6 @@ def terminalComparison [HasTerminal C] [HasTerminal D] : G.obj (⊤_ C) ⟶ ⊤_
   terminal.from _
 #align category_theory.limits.terminal_comparison CategoryTheory.Limits.terminalComparison
 
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 -- TODO: Show this is an isomorphism if and only if `G` preserves initial objects.
 /--
 The comparison morphism from the initial object in the target category to the image of the initial
@@ -783,12 +735,6 @@ def limitOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) :
 #align category_theory.limits.limit_of_diagram_initial CategoryTheory.Limits.limitOfDiagramInitial
 -/
 
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 -- See note [dsimp, simp]
 -- This is reducible to allow usage of lemmas about `cone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has an initial object then the image of it is isomorphic
@@ -798,12 +744,6 @@ def limitOfInitial (F : J ⥤ C) [HasInitial J] [HasLimit F] : limit F ≅ F.obj
   IsLimit.conePointUniqueUpToIso (limit.isLimit _) (limitOfDiagramInitial initialIsInitial F)
 #align category_theory.limits.limit_of_initial CategoryTheory.Limits.limitOfInitial
 
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 /-- From a functor `F : J ⥤ C`, given a terminal object of `J`, construct a cone for `J`,
 provided that the morphisms in the diagram are isomorphisms.
 In `limit_of_diagram_terminal` we show it is a limit cone. -/
@@ -821,12 +761,6 @@ def coneOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
           hX.hom_ext (hX.from i) (f ≫ hX.from j)] }
 #align category_theory.limits.cone_of_diagram_terminal CategoryTheory.Limits.coneOfDiagramTerminal
 
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 /-- From a functor `F : J ⥤ C`, given a terminal object of `J` and that the morphisms in the
 diagram are isomorphisms, show the cone `cone_of_diagram_terminal` is a limit. -/
 def limitOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
@@ -834,12 +768,6 @@ def limitOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
     where lift S := S.π.app _
 #align category_theory.limits.limit_of_diagram_terminal CategoryTheory.Limits.limitOfDiagramTerminal
 
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 -- This is reducible to allow usage of lemmas about `cone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has a terminal object and all the morphisms in the diagram
 are isomorphisms, then the image of the terminal object is isomorphic to the limit of `F`. -/
@@ -875,12 +803,6 @@ def colimitOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) :
 #align category_theory.limits.colimit_of_diagram_terminal CategoryTheory.Limits.colimitOfDiagramTerminal
 -/
 
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 -- This is reducible to allow usage of lemmas about `cocone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has a terminal object then the image of it is isomorphic
 to the colimit of `F`. -/
@@ -890,12 +812,6 @@ def colimitOfTerminal (F : J ⥤ C) [HasTerminal J] [HasColimit F] : colimit F 
     (colimitOfDiagramTerminal terminalIsTerminal F)
 #align category_theory.limits.colimit_of_terminal CategoryTheory.Limits.colimitOfTerminal
 
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 /-- From a functor `F : J ⥤ C`, given an initial object of `J`, construct a cocone for `J`,
 provided that the morphisms in the diagram are isomorphisms.
 In `colimit_of_diagram_initial` we show it is a colimit cocone. -/
@@ -913,12 +829,6 @@ def coconeOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
           hX.hom_ext (hX.to i ≫ f) (hX.to j)] }
 #align category_theory.limits.cocone_of_diagram_initial CategoryTheory.Limits.coconeOfDiagramInitial
 
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 /-- From a functor `F : J ⥤ C`, given an initial object of `J` and that the morphisms in the
 diagram are isomorphisms, show the cone `cocone_of_diagram_initial` is a colimit. -/
 def colimitOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
@@ -926,12 +836,6 @@ def colimitOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
     where desc S := S.ι.app _
 #align category_theory.limits.colimit_of_diagram_initial CategoryTheory.Limits.colimitOfDiagramInitial
 
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 -- This is reducible to allow usage of lemmas about `cocone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has an initial object and all the morphisms in the diagram
 are isomorphisms, then the image of the initial object is isomorphic to the colimit of `F`. -/
@@ -942,12 +846,6 @@ def colimitOfInitial (F : J ⥤ C) [HasInitial J] [HasColimit F]
     (colimitOfDiagramInitial initialIsInitial _)
 #align category_theory.limits.colimit_of_initial CategoryTheory.Limits.colimitOfInitial
 
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 /-- If `j` is initial in the index category, then the map `limit.π F j` is an isomorphism.
 -/
 theorem isIso_π_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasLimit F] :
@@ -955,44 +853,20 @@ theorem isIso_π_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasLimit
   ⟨⟨limit.lift _ (coneOfDiagramInitial I F), ⟨by ext; simp, by simp⟩⟩⟩
 #align category_theory.limits.is_iso_π_of_is_initial CategoryTheory.Limits.isIso_π_of_isInitial
 
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 instance isIso_π_initial [HasInitial J] (F : J ⥤ C) [HasLimit F] : IsIso (limit.π F (⊥_ J)) :=
   isIso_π_of_isInitial initialIsInitial F
 #align category_theory.limits.is_iso_π_initial CategoryTheory.Limits.isIso_π_initial
 
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 theorem isIso_π_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasLimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (limit.π F j) :=
   ⟨⟨limit.lift _ (coneOfDiagramTerminal I F), by ext; simp, by simp⟩⟩
 #align category_theory.limits.is_iso_π_of_is_terminal CategoryTheory.Limits.isIso_π_of_isTerminal
 
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 instance isIso_π_terminal [HasTerminal J] (F : J ⥤ C) [HasLimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (limit.π F (⊤_ J)) :=
   isIso_π_of_isTerminal terminalIsTerminal F
 #align category_theory.limits.is_iso_π_terminal CategoryTheory.Limits.isIso_π_terminal
 
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 /-- If `j` is terminal in the index category, then the map `colimit.ι F j` is an isomorphism.
 -/
 theorem isIso_ι_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasColimit F] :
@@ -1000,33 +874,15 @@ theorem isIso_ι_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasColi
   ⟨⟨colimit.desc _ (coconeOfDiagramTerminal I F), ⟨by simp, by ext; simp⟩⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_terminal CategoryTheory.Limits.isIso_ι_of_isTerminal
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_iso_ι_terminal CategoryTheory.Limits.isIso_ι_terminalₓ'. -/
 instance isIso_ι_terminal [HasTerminal J] (F : J ⥤ C) [HasColimit F] : IsIso (colimit.ι F (⊤_ J)) :=
   isIso_ι_of_isTerminal terminalIsTerminal F
 #align category_theory.limits.is_iso_ι_terminal CategoryTheory.Limits.isIso_ι_terminal
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_iso_ι_of_is_initial CategoryTheory.Limits.isIso_ι_of_isInitialₓ'. -/
 theorem isIso_ι_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasColimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (colimit.ι F j) :=
   ⟨⟨colimit.desc _ (coconeOfDiagramInitial I F), ⟨by tidy, by ext; simp⟩⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_initial CategoryTheory.Limits.isIso_ι_of_isInitial
 
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 instance isIso_ι_initial [HasInitial J] (F : J ⥤ C) [HasColimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (colimit.ι F (⊥_ J)) :=
   isIso_ι_of_isInitial initialIsInitial F

f4758115

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -294,9 +294,7 @@ def isLimitChangeEmptyCone {c₁ : Cone F₁} (hl : IsLimit c₁) (c₂ : Cone F
     IsLimit c₂ where
   lift c := hl.lift ⟨c.pt, by tidy⟩ ≫ hi.Hom
   fac _ j := j.as.elim
-  uniq c f _ := by
-    erw [← hl.uniq ⟨c.X, by tidy⟩ (f ≫ hi.inv) fun j => j.as.elim]
-    simp
+  uniq c f _ := by erw [← hl.uniq ⟨c.X, by tidy⟩ (f ≫ hi.inv) fun j => j.as.elim]; simp
 #align category_theory.limits.is_limit_change_empty_cone CategoryTheory.Limits.isLimitChangeEmptyCone
 -/
 
@@ -338,9 +336,7 @@ def isColimitChangeEmptyCocone {c₁ : Cocone F₁} (hl : IsColimit c₁) (c₂
     where
   desc c := hi.inv ≫ hl.desc ⟨c.pt, by tidy⟩
   fac _ j := j.as.elim
-  uniq c f _ := by
-    erw [← hl.uniq ⟨c.X, by tidy⟩ (hi.hom ≫ f) fun j => j.as.elim]
-    simp
+  uniq c f _ := by erw [← hl.uniq ⟨c.X, by tidy⟩ (hi.hom ≫ f) fun j => j.as.elim]; simp
 #align category_theory.limits.is_colimit_change_empty_cocone CategoryTheory.Limits.isColimitChangeEmptyCocone
 -/
 
@@ -875,10 +871,7 @@ def colimitOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) :
     IsColimit (coconeOfDiagramTerminal tX F)
     where
   desc s := s.ι.app X
-  uniq s m w :=
-    by
-    rw [← w X, cocone_of_diagram_terminal_ι_app, tX.hom_ext (tX.from X) (𝟙 _)]
-    simp
+  uniq s m w := by rw [← w X, cocone_of_diagram_terminal_ι_app, tX.hom_ext (tX.from X) (𝟙 _)]; simp
 #align category_theory.limits.colimit_of_diagram_terminal CategoryTheory.Limits.colimitOfDiagramTerminal
 -/
 
@@ -959,10 +952,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.limits
 -/
 theorem isIso_π_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasLimit F] :
     IsIso (limit.π F j) :=
-  ⟨⟨limit.lift _ (coneOfDiagramInitial I F),
-      ⟨by
-        ext
-        simp, by simp⟩⟩⟩
+  ⟨⟨limit.lift _ (coneOfDiagramInitial I F), ⟨by ext; simp, by simp⟩⟩⟩
 #align category_theory.limits.is_iso_π_of_is_initial CategoryTheory.Limits.isIso_π_of_isInitial
 
 /- warning: category_theory.limits.is_iso_π_initial -> CategoryTheory.Limits.isIso_π_initial is a dubious translation:
@@ -983,9 +973,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_iso_π_of_is_terminal CategoryTheory.Limits.isIso_π_of_isTerminalₓ'. -/
 theorem isIso_π_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasLimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (limit.π F j) :=
-  ⟨⟨limit.lift _ (coneOfDiagramTerminal I F), by
-      ext
-      simp, by simp⟩⟩
+  ⟨⟨limit.lift _ (coneOfDiagramTerminal I F), by ext; simp, by simp⟩⟩
 #align category_theory.limits.is_iso_π_of_is_terminal CategoryTheory.Limits.isIso_π_of_isTerminal
 
 /- warning: category_theory.limits.is_iso_π_terminal -> CategoryTheory.Limits.isIso_π_terminal is a dubious translation:
@@ -1009,10 +997,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.limits
 -/
 theorem isIso_ι_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasColimit F] :
     IsIso (colimit.ι F j) :=
-  ⟨⟨colimit.desc _ (coconeOfDiagramTerminal I F),
-      ⟨by simp, by
-        ext
-        simp⟩⟩⟩
+  ⟨⟨colimit.desc _ (coconeOfDiagramTerminal I F), ⟨by simp, by ext; simp⟩⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_terminal CategoryTheory.Limits.isIso_ι_of_isTerminal
 
 /- warning: category_theory.limits.is_iso_ι_terminal -> CategoryTheory.Limits.isIso_ι_terminal is a dubious translation:
@@ -1033,10 +1018,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_iso_ι_of_is_initial CategoryTheory.Limits.isIso_ι_of_isInitialₓ'. -/
 theorem isIso_ι_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasColimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (colimit.ι F j) :=
-  ⟨⟨colimit.desc _ (coconeOfDiagramInitial I F),
-      ⟨by tidy, by
-        ext
-        simp⟩⟩⟩
+  ⟨⟨colimit.desc _ (coconeOfDiagramInitial I F), ⟨by tidy, by ext; simp⟩⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_initial CategoryTheory.Limits.isIso_ι_of_isInitial
 
 /- warning: category_theory.limits.is_iso_ι_initial -> CategoryTheory.Limits.isIso_ι_initial is a dubious translation:

f4758115

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -69,10 +69,7 @@ abbrev IsInitial (X : C) :=
 -/
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_terminal_equiv_unique CategoryTheory.Limits.isTerminalEquivUniqueₓ'. -/
 /-- An object `Y` is terminal iff for every `X` there is a unique morphism `X ⟶ Y`. -/
 def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
@@ -117,10 +114,7 @@ def IsTerminal.ofIso {Y Z : C} (hY : IsTerminal Y) (i : Y ≅ Z) : IsTerminal Z
 -/
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_initial_equiv_unique CategoryTheory.Limits.isInitialEquivUniqueₓ'. -/
 /-- An object `X` is initial iff for every `Y` there is a unique morphism `X ⟶ Y`. -/
 def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :
@@ -611,10 +605,7 @@ def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasT
 #align category_theory.limits.limit_const_terminal CategoryTheory.Limits.limitConstTerminal
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.limit_const_terminal_inv_π CategoryTheory.Limits.limitConstTerminal_inv_πₓ'. -/
 @[simp, reassoc]
 theorem limitConstTerminal_inv_π {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C]
@@ -651,10 +642,7 @@ def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [Has
 #align category_theory.limits.colimit_const_initial CategoryTheory.Limits.colimitConstInitial
 
 /- warning: category_theory.limits.ι_colimit_const_initial_hom -> CategoryTheory.Limits.ι_colimitConstInitial_hom is a dubious translation:
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_inst_3 _inst_4)) (CategoryTheory.Limits.initial.{u1, u2} C _inst_3 _inst_4) (CategoryTheory.Limits.colimitConstInitial.{u4, u3, u2, u1} J _inst_2 C _inst_3 _inst_4))) (CategoryTheory.Limits.initial.to.{u1, u2} C _inst_3 _inst_4 (CategoryTheory.Limits.initial.{u1, u2} C _inst_3 _inst_4))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.ι_colimit_const_initial_hom CategoryTheory.Limits.ι_colimitConstInitial_homₓ'. -/
 @[simp, reassoc]
 theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C]

f4758115

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -616,7 +616,7 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u3, u4} J] {C : Type.{u2}} [_inst_3 : CategoryTheory.Category.{u1, u2} C] [_inst_4 : CategoryTheory.Limits.HasTerminal.{u1, u2} C _inst_3] {j : J}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Limits.terminal.{u1, u2} C _inst_3 _inst_4) (Prefunctor.obj.{succ u3, succ u1, u4, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u3, u4} J (CategoryTheory.Category.toCategoryStruct.{u3, u4} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u3, u1, u4, u2} J _inst_2 C _inst_3 (Prefunctor.obj.{succ u1, max (succ u4) (succ u1), u2, max (max (max u4 u3) u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u1, max u4 u1, u2, max (max (max u4 u3) u2) u1} C _inst_3 (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.const.{u3, u1, u4, u2} J _inst_2 C _inst_3)) (CategoryTheory.Limits.terminal.{u1, u2} C _inst_3 _inst_4))) j)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3) (CategoryTheory.Limits.terminal.{u1, u2} C _inst_3 _inst_4) (CategoryTheory.Limits.limit.{u3, u4, u1, u2} J _inst_2 C _inst_3 (Prefunctor.obj.{succ u1, max (succ u4) (succ u1), u2, max (max (max u4 u3) u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u1, max u4 u1, u2, max (max (max u4 u3) u2) u1} C _inst_3 (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.const.{u3, u1, u4, u2} J _inst_2 C _inst_3)) (CategoryTheory.Limits.terminal.{u1, u2} C _inst_3 _inst_4)) (CategoryTheory.Limits.instHasLimitObjToQuiverToCategoryStructFunctorToQuiverToCategoryStructCategoryToPrefunctorConstTerminal.{u4, u3, u2, u1} J _inst_2 C _inst_3 _inst_4)) (Prefunctor.obj.{succ u3, succ u1, u4, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u3, u4} J (CategoryTheory.Category.toCategoryStruct.{u3, u4} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u3, u1, u4, u2} J _inst_2 C _inst_3 (Prefunctor.obj.{succ u1, max (succ u4) (succ u1), u2, max (max (max u4 u3) u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u1, max u4 u1, u2, max (max (max u4 u3) u2) u1} C _inst_3 (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.const.{u3, u1, u4, u2} J _inst_2 C _inst_3)) (CategoryTheory.Limits.terminal.{u1, u2} C _inst_3 _inst_4))) j) (CategoryTheory.Iso.inv.{u1, u2} C _inst_3 (CategoryTheory.Limits.limit.{u3, u4, u1, u2} J _inst_2 C _inst_3 (Prefunctor.obj.{succ u1, max (succ u4) (succ u1), u2, max (max (max u4 u3) u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u1, max u4 u1, u2, max (max (max u4 u3) u2) u1} C _inst_3 (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.const.{u3, u1, u4, u2} J _inst_2 C _inst_3)) (CategoryTheory.Limits.terminal.{u1, u2} C _inst_3 _inst_4)) (CategoryTheory.Limits.instHasLimitObjToQuiverToCategoryStructFunctorToQuiverToCategoryStructCategoryToPrefunctorConstTerminal.{u4, u3, u2, u1} J _inst_2 C _inst_3 _inst_4)) (CategoryTheory.Limits.terminal.{u1, u2} C _inst_3 _inst_4) (CategoryTheory.Limits.limitConstTerminal.{u4, u3, u2, u1} J _inst_2 C _inst_3 _inst_4)) (CategoryTheory.Limits.limit.π.{u3, u4, u1, u2} J _inst_2 C _inst_3 (Prefunctor.obj.{succ u1, max (succ u4) (succ u1), u2, max (max (max u4 u3) u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u1, max u4 u1, u2, max (max (max u4 u3) u2) u1} C _inst_3 (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.const.{u3, u1, u4, u2} J _inst_2 C _inst_3)) (CategoryTheory.Limits.terminal.{u1, u2} C _inst_3 _inst_4)) (CategoryTheory.Limits.instHasLimitObjToQuiverToCategoryStructFunctorToQuiverToCategoryStructCategoryToPrefunctorConstTerminal.{u4, u3, u2, u1} J _inst_2 C _inst_3 _inst_4) j)) (CategoryTheory.Limits.terminal.from.{u1, u2} C _inst_3 _inst_4 (CategoryTheory.Limits.terminal.{u1, u2} C _inst_3 _inst_4))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.limit_const_terminal_inv_π CategoryTheory.Limits.limitConstTerminal_inv_πₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem limitConstTerminal_inv_π {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C]
     {j : J} :
     limitConstTerminal.inv ≫ limit.π ((CategoryTheory.Functor.const J).obj (⊤_ C)) j =
@@ -656,7 +656,7 @@ lean 3 declaration is
 but is expected to have type
   forall {J : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u3, u4} J] {C : Type.{u2}} [_inst_3 : CategoryTheory.Category.{u1, u2} C] [_inst_4 : CategoryTheory.Limits.HasInitial.{u1, u2} C _inst_3] {j : J}, Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (Prefunctor.obj.{succ u3, succ u1, u4, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u3, u4} J (CategoryTheory.Category.toCategoryStruct.{u3, u4} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u3, u1, u4, u2} J _inst_2 C _inst_3 (Prefunctor.obj.{succ u1, max (succ u4) (succ u1), u2, max (max (max u4 u3) u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u1, max u4 u1, u2, max (max (max u4 u3) u2) u1} C _inst_3 (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.const.{u3, u1, u4, u2} J _inst_2 C _inst_3)) (CategoryTheory.Limits.initial.{u1, u2} C _inst_3 _inst_4))) j) (CategoryTheory.Limits.initial.{u1, u2} C _inst_3 _inst_4)) (CategoryTheory.CategoryStruct.comp.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3) (Prefunctor.obj.{succ u3, succ u1, u4, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u3, u4} J (CategoryTheory.Category.toCategoryStruct.{u3, u4} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u3, u1, u4, u2} J _inst_2 C _inst_3 (Prefunctor.obj.{succ u1, max (succ u4) (succ u1), u2, max (max (max u4 u3) u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u1, max u4 u1, u2, max (max (max u4 u3) u2) u1} C _inst_3 (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.const.{u3, u1, u4, u2} J _inst_2 C _inst_3)) (CategoryTheory.Limits.initial.{u1, u2} C _inst_3 _inst_4))) j) (CategoryTheory.Limits.colimit.{u3, u4, u1, u2} J _inst_2 C _inst_3 (Prefunctor.obj.{succ u1, max (succ u4) (succ u1), u2, max (max (max u4 u3) u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u1, max u4 u1, u2, max (max (max u4 u3) u2) u1} C _inst_3 (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.const.{u3, u1, u4, u2} J _inst_2 C _inst_3)) (CategoryTheory.Limits.initial.{u1, u2} C _inst_3 _inst_4)) (CategoryTheory.Limits.instHasColimitObjToQuiverToCategoryStructFunctorToQuiverToCategoryStructCategoryToPrefunctorConstInitial.{u4, u3, u2, u1} J _inst_2 C _inst_3 _inst_4)) (CategoryTheory.Limits.initial.{u1, u2} C _inst_3 _inst_4) (CategoryTheory.Limits.colimit.ι.{u3, u4, u1, u2} J _inst_2 C _inst_3 (Prefunctor.obj.{succ u1, max (succ u4) (succ u1), u2, max (max (max u4 u3) u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u1, max u4 u1, u2, max (max (max u4 u3) u2) u1} C _inst_3 (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.const.{u3, u1, u4, u2} J _inst_2 C _inst_3)) (CategoryTheory.Limits.initial.{u1, u2} C _inst_3 _inst_4)) (CategoryTheory.Limits.instHasColimitObjToQuiverToCategoryStructFunctorToQuiverToCategoryStructCategoryToPrefunctorConstInitial.{u4, u3, u2, u1} J _inst_2 C _inst_3 _inst_4) j) (CategoryTheory.Iso.hom.{u1, u2} C _inst_3 (CategoryTheory.Limits.colimit.{u3, u4, u1, u2} J _inst_2 C _inst_3 (Prefunctor.obj.{succ u1, max (succ u4) (succ u1), u2, max (max (max u4 u3) u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_3)) (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u4 u1, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3))) (CategoryTheory.Functor.toPrefunctor.{u1, max u4 u1, u2, max (max (max u4 u3) u2) u1} C _inst_3 (CategoryTheory.Functor.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.category.{u3, u1, u4, u2} J _inst_2 C _inst_3) (CategoryTheory.Functor.const.{u3, u1, u4, u2} J _inst_2 C _inst_3)) (CategoryTheory.Limits.initial.{u1, u2} C _inst_3 _inst_4)) (CategoryTheory.Limits.instHasColimitObjToQuiverToCategoryStructFunctorToQuiverToCategoryStructCategoryToPrefunctorConstInitial.{u4, u3, u2, u1} J _inst_2 C _inst_3 _inst_4)) (CategoryTheory.Limits.initial.{u1, u2} C _inst_3 _inst_4) (CategoryTheory.Limits.colimitConstInitial.{u4, u3, u2, u1} J _inst_2 C _inst_3 _inst_4))) (CategoryTheory.Limits.initial.to.{u1, u2} C _inst_3 _inst_4 (CategoryTheory.Limits.initial.{u1, u2} C _inst_3 _inst_4))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.ι_colimit_const_initial_hom CategoryTheory.Limits.ι_colimitConstInitial_homₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C]
     {j : J} :
     colimit.ι ((CategoryTheory.Functor.const J).obj (⊥_ C)) j ≫ colimitConstInitial.Hom =

f4758115

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -98,7 +98,7 @@ def IsTerminal.ofUnique (Y : C) [h : ∀ X : C, Unique (X ⟶ Y)] : IsTerminal Y
 
 /- warning: category_theory.limits.is_terminal_top -> CategoryTheory.Limits.isTerminalTop is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_2)], CategoryTheory.Limits.IsTerminal.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))
+  forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_2)], CategoryTheory.Limits.IsTerminal.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_2) _inst_3))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_2)], CategoryTheory.Limits.IsTerminal.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_terminal_top CategoryTheory.Limits.isTerminalTopₓ'. -/
@@ -146,7 +146,7 @@ def IsInitial.ofUnique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : IsInitial X
 
 /- warning: category_theory.limits.is_initial_bot -> CategoryTheory.Limits.isInitialBot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_2)], CategoryTheory.Limits.IsInitial.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))
+  forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_2)], CategoryTheory.Limits.IsInitial.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_2) _inst_3))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_2)], CategoryTheory.Limits.IsInitial.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_initial_bot CategoryTheory.Limits.isInitialBotₓ'. -/

f4758115

bump to nightly-2023-04-20-00

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

d6678ca6

Diff

@@ -120,7 +120,7 @@ def IsTerminal.ofIso {Y Z : C} (hY : IsTerminal Y) (i : Y ≅ Z) : IsTerminal Z
 lean 3 declaration is
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 but is expected to have type
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u1} (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.const.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1)) X)) h._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2136.2149)]) (CategoryTheory.Discrete.mk.{0} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2193) (fun (a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2108 : PEmpty.{1}) => PEmpty.casesOn.{succ u1, 1} (fun (t._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2164 : PEmpty.{1}) => (Eq.{1} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2108 t._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2164) -> ([mdata noImplicitLambda:1 Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.Category.toCategoryStruct.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 F) (CategoryTheory.Discrete.mk.{0} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2108)) (Prefunctor.obj.{1, succ u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.Category.toCategoryStruct.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.const.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1)) X)) (CategoryTheory.Discrete.mk.{0} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2108))])) a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2108 (Eq.refl.{1} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2108))) (Prefunctor.map.{1, succ u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.Category.toCategoryStruct.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.const.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1)) X)) (CategoryTheory.Discrete.mk.{0} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2193) Y f))])) a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2193 (Eq.refl.{1} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2193)))))) (forall (Y : C), Unique.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_initial_equiv_unique CategoryTheory.Limits.isInitialEquivUniqueₓ'. -/
 /-- An object `X` is initial iff for every `Y` there is a unique morphism `X ⟶ Y`. -/
 def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :

f4758115

bump to nightly-2023-03-11-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

cd44fb92

Diff

@@ -72,7 +72,7 @@ abbrev IsInitial (X : C) :=
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (F : CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (Y : C), Equiv.{max 1 (succ u2) (succ u1), max (succ u2) (succ u1)} (CategoryTheory.Limits.IsLimit.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 F (CategoryTheory.Limits.Cone.mk.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 F Y (CategoryTheory.NatTrans.mk.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.const.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) Y) F (CategoryTheory.Limits.isTerminalEquivUnique._aux1.{u2, u1} C _inst_1 F Y) (CategoryTheory.Limits.isTerminalEquivUnique._proof_1.{u2, u1} C _inst_1 F Y)))) (forall (X : C), Unique.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y))
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] (F : CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (Y : C), Equiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (CategoryTheory.Limits.IsLimit.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 F (CategoryTheory.Limits.Cone.mk.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 F Y (CategoryTheory.NatTrans.mk.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.const.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1)) Y) F (fun (h._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.852 : CategoryTheory.Discrete.{0} PEmpty.{1}) => CategoryTheory.Limits.asEmptyCone.match_1.{succ u1} (fun (h._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.852.864 : CategoryTheory.Discrete.{0} PEmpty.{1}) => [mdata noImplicitLambda:1 Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.Category.toCategoryStruct.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.const.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1)) Y)) h._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.852.864) (Prefunctor.obj.{1, succ u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.Category.toCategoryStruct.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 F) h._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.852.864)]) h._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.852 (fun (a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.824 : PEmpty.{1}) => PEmpty.casesOn.{succ u1, 1} (fun (t._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.879 : PEmpty.{1}) => (Eq.{1} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.824 t._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.879) -> ([mdata noImplicitLambda:1 Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) 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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_terminal_equiv_unique CategoryTheory.Limits.isTerminalEquivUniqueₓ'. -/
 /-- An object `Y` is terminal iff for every `X` there is a unique morphism `X ⟶ Y`. -/
 def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
@@ -120,7 +120,7 @@ def IsTerminal.ofIso {Y Z : C} (hY : IsTerminal Y) (i : Y ≅ Z) : IsTerminal Z
 lean 3 declaration is
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 but is expected to have type
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C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 F) h._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2193.2205) (Prefunctor.obj.{1, succ u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.Category.toCategoryStruct.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}))) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) 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X)) h._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2127.2140)]) (CategoryTheory.Discrete.mk.{0} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2184) (fun (a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2099 : PEmpty.{1}) => PEmpty.casesOn.{succ u1, 1} (fun (t._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2155 : PEmpty.{1}) => (Eq.{1} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2099 t._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2155) -> ([mdata noImplicitLambda:1 Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.Category.toCategoryStruct.{0, 0} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}))) C 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_inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.Functor.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1) (CategoryTheory.Functor.const.{0, u1, 0, u2} (CategoryTheory.Discrete.{0} PEmpty.{1}) (CategoryTheory.discreteCategory.{0} PEmpty.{1}) C _inst_1)) X)) (CategoryTheory.Discrete.mk.{0} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2184) Y f))])) a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2184 (Eq.refl.{1} PEmpty.{1} a._@.Mathlib.CategoryTheory.Limits.Shapes.Terminal._hyg.2184)))))) (forall (Y : C), Unique.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_initial_equiv_unique CategoryTheory.Limits.isInitialEquivUniqueₓ'. -/
 /-- An object `X` is initial iff for every `Y` there is a unique morphism `X ⟶ Y`. -/
 def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :

f4758115

bump to nightly-2023-03-09-03

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

061741a1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module category_theory.limits.shapes.terminal
-! leanprover-community/mathlib commit 239d882c4fb58361ee8b3b39fb2091320edef10a
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.CategoryTheory.Category.Preorder
 /-!
 # Initial and terminal objects in a category.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## References
 * [Stacks: Initial and final objects](https://stacks.math.columbia.edu/tag/002B)
 -/

239d882c

bump to nightly-2023-03-02-10

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

01978261

Diff

@@ -33,30 +33,44 @@ variable {C : Type u₁} [Category.{v₁} C]
 
 attribute [local tidy] tactic.discrete_cases
 
+#print CategoryTheory.Limits.asEmptyCone /-
 /-- Construct a cone for the empty diagram given an object. -/
 @[simps]
 def asEmptyCone (X : C) : Cone (Functor.empty.{0} C) :=
   { pt
     π := by tidy }
 #align category_theory.limits.as_empty_cone CategoryTheory.Limits.asEmptyCone
+-/
 
+#print CategoryTheory.Limits.asEmptyCocone /-
 /-- Construct a cocone for the empty diagram given an object. -/
 @[simps]
 def asEmptyCocone (X : C) : Cocone (Functor.empty.{0} C) :=
   { pt
     ι := by tidy }
 #align category_theory.limits.as_empty_cocone CategoryTheory.Limits.asEmptyCocone
+-/
 
+#print CategoryTheory.Limits.IsTerminal /-
 /-- `X` is terminal if the cone it induces on the empty diagram is limiting. -/
 abbrev IsTerminal (X : C) :=
   IsLimit (asEmptyCone X)
 #align category_theory.limits.is_terminal CategoryTheory.Limits.IsTerminal
+-/
 
+#print CategoryTheory.Limits.IsInitial /-
 /-- `X` is initial if the cocone it induces on the empty diagram is colimiting. -/
 abbrev IsInitial (X : C) :=
   IsColimit (asEmptyCocone X)
 #align category_theory.limits.is_initial CategoryTheory.Limits.IsInitial
+-/
 
+/- warning: category_theory.limits.is_terminal_equiv_unique -> CategoryTheory.Limits.isTerminalEquivUnique is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_terminal_equiv_unique CategoryTheory.Limits.isTerminalEquivUniqueₓ'. -/
 /-- An object `Y` is terminal iff for every `X` there is a unique morphism `X ⟶ Y`. -/
 def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
     IsLimit (⟨Y, by tidy⟩ : Cone F) ≃ ∀ X : C, Unique (X ⟶ Y)
@@ -71,24 +85,40 @@ def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
   right_inv := by tidy
 #align category_theory.limits.is_terminal_equiv_unique CategoryTheory.Limits.isTerminalEquivUnique
 
+#print CategoryTheory.Limits.IsTerminal.ofUnique /-
 /-- An object `Y` is terminal if for every `X` there is a unique morphism `X ⟶ Y`
     (as an instance). -/
 def IsTerminal.ofUnique (Y : C) [h : ∀ X : C, Unique (X ⟶ Y)] : IsTerminal Y
     where lift s := (h s.pt).default
 #align category_theory.limits.is_terminal.of_unique CategoryTheory.Limits.IsTerminal.ofUnique
+-/
 
+/- warning: category_theory.limits.is_terminal_top -> CategoryTheory.Limits.isTerminalTop is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_2)], CategoryTheory.Limits.IsTerminal.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_2)], CategoryTheory.Limits.IsTerminal.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_terminal_top CategoryTheory.Limits.isTerminalTopₓ'. -/
 /-- If `α` is a preorder with top, then `⊤` is a terminal object. -/
 def isTerminalTop {α : Type _} [Preorder α] [OrderTop α] : IsTerminal (⊤ : α) :=
   IsTerminal.ofUnique _
 #align category_theory.limits.is_terminal_top CategoryTheory.Limits.isTerminalTop
 
+#print CategoryTheory.Limits.IsTerminal.ofIso /-
 /-- Transport a term of type `is_terminal` across an isomorphism. -/
 def IsTerminal.ofIso {Y Z : C} (hY : IsTerminal Y) (i : Y ≅ Z) : IsTerminal Z :=
   IsLimit.ofIsoLimit hY
     { Hom := { Hom := i.Hom }
       inv := { Hom := i.inv } }
 #align category_theory.limits.is_terminal.of_iso CategoryTheory.Limits.IsTerminal.ofIso
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_initial_equiv_unique CategoryTheory.Limits.isInitialEquivUniqueₓ'. -/
 /-- An object `X` is initial iff for every `Y` there is a unique morphism `X ⟶ Y`. -/
 def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :
     IsColimit (⟨X, by tidy⟩ : Cocone F) ≃ ∀ Y : C, Unique (X ⟶ Y)
@@ -103,85 +133,120 @@ def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :
   right_inv := by tidy
 #align category_theory.limits.is_initial_equiv_unique CategoryTheory.Limits.isInitialEquivUnique
 
+#print CategoryTheory.Limits.IsInitial.ofUnique /-
 /-- An object `X` is initial if for every `Y` there is a unique morphism `X ⟶ Y`
     (as an instance). -/
 def IsInitial.ofUnique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : IsInitial X
     where desc s := (h s.pt).default
 #align category_theory.limits.is_initial.of_unique CategoryTheory.Limits.IsInitial.ofUnique
+-/
 
+/- warning: category_theory.limits.is_initial_bot -> CategoryTheory.Limits.isInitialBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_2)], CategoryTheory.Limits.IsInitial.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_2)], CategoryTheory.Limits.IsInitial.{u1, u1} α (Preorder.smallCategory.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_initial_bot CategoryTheory.Limits.isInitialBotₓ'. -/
 /-- If `α` is a preorder with bot, then `⊥` is an initial object. -/
 def isInitialBot {α : Type _} [Preorder α] [OrderBot α] : IsInitial (⊥ : α) :=
   IsInitial.ofUnique _
 #align category_theory.limits.is_initial_bot CategoryTheory.Limits.isInitialBot
 
+#print CategoryTheory.Limits.IsInitial.ofIso /-
 /-- Transport a term of type `is_initial` across an isomorphism. -/
 def IsInitial.ofIso {X Y : C} (hX : IsInitial X) (i : X ≅ Y) : IsInitial Y :=
   IsColimit.ofIsoColimit hX
     { Hom := { Hom := i.Hom }
       inv := { Hom := i.inv } }
 #align category_theory.limits.is_initial.of_iso CategoryTheory.Limits.IsInitial.ofIso
+-/
 
+#print CategoryTheory.Limits.IsTerminal.from /-
 /-- Give the morphism to a terminal object from any other. -/
 def IsTerminal.from {X : C} (t : IsTerminal X) (Y : C) : Y ⟶ X :=
   t.lift (asEmptyCone Y)
 #align category_theory.limits.is_terminal.from CategoryTheory.Limits.IsTerminal.from
+-/
 
+#print CategoryTheory.Limits.IsTerminal.hom_ext /-
 /-- Any two morphisms to a terminal object are equal. -/
 theorem IsTerminal.hom_ext {X Y : C} (t : IsTerminal X) (f g : Y ⟶ X) : f = g :=
   t.hom_ext (by tidy)
 #align category_theory.limits.is_terminal.hom_ext CategoryTheory.Limits.IsTerminal.hom_ext
+-/
 
+#print CategoryTheory.Limits.IsTerminal.comp_from /-
 @[simp]
 theorem IsTerminal.comp_from {Z : C} (t : IsTerminal Z) {X Y : C} (f : X ⟶ Y) :
     f ≫ t.from Y = t.from X :=
   t.hom_ext _ _
 #align category_theory.limits.is_terminal.comp_from CategoryTheory.Limits.IsTerminal.comp_from
+-/
 
+#print CategoryTheory.Limits.IsTerminal.from_self /-
 @[simp]
 theorem IsTerminal.from_self {X : C} (t : IsTerminal X) : t.from X = 𝟙 X :=
   t.hom_ext _ _
 #align category_theory.limits.is_terminal.from_self CategoryTheory.Limits.IsTerminal.from_self
+-/
 
+#print CategoryTheory.Limits.IsInitial.to /-
 /-- Give the morphism from an initial object to any other. -/
 def IsInitial.to {X : C} (t : IsInitial X) (Y : C) : X ⟶ Y :=
   t.desc (asEmptyCocone Y)
 #align category_theory.limits.is_initial.to CategoryTheory.Limits.IsInitial.to
+-/
 
+#print CategoryTheory.Limits.IsInitial.hom_ext /-
 /-- Any two morphisms from an initial object are equal. -/
 theorem IsInitial.hom_ext {X Y : C} (t : IsInitial X) (f g : X ⟶ Y) : f = g :=
   t.hom_ext (by tidy)
 #align category_theory.limits.is_initial.hom_ext CategoryTheory.Limits.IsInitial.hom_ext
+-/
 
+#print CategoryTheory.Limits.IsInitial.to_comp /-
 @[simp]
 theorem IsInitial.to_comp {X : C} (t : IsInitial X) {Y Z : C} (f : Y ⟶ Z) : t.to Y ≫ f = t.to Z :=
   t.hom_ext _ _
 #align category_theory.limits.is_initial.to_comp CategoryTheory.Limits.IsInitial.to_comp
+-/
 
+#print CategoryTheory.Limits.IsInitial.to_self /-
 @[simp]
 theorem IsInitial.to_self {X : C} (t : IsInitial X) : t.to X = 𝟙 X :=
   t.hom_ext _ _
 #align category_theory.limits.is_initial.to_self CategoryTheory.Limits.IsInitial.to_self
+-/
 
+#print CategoryTheory.Limits.IsTerminal.isSplitMono_from /-
 /-- Any morphism from a terminal object is split mono. -/
 theorem IsTerminal.isSplitMono_from {X Y : C} (t : IsTerminal X) (f : X ⟶ Y) : IsSplitMono f :=
   IsSplitMono.mk' ⟨t.from _, t.hom_ext _ _⟩
 #align category_theory.limits.is_terminal.is_split_mono_from CategoryTheory.Limits.IsTerminal.isSplitMono_from
+-/
 
+#print CategoryTheory.Limits.IsInitial.isSplitEpi_to /-
 /-- Any morphism to an initial object is split epi. -/
 theorem IsInitial.isSplitEpi_to {X Y : C} (t : IsInitial X) (f : Y ⟶ X) : IsSplitEpi f :=
   IsSplitEpi.mk' ⟨t.to _, t.hom_ext _ _⟩
 #align category_theory.limits.is_initial.is_split_epi_to CategoryTheory.Limits.IsInitial.isSplitEpi_to
+-/
 
+#print CategoryTheory.Limits.IsTerminal.mono_from /-
 /-- Any morphism from a terminal object is mono. -/
 theorem IsTerminal.mono_from {X Y : C} (t : IsTerminal X) (f : X ⟶ Y) : Mono f := by
   haveI := t.is_split_mono_from f <;> infer_instance
 #align category_theory.limits.is_terminal.mono_from CategoryTheory.Limits.IsTerminal.mono_from
+-/
 
+#print CategoryTheory.Limits.IsInitial.epi_to /-
 /-- Any morphism to an initial object is epi. -/
 theorem IsInitial.epi_to {X Y : C} (t : IsInitial X) (f : Y ⟶ X) : Epi f := by
   haveI := t.is_split_epi_to f <;> infer_instance
 #align category_theory.limits.is_initial.epi_to CategoryTheory.Limits.IsInitial.epi_to
+-/
 
+#print CategoryTheory.Limits.IsTerminal.uniqueUpToIso /-
 /-- If `T` and `T'` are terminal, they are isomorphic. -/
 @[simps]
 def IsTerminal.uniqueUpToIso {T T' : C} (hT : IsTerminal T) (hT' : IsTerminal T') : T ≅ T'
@@ -189,7 +254,9 @@ def IsTerminal.uniqueUpToIso {T T' : C} (hT : IsTerminal T) (hT' : IsTerminal T'
   Hom := hT'.from _
   inv := hT.from _
 #align category_theory.limits.is_terminal.unique_up_to_iso CategoryTheory.Limits.IsTerminal.uniqueUpToIso
+-/
 
+#print CategoryTheory.Limits.IsInitial.uniqueUpToIso /-
 /-- If `I` and `I'` are initial, they are isomorphic. -/
 @[simps]
 def IsInitial.uniqueUpToIso {I I' : C} (hI : IsInitial I) (hI' : IsInitial I') : I ≅ I'
@@ -197,27 +264,33 @@ def IsInitial.uniqueUpToIso {I I' : C} (hI : IsInitial I) (hI' : IsInitial I') :
   Hom := hI.to _
   inv := hI'.to _
 #align category_theory.limits.is_initial.unique_up_to_iso CategoryTheory.Limits.IsInitial.uniqueUpToIso
+-/
 
 variable (C)
 
+#print CategoryTheory.Limits.HasTerminal /-
 /-- A category has a terminal object if it has a limit over the empty diagram.
 Use `has_terminal_of_unique` to construct instances.
 -/
 abbrev HasTerminal :=
   HasLimitsOfShape (Discrete.{0} PEmpty) C
 #align category_theory.limits.has_terminal CategoryTheory.Limits.HasTerminal
+-/
 
+#print CategoryTheory.Limits.HasInitial /-
 /-- A category has an initial object if it has a colimit over the empty diagram.
 Use `has_initial_of_unique` to construct instances.
 -/
 abbrev HasInitial :=
   HasColimitsOfShape (Discrete.{0} PEmpty) C
 #align category_theory.limits.has_initial CategoryTheory.Limits.HasInitial
+-/
 
 section Univ
 
 variable (X : C) {F₁ : Discrete.{w} PEmpty ⥤ C} {F₂ : Discrete.{w'} PEmpty ⥤ C}
 
+#print CategoryTheory.Limits.isLimitChangeEmptyCone /-
 /-- Being terminal is independent of the empty diagram, its universe, and the cone over it,
     as long as the cone points are isomorphic. -/
 def isLimitChangeEmptyCone {c₁ : Cone F₁} (hl : IsLimit c₁) (c₂ : Cone F₂) (hi : c₁.pt ≅ c₂.pt) :
@@ -228,7 +301,9 @@ def isLimitChangeEmptyCone {c₁ : Cone F₁} (hl : IsLimit c₁) (c₂ : Cone F
     erw [← hl.uniq ⟨c.X, by tidy⟩ (f ≫ hi.inv) fun j => j.as.elim]
     simp
 #align category_theory.limits.is_limit_change_empty_cone CategoryTheory.Limits.isLimitChangeEmptyCone
+-/
 
+#print CategoryTheory.Limits.isLimitEmptyConeEquiv /-
 /-- Replacing an empty cone in `is_limit` by another with the same cone point
     is an equivalence. -/
 def isLimitEmptyConeEquiv (c₁ : Cone F₁) (c₂ : Cone F₂) (h : c₁.pt ≅ c₂.pt) :
@@ -239,20 +314,26 @@ def isLimitEmptyConeEquiv (c₁ : Cone F₁) (c₂ : Cone F₂) (h : c₁.pt ≅
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_limit_empty_cone_equiv CategoryTheory.Limits.isLimitEmptyConeEquiv
+-/
 
-theorem has_terminal_change_diagram (h : HasLimit F₁) : HasLimit F₂ :=
+#print CategoryTheory.Limits.hasTerminalChangeDiagram /-
+theorem hasTerminalChangeDiagram (h : HasLimit F₁) : HasLimit F₂ :=
   ⟨⟨⟨⟨limit F₁, by tidy⟩, isLimitChangeEmptyCone C (limit.isLimit F₁) _ (eqToIso rfl)⟩⟩⟩
-#align category_theory.limits.has_terminal_change_diagram CategoryTheory.Limits.has_terminal_change_diagram
+#align category_theory.limits.has_terminal_change_diagram CategoryTheory.Limits.hasTerminalChangeDiagram
+-/
 
-theorem has_terminal_change_universe [h : HasLimitsOfShape (Discrete.{w} PEmpty) C] :
+#print CategoryTheory.Limits.hasTerminalChangeUniverse /-
+theorem hasTerminalChangeUniverse [h : HasLimitsOfShape (Discrete.{w} PEmpty) C] :
     HasLimitsOfShape (Discrete.{w'} PEmpty) C :=
   {
     HasLimit := fun J =>
-      has_terminal_change_diagram C
+      hasTerminalChangeDiagram C
         (let f := h.1
         f (Functor.empty C)) }
-#align category_theory.limits.has_terminal_change_universe CategoryTheory.Limits.has_terminal_change_universe
+#align category_theory.limits.has_terminal_change_universe CategoryTheory.Limits.hasTerminalChangeUniverse
+-/
 
+#print CategoryTheory.Limits.isColimitChangeEmptyCocone /-
 /-- Being initial is independent of the empty diagram, its universe, and the cocone over it,
     as long as the cocone points are isomorphic. -/
 def isColimitChangeEmptyCocone {c₁ : Cocone F₁} (hl : IsColimit c₁) (c₂ : Cocone F₂)
@@ -264,7 +345,9 @@ def isColimitChangeEmptyCocone {c₁ : Cocone F₁} (hl : IsColimit c₁) (c₂
     erw [← hl.uniq ⟨c.X, by tidy⟩ (hi.hom ≫ f) fun j => j.as.elim]
     simp
 #align category_theory.limits.is_colimit_change_empty_cocone CategoryTheory.Limits.isColimitChangeEmptyCocone
+-/
 
+#print CategoryTheory.Limits.isColimitEmptyCoconeEquiv /-
 /-- Replacing an empty cocone in `is_colimit` by another with the same cocone point
     is an equivalence. -/
 def isColimitEmptyCoconeEquiv (c₁ : Cocone F₁) (c₂ : Cocone F₂) (h : c₁.pt ≅ c₂.pt) :
@@ -275,22 +358,28 @@ def isColimitEmptyCoconeEquiv (c₁ : Cocone F₁) (c₂ : Cocone F₂) (h : c
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_colimit_empty_cocone_equiv CategoryTheory.Limits.isColimitEmptyCoconeEquiv
+-/
 
-theorem has_initial_change_diagram (h : HasColimit F₁) : HasColimit F₂ :=
+#print CategoryTheory.Limits.hasInitialChangeDiagram /-
+theorem hasInitialChangeDiagram (h : HasColimit F₁) : HasColimit F₂ :=
   ⟨⟨⟨⟨colimit F₁, by tidy⟩, isColimitChangeEmptyCocone C (colimit.isColimit F₁) _ (eqToIso rfl)⟩⟩⟩
-#align category_theory.limits.has_initial_change_diagram CategoryTheory.Limits.has_initial_change_diagram
+#align category_theory.limits.has_initial_change_diagram CategoryTheory.Limits.hasInitialChangeDiagram
+-/
 
-theorem has_initial_change_universe [h : HasColimitsOfShape (Discrete.{w} PEmpty) C] :
+#print CategoryTheory.Limits.hasInitialChangeUniverse /-
+theorem hasInitialChangeUniverse [h : HasColimitsOfShape (Discrete.{w} PEmpty) C] :
     HasColimitsOfShape (Discrete.{w'} PEmpty) C :=
   {
     HasColimit := fun J =>
-      has_initial_change_diagram C
+      hasInitialChangeDiagram C
         (let f := h.1
         f (Functor.empty C)) }
-#align category_theory.limits.has_initial_change_universe CategoryTheory.Limits.has_initial_change_universe
+#align category_theory.limits.has_initial_change_universe CategoryTheory.Limits.hasInitialChangeUniverse
+-/
 
 end Univ
 
+#print CategoryTheory.Limits.terminal /-
 /-- An arbitrary choice of terminal object, if one exists.
 You can use the notation `⊤_ C`.
 This object is characterized by having a unique morphism from any object.
@@ -298,7 +387,9 @@ This object is characterized by having a unique morphism from any object.
 abbrev terminal [HasTerminal C] : C :=
   limit (Functor.empty.{0} C)
 #align category_theory.limits.terminal CategoryTheory.Limits.terminal
+-/
 
+#print CategoryTheory.Limits.initial /-
 /-- An arbitrary choice of initial object, if one exists.
 You can use the notation `⊥_ C`.
 This object is characterized by having a unique morphism to any object.
@@ -306,6 +397,7 @@ This object is characterized by having a unique morphism to any object.
 abbrev initial [HasInitial C] : C :=
   colimit (Functor.empty.{0} C)
 #align category_theory.limits.initial CategoryTheory.Limits.initial
+-/
 
 -- mathport name: «expr⊤_ »
 notation "⊤_ " C:20 => terminal C
@@ -317,129 +409,177 @@ section
 
 variable {C}
 
+#print CategoryTheory.Limits.hasTerminal_of_unique /-
 /-- We can more explicitly show that a category has a terminal object by specifying the object,
 and showing there is a unique morphism to it from any other object. -/
 theorem hasTerminal_of_unique (X : C) [h : ∀ Y : C, Unique (Y ⟶ X)] : HasTerminal C :=
   { HasLimit := fun F => HasLimit.mk ⟨_, (isTerminalEquivUnique F X).invFun h⟩ }
 #align category_theory.limits.has_terminal_of_unique CategoryTheory.Limits.hasTerminal_of_unique
+-/
 
+#print CategoryTheory.Limits.IsTerminal.hasTerminal /-
 theorem IsTerminal.hasTerminal {X : C} (h : IsTerminal X) : HasTerminal C :=
   { HasLimit := fun F => HasLimit.mk ⟨⟨X, by tidy⟩, isLimitChangeEmptyCone _ h _ (Iso.refl _)⟩ }
 #align category_theory.limits.is_terminal.has_terminal CategoryTheory.Limits.IsTerminal.hasTerminal
+-/
 
+#print CategoryTheory.Limits.hasInitial_of_unique /-
 /-- We can more explicitly show that a category has an initial object by specifying the object,
 and showing there is a unique morphism from it to any other object. -/
 theorem hasInitial_of_unique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : HasInitial C :=
   { HasColimit := fun F => HasColimit.mk ⟨_, (isInitialEquivUnique F X).invFun h⟩ }
 #align category_theory.limits.has_initial_of_unique CategoryTheory.Limits.hasInitial_of_unique
+-/
 
+#print CategoryTheory.Limits.IsInitial.hasInitial /-
 theorem IsInitial.hasInitial {X : C} (h : IsInitial X) : HasInitial C :=
   {
     HasColimit := fun F =>
       HasColimit.mk ⟨⟨X, by tidy⟩, isColimitChangeEmptyCocone _ h _ (Iso.refl _)⟩ }
 #align category_theory.limits.is_initial.has_initial CategoryTheory.Limits.IsInitial.hasInitial
+-/
 
+#print CategoryTheory.Limits.terminal.from /-
 /-- The map from an object to the terminal object. -/
 abbrev terminal.from [HasTerminal C] (P : C) : P ⟶ ⊤_ C :=
   limit.lift (Functor.empty C) (asEmptyCone P)
 #align category_theory.limits.terminal.from CategoryTheory.Limits.terminal.from
+-/
 
+#print CategoryTheory.Limits.initial.to /-
 /-- The map to an object from the initial object. -/
 abbrev initial.to [HasInitial C] (P : C) : ⊥_ C ⟶ P :=
   colimit.desc (Functor.empty C) (asEmptyCocone P)
 #align category_theory.limits.initial.to CategoryTheory.Limits.initial.to
+-/
 
+#print CategoryTheory.Limits.terminalIsTerminal /-
 /-- A terminal object is terminal. -/
 def terminalIsTerminal [HasTerminal C] : IsTerminal (⊤_ C) where lift s := terminal.from _
 #align category_theory.limits.terminal_is_terminal CategoryTheory.Limits.terminalIsTerminal
+-/
 
+#print CategoryTheory.Limits.initialIsInitial /-
 /-- An initial object is initial. -/
 def initialIsInitial [HasInitial C] : IsInitial (⊥_ C) where desc s := initial.to _
 #align category_theory.limits.initial_is_initial CategoryTheory.Limits.initialIsInitial
+-/
 
+#print CategoryTheory.Limits.uniqueToTerminal /-
 instance uniqueToTerminal [HasTerminal C] (P : C) : Unique (P ⟶ ⊤_ C) :=
   isTerminalEquivUnique _ (⊤_ C) terminalIsTerminal P
 #align category_theory.limits.unique_to_terminal CategoryTheory.Limits.uniqueToTerminal
+-/
 
+#print CategoryTheory.Limits.uniqueFromInitial /-
 instance uniqueFromInitial [HasInitial C] (P : C) : Unique (⊥_ C ⟶ P) :=
   isInitialEquivUnique _ (⊥_ C) initialIsInitial P
 #align category_theory.limits.unique_from_initial CategoryTheory.Limits.uniqueFromInitial
+-/
 
+#print CategoryTheory.Limits.terminal.comp_from /-
 @[simp]
 theorem terminal.comp_from [HasTerminal C] {P Q : C} (f : P ⟶ Q) :
     f ≫ terminal.from Q = terminal.from P := by tidy
 #align category_theory.limits.terminal.comp_from CategoryTheory.Limits.terminal.comp_from
+-/
 
+#print CategoryTheory.Limits.initial.to_comp /-
 @[simp]
 theorem initial.to_comp [HasInitial C] {P Q : C} (f : P ⟶ Q) : initial.to P ≫ f = initial.to Q := by
   tidy
 #align category_theory.limits.initial.to_comp CategoryTheory.Limits.initial.to_comp
+-/
 
+#print CategoryTheory.Limits.initialIsoIsInitial /-
 /-- The (unique) isomorphism between the chosen initial object and any other initial object. -/
 @[simp]
 def initialIsoIsInitial [HasInitial C] {P : C} (t : IsInitial P) : ⊥_ C ≅ P :=
   initialIsInitial.uniqueUpToIso t
 #align category_theory.limits.initial_iso_is_initial CategoryTheory.Limits.initialIsoIsInitial
+-/
 
+#print CategoryTheory.Limits.terminalIsoIsTerminal /-
 /-- The (unique) isomorphism between the chosen terminal object and any other terminal object. -/
 @[simp]
 def terminalIsoIsTerminal [HasTerminal C] {P : C} (t : IsTerminal P) : ⊤_ C ≅ P :=
   terminalIsTerminal.uniqueUpToIso t
 #align category_theory.limits.terminal_iso_is_terminal CategoryTheory.Limits.terminalIsoIsTerminal
+-/
 
+#print CategoryTheory.Limits.terminal.isSplitMono_from /-
 /-- Any morphism from a terminal object is split mono. -/
 instance terminal.isSplitMono_from {Y : C} [HasTerminal C] (f : ⊤_ C ⟶ Y) : IsSplitMono f :=
   IsTerminal.isSplitMono_from terminalIsTerminal _
 #align category_theory.limits.terminal.is_split_mono_from CategoryTheory.Limits.terminal.isSplitMono_from
+-/
 
+#print CategoryTheory.Limits.initial.isSplitEpi_to /-
 /-- Any morphism to an initial object is split epi. -/
 instance initial.isSplitEpi_to {Y : C} [HasInitial C] (f : Y ⟶ ⊥_ C) : IsSplitEpi f :=
   IsInitial.isSplitEpi_to initialIsInitial _
 #align category_theory.limits.initial.is_split_epi_to CategoryTheory.Limits.initial.isSplitEpi_to
+-/
 
+#print CategoryTheory.Limits.terminalOpOfInitial /-
 /-- An initial object is terminal in the opposite category. -/
 def terminalOpOfInitial {X : C} (t : IsInitial X) : IsTerminal (Opposite.op X)
     where
   lift s := (t.to s.pt.unop).op
   uniq s m w := Quiver.Hom.unop_inj (t.hom_ext _ _)
 #align category_theory.limits.terminal_op_of_initial CategoryTheory.Limits.terminalOpOfInitial
+-/
 
+#print CategoryTheory.Limits.terminalUnopOfInitial /-
 /-- An initial object in the opposite category is terminal in the original category. -/
 def terminalUnopOfInitial {X : Cᵒᵖ} (t : IsInitial X) : IsTerminal X.unop
     where
   lift s := (t.to (Opposite.op s.pt)).unop
   uniq s m w := Quiver.Hom.op_inj (t.hom_ext _ _)
 #align category_theory.limits.terminal_unop_of_initial CategoryTheory.Limits.terminalUnopOfInitial
+-/
 
+#print CategoryTheory.Limits.initialOpOfTerminal /-
 /-- A terminal object is initial in the opposite category. -/
 def initialOpOfTerminal {X : C} (t : IsTerminal X) : IsInitial (Opposite.op X)
     where
   desc s := (t.from s.pt.unop).op
   uniq s m w := Quiver.Hom.unop_inj (t.hom_ext _ _)
 #align category_theory.limits.initial_op_of_terminal CategoryTheory.Limits.initialOpOfTerminal
+-/
 
+#print CategoryTheory.Limits.initialUnopOfTerminal /-
 /-- A terminal object in the opposite category is initial in the original category. -/
 def initialUnopOfTerminal {X : Cᵒᵖ} (t : IsTerminal X) : IsInitial X.unop
     where
   desc s := (t.from (Opposite.op s.pt)).unop
   uniq s m w := Quiver.Hom.op_inj (t.hom_ext _ _)
 #align category_theory.limits.initial_unop_of_terminal CategoryTheory.Limits.initialUnopOfTerminal
+-/
 
+#print CategoryTheory.Limits.hasInitial_op_of_hasTerminal /-
 instance hasInitial_op_of_hasTerminal [HasTerminal C] : HasInitial Cᵒᵖ :=
   (initialOpOfTerminal terminalIsTerminal).HasInitial
 #align category_theory.limits.has_initial_op_of_has_terminal CategoryTheory.Limits.hasInitial_op_of_hasTerminal
+-/
 
+#print CategoryTheory.Limits.hasTerminal_op_of_hasInitial /-
 instance hasTerminal_op_of_hasInitial [HasInitial C] : HasTerminal Cᵒᵖ :=
   (terminalOpOfInitial initialIsInitial).HasTerminal
 #align category_theory.limits.has_terminal_op_of_has_initial CategoryTheory.Limits.hasTerminal_op_of_hasInitial
+-/
 
+#print CategoryTheory.Limits.hasTerminal_of_hasInitial_op /-
 theorem hasTerminal_of_hasInitial_op [HasInitial Cᵒᵖ] : HasTerminal C :=
   (terminalUnopOfInitial initialIsInitial).HasTerminal
 #align category_theory.limits.has_terminal_of_has_initial_op CategoryTheory.Limits.hasTerminal_of_hasInitial_op
+-/
 
+#print CategoryTheory.Limits.hasInitial_of_hasTerminal_op /-
 theorem hasInitial_of_hasTerminal_op [HasTerminal Cᵒᵖ] : HasInitial C :=
   (initialUnopOfTerminal terminalIsTerminal).HasInitial
 #align category_theory.limits.has_initial_of_has_terminal_op CategoryTheory.Limits.hasInitial_of_hasTerminal_op
+-/
 
 instance {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C] :
     HasLimit ((CategoryTheory.Functor.const J).obj (⊤_ C)) :=
@@ -449,6 +589,12 @@ instance {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C] :
           π := { app := fun _ => terminal.from _ } }
       IsLimit := { lift := fun s => terminal.from _ } }
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.limit_const_terminal CategoryTheory.Limits.limitConstTerminalₓ'. -/
 /-- The limit of the constant `⊤_ C` functor is `⊤_ C`. -/
 @[simps Hom]
 def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C] :
@@ -461,6 +607,12 @@ def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasT
         π := { app := fun j => terminal.from _ } }
 #align category_theory.limits.limit_const_terminal CategoryTheory.Limits.limitConstTerminal
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.limit_const_terminal_inv_π CategoryTheory.Limits.limitConstTerminal_inv_πₓ'. -/
 @[simp, reassoc.1]
 theorem limitConstTerminal_inv_π {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C]
     {j : J} :
@@ -477,6 +629,12 @@ instance {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
           ι := { app := fun _ => initial.to _ } }
       IsColimit := { desc := fun s => initial.to _ } }
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.colimit_const_initial CategoryTheory.Limits.colimitConstInitialₓ'. -/
 /-- The colimit of the constant `⊥_ C` functor is `⊥_ C`. -/
 @[simps inv]
 def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
@@ -489,6 +647,12 @@ def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [Has
   inv := initial.to _
 #align category_theory.limits.colimit_const_initial CategoryTheory.Limits.colimitConstInitial
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.ι_colimit_const_initial_hom CategoryTheory.Limits.ι_colimitConstInitial_homₓ'. -/
 @[simp, reassoc.1]
 theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C]
     {j : J} :
@@ -497,6 +661,7 @@ theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Categ
   by ext ⟨⟨⟩⟩
 #align category_theory.limits.ι_colimit_const_initial_hom CategoryTheory.Limits.ι_colimitConstInitial_hom
 
+#print CategoryTheory.Limits.InitialMonoClass /-
 /-- A category is a `initial_mono_class` if the canonical morphism of an initial object is a
 monomorphism.  In practice, this is most useful when given an arbitrary morphism out of the chosen
 initial object, see `initial.mono_from`.
@@ -508,18 +673,24 @@ TODO: This is a condition satisfied by categories with zero objects and morphism
 class InitialMonoClass (C : Type u₁) [Category.{v₁} C] : Prop where
   isInitial_mono_from : ∀ {I} (X : C) (hI : IsInitial I), Mono (hI.to X)
 #align category_theory.limits.initial_mono_class CategoryTheory.Limits.InitialMonoClass
+-/
 
+#print CategoryTheory.Limits.IsInitial.mono_from /-
 theorem IsInitial.mono_from [InitialMonoClass C] {I} {X : C} (hI : IsInitial I) (f : I ⟶ X) :
     Mono f := by
   rw [hI.hom_ext f (hI.to X)]
   apply initial_mono_class.is_initial_mono_from
 #align category_theory.limits.is_initial.mono_from CategoryTheory.Limits.IsInitial.mono_from
+-/
 
+#print CategoryTheory.Limits.initial.mono_from /-
 instance (priority := 100) initial.mono_from [HasInitial C] [InitialMonoClass C] (X : C)
     (f : ⊥_ C ⟶ X) : Mono f :=
   initialIsInitial.mono_from f
 #align category_theory.limits.initial.mono_from CategoryTheory.Limits.initial.mono_from
+-/
 
+#print CategoryTheory.Limits.InitialMonoClass.of_isInitial /-
 /-- To show a category is a `initial_mono_class` it suffices to give an initial object such that
 every morphism out of it is a monomorphism. -/
 theorem InitialMonoClass.of_isInitial {I : C} (hI : IsInitial I) (h : ∀ X, Mono (hI.to X)) :
@@ -530,32 +701,45 @@ theorem InitialMonoClass.of_isInitial {I : C} (hI : IsInitial I) (h : ∀ X, Mon
       rw [hI'.hom_ext (hI'.to X) ((hI'.unique_up_to_iso hI).Hom ≫ hI.to X)]
       apply mono_comp }
 #align category_theory.limits.initial_mono_class.of_is_initial CategoryTheory.Limits.InitialMonoClass.of_isInitial
+-/
 
+#print CategoryTheory.Limits.InitialMonoClass.of_initial /-
 /-- To show a category is a `initial_mono_class` it suffices to show every morphism out of the
 initial object is a monomorphism. -/
 theorem InitialMonoClass.of_initial [HasInitial C] (h : ∀ X : C, Mono (initial.to X)) :
     InitialMonoClass C :=
   InitialMonoClass.of_isInitial initialIsInitial h
 #align category_theory.limits.initial_mono_class.of_initial CategoryTheory.Limits.InitialMonoClass.of_initial
+-/
 
+#print CategoryTheory.Limits.InitialMonoClass.of_isTerminal /-
 /-- To show a category is a `initial_mono_class` it suffices to show the unique morphism from an
 initial object to a terminal object is a monomorphism. -/
 theorem InitialMonoClass.of_isTerminal {I T : C} (hI : IsInitial I) (hT : IsTerminal T)
     (f : Mono (hI.to T)) : InitialMonoClass C :=
   InitialMonoClass.of_isInitial hI fun X => mono_of_mono_fac (hI.hom_ext (_ ≫ hT.from X) (hI.to T))
 #align category_theory.limits.initial_mono_class.of_is_terminal CategoryTheory.Limits.InitialMonoClass.of_isTerminal
+-/
 
+#print CategoryTheory.Limits.InitialMonoClass.of_terminal /-
 /-- To show a category is a `initial_mono_class` it suffices to show the unique morphism from the
 initial object to a terminal object is a monomorphism. -/
 theorem InitialMonoClass.of_terminal [HasInitial C] [HasTerminal C] (h : Mono (initial.to (⊤_ C))) :
     InitialMonoClass C :=
   InitialMonoClass.of_isTerminal initialIsInitial terminalIsTerminal h
 #align category_theory.limits.initial_mono_class.of_terminal CategoryTheory.Limits.InitialMonoClass.of_terminal
+-/
 
 section Comparison
 
 variable {D : Type u₂} [Category.{v₂} D] (G : C ⥤ D)
 
+/- warning: category_theory.limits.terminal_comparison -> CategoryTheory.Limits.terminalComparison is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) [_inst_3 : CategoryTheory.Limits.HasTerminal.{u1, u3} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasTerminal.{u2, u4} D _inst_2], Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G (CategoryTheory.Limits.terminal.{u1, u3} C _inst_1 _inst_3)) (CategoryTheory.Limits.terminal.{u2, u4} D _inst_2 _inst_4)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) [_inst_3 : CategoryTheory.Limits.HasTerminal.{u1, u3} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasTerminal.{u2, u4} D _inst_2], Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.terminal.{u1, u3} C _inst_1 _inst_3)) (CategoryTheory.Limits.terminal.{u2, u4} D _inst_2 _inst_4)
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.terminal_comparison CategoryTheory.Limits.terminalComparisonₓ'. -/
 /-- The comparison morphism from the image of a terminal object to the terminal object in the target
 category.
 This is an isomorphism iff `G` preserves terminal objects, see
@@ -565,6 +749,12 @@ def terminalComparison [HasTerminal C] [HasTerminal D] : G.obj (⊤_ C) ⟶ ⊤_
   terminal.from _
 #align category_theory.limits.terminal_comparison CategoryTheory.Limits.terminalComparison
 
+/- warning: category_theory.limits.initial_comparison -> CategoryTheory.Limits.initialComparison is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) [_inst_3 : CategoryTheory.Limits.HasInitial.{u1, u3} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasInitial.{u2, u4} D _inst_2], Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Limits.initial.{u2, u4} D _inst_2 _inst_4) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G (CategoryTheory.Limits.initial.{u1, u3} C _inst_1 _inst_3))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) [_inst_3 : CategoryTheory.Limits.HasInitial.{u1, u3} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasInitial.{u2, u4} D _inst_2], Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Limits.initial.{u2, u4} D _inst_2 _inst_4) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) (CategoryTheory.Limits.initial.{u1, u3} C _inst_1 _inst_3))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.initial_comparison CategoryTheory.Limits.initialComparisonₓ'. -/
 -- TODO: Show this is an isomorphism if and only if `G` preserves initial objects.
 /--
 The comparison morphism from the initial object in the target category to the image of the initial
@@ -578,6 +768,7 @@ end Comparison
 
 variable {J : Type u} [Category.{v} J]
 
+#print CategoryTheory.Limits.coneOfDiagramInitial /-
 /-- From a functor `F : J ⥤ C`, given an initial object of `J`, construct a cone for `J`.
 In `limit_of_diagram_initial` we show it is a limit cone. -/
 @[simps]
@@ -590,7 +781,9 @@ def coneOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) : Cone F
         dsimp
         rw [← F.map_comp, category.id_comp, tX.hom_ext (tX.to j ≫ k) (tX.to j')] }
 #align category_theory.limits.cone_of_diagram_initial CategoryTheory.Limits.coneOfDiagramInitial
+-/
 
+#print CategoryTheory.Limits.limitOfDiagramInitial /-
 /-- From a functor `F : J ⥤ C`, given an initial object of `J`, show the cone
 `cone_of_diagram_initial` is a limit. -/
 def limitOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) :
@@ -601,7 +794,14 @@ def limitOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) :
     rw [← w X, cone_of_diagram_initial_π_app, tX.hom_ext (tX.to X) (𝟙 _)]
     dsimp; simp
 #align category_theory.limits.limit_of_diagram_initial CategoryTheory.Limits.limitOfDiagramInitial
+-/
 
+/- warning: category_theory.limits.limit_of_initial -> CategoryTheory.Limits.limitOfInitial is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u2, u4} C] {J : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} J] (F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_2 C _inst_1) [_inst_3 : CategoryTheory.Limits.HasInitial.{u1, u3} J _inst_2] [_inst_4 : CategoryTheory.Limits.HasLimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F], CategoryTheory.Iso.{u2, u4} C _inst_1 (CategoryTheory.Limits.limit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_2 C _inst_1 F (CategoryTheory.Limits.initial.{u1, u3} J _inst_2 _inst_3))
+but is expected to have type
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u2, u4} C] {J : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} J] (F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_2 C _inst_1) [_inst_3 : CategoryTheory.Limits.HasInitial.{u1, u3} J _inst_2] [_inst_4 : CategoryTheory.Limits.HasLimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F], CategoryTheory.Iso.{u2, u4} C _inst_1 (CategoryTheory.Limits.limit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) (CategoryTheory.Limits.initial.{u1, u3} J _inst_2 _inst_3))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.limit_of_initial CategoryTheory.Limits.limitOfInitialₓ'. -/
 -- See note [dsimp, simp]
 -- This is reducible to allow usage of lemmas about `cone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has an initial object then the image of it is isomorphic
@@ -611,6 +811,12 @@ def limitOfInitial (F : J ⥤ C) [HasInitial J] [HasLimit F] : limit F ≅ F.obj
   IsLimit.conePointUniqueUpToIso (limit.isLimit _) (limitOfDiagramInitial initialIsInitial F)
 #align category_theory.limits.limit_of_initial CategoryTheory.Limits.limitOfInitial
 
+/- warning: category_theory.limits.cone_of_diagram_terminal -> CategoryTheory.Limits.coneOfDiagramTerminal is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.cone_of_diagram_terminal CategoryTheory.Limits.coneOfDiagramTerminalₓ'. -/
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J`, construct a cone for `J`,
 provided that the morphisms in the diagram are isomorphisms.
 In `limit_of_diagram_terminal` we show it is a limit cone. -/
@@ -628,6 +834,12 @@ def coneOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
           hX.hom_ext (hX.from i) (f ≫ hX.from j)] }
 #align category_theory.limits.cone_of_diagram_terminal CategoryTheory.Limits.coneOfDiagramTerminal
 
+/- warning: category_theory.limits.limit_of_diagram_terminal -> CategoryTheory.Limits.limitOfDiagramTerminal is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.limit_of_diagram_terminal CategoryTheory.Limits.limitOfDiagramTerminalₓ'. -/
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J` and that the morphisms in the
 diagram are isomorphisms, show the cone `cone_of_diagram_terminal` is a limit. -/
 def limitOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
@@ -635,6 +847,12 @@ def limitOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
     where lift S := S.π.app _
 #align category_theory.limits.limit_of_diagram_terminal CategoryTheory.Limits.limitOfDiagramTerminal
 
+/- warning: category_theory.limits.limit_of_terminal -> CategoryTheory.Limits.limitOfTerminal is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.limit_of_terminal CategoryTheory.Limits.limitOfTerminalₓ'. -/
 -- This is reducible to allow usage of lemmas about `cone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has a terminal object and all the morphisms in the diagram
 are isomorphisms, then the image of the terminal object is isomorphic to the limit of `F`. -/
@@ -644,6 +862,7 @@ def limitOfTerminal (F : J ⥤ C) [HasTerminal J] [HasLimit F]
   IsLimit.conePointUniqueUpToIso (limit.isLimit _) (limitOfDiagramTerminal terminalIsTerminal F)
 #align category_theory.limits.limit_of_terminal CategoryTheory.Limits.limitOfTerminal
 
+#print CategoryTheory.Limits.coconeOfDiagramTerminal /-
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J`, construct a cocone for `J`.
 In `colimit_of_diagram_terminal` we show it is a colimit cocone. -/
 @[simps]
@@ -656,7 +875,9 @@ def coconeOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) : Cocone F
         dsimp
         rw [← F.map_comp, category.comp_id, tX.hom_ext (k ≫ tX.from j') (tX.from j)] }
 #align category_theory.limits.cocone_of_diagram_terminal CategoryTheory.Limits.coconeOfDiagramTerminal
+-/
 
+#print CategoryTheory.Limits.colimitOfDiagramTerminal /-
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J`, show the cocone
 `cocone_of_diagram_terminal` is a colimit. -/
 def colimitOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) :
@@ -668,7 +889,14 @@ def colimitOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) :
     rw [← w X, cocone_of_diagram_terminal_ι_app, tX.hom_ext (tX.from X) (𝟙 _)]
     simp
 #align category_theory.limits.colimit_of_diagram_terminal CategoryTheory.Limits.colimitOfDiagramTerminal
+-/
 
+/- warning: category_theory.limits.colimit_of_terminal -> CategoryTheory.Limits.colimitOfTerminal is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.colimit_of_terminal CategoryTheory.Limits.colimitOfTerminalₓ'. -/
 -- This is reducible to allow usage of lemmas about `cocone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has a terminal object then the image of it is isomorphic
 to the colimit of `F`. -/
@@ -678,6 +906,12 @@ def colimitOfTerminal (F : J ⥤ C) [HasTerminal J] [HasColimit F] : colimit F 
     (colimitOfDiagramTerminal terminalIsTerminal F)
 #align category_theory.limits.colimit_of_terminal CategoryTheory.Limits.colimitOfTerminal
 
+/- warning: category_theory.limits.cocone_of_diagram_initial -> CategoryTheory.Limits.coconeOfDiagramInitial is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.cocone_of_diagram_initial CategoryTheory.Limits.coconeOfDiagramInitialₓ'. -/
 /-- From a functor `F : J ⥤ C`, given an initial object of `J`, construct a cocone for `J`,
 provided that the morphisms in the diagram are isomorphisms.
 In `colimit_of_diagram_initial` we show it is a colimit cocone. -/
@@ -695,6 +929,12 @@ def coconeOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
           hX.hom_ext (hX.to i ≫ f) (hX.to j)] }
 #align category_theory.limits.cocone_of_diagram_initial CategoryTheory.Limits.coconeOfDiagramInitial
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.colimit_of_diagram_initial CategoryTheory.Limits.colimitOfDiagramInitialₓ'. -/
 /-- From a functor `F : J ⥤ C`, given an initial object of `J` and that the morphisms in the
 diagram are isomorphisms, show the cone `cocone_of_diagram_initial` is a colimit. -/
 def colimitOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
@@ -702,6 +942,12 @@ def colimitOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
     where desc S := S.ι.app _
 #align category_theory.limits.colimit_of_diagram_initial CategoryTheory.Limits.colimitOfDiagramInitial
 
+/- warning: category_theory.limits.colimit_of_initial -> CategoryTheory.Limits.colimitOfInitial is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.colimit_of_initial CategoryTheory.Limits.colimitOfInitialₓ'. -/
 -- This is reducible to allow usage of lemmas about `cocone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has an initial object and all the morphisms in the diagram
 are isomorphisms, then the image of the initial object is isomorphic to the colimit of `F`. -/
@@ -712,6 +958,12 @@ def colimitOfInitial (F : J ⥤ C) [HasInitial J] [HasColimit F]
     (colimitOfDiagramInitial initialIsInitial _)
 #align category_theory.limits.colimit_of_initial CategoryTheory.Limits.colimitOfInitial
 
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 /-- If `j` is initial in the index category, then the map `limit.π F j` is an isomorphism.
 -/
 theorem isIso_π_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasLimit F] :
@@ -722,10 +974,22 @@ theorem isIso_π_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasLimit
         simp, by simp⟩⟩⟩
 #align category_theory.limits.is_iso_π_of_is_initial CategoryTheory.Limits.isIso_π_of_isInitial
 
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 instance isIso_π_initial [HasInitial J] (F : J ⥤ C) [HasLimit F] : IsIso (limit.π F (⊥_ J)) :=
   isIso_π_of_isInitial initialIsInitial F
 #align category_theory.limits.is_iso_π_initial CategoryTheory.Limits.isIso_π_initial
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_iso_π_of_is_terminal CategoryTheory.Limits.isIso_π_of_isTerminalₓ'. -/
 theorem isIso_π_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasLimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (limit.π F j) :=
   ⟨⟨limit.lift _ (coneOfDiagramTerminal I F), by
@@ -733,11 +997,23 @@ theorem isIso_π_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasLimi
       simp, by simp⟩⟩
 #align category_theory.limits.is_iso_π_of_is_terminal CategoryTheory.Limits.isIso_π_of_isTerminal
 
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+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u2, u4} C] {J : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} J] [_inst_3 : CategoryTheory.Limits.HasTerminal.{u1, u3} J _inst_2] (F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_2 C _inst_1) [_inst_4 : CategoryTheory.Limits.HasLimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F] [_inst_5 : forall (i : J) (j : J) (f : Quiver.Hom.{succ u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) i j), CategoryTheory.IsIso.{u2, u4} C _inst_1 (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) j) (Prefunctor.map.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) i j f)], CategoryTheory.IsIso.{u2, u4} C _inst_1 (CategoryTheory.Limits.limit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) (CategoryTheory.Limits.terminal.{u1, u3} J _inst_2 _inst_3)) (CategoryTheory.Limits.limit.π.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4 (CategoryTheory.Limits.terminal.{u1, u3} J _inst_2 _inst_3))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_iso_π_terminal CategoryTheory.Limits.isIso_π_terminalₓ'. -/
 instance isIso_π_terminal [HasTerminal J] (F : J ⥤ C) [HasLimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (limit.π F (⊤_ J)) :=
   isIso_π_of_isTerminal terminalIsTerminal F
 #align category_theory.limits.is_iso_π_terminal CategoryTheory.Limits.isIso_π_terminal
 
+/- warning: category_theory.limits.is_iso_ι_of_is_terminal -> CategoryTheory.Limits.isIso_ι_of_isTerminal is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u2, u4} C] {J : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} J] {j : J}, (CategoryTheory.Limits.IsTerminal.{u1, u3} J _inst_2 j) -> (forall (F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_2 C _inst_1) [_inst_3 : CategoryTheory.Limits.HasColimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F], CategoryTheory.IsIso.{u2, u4} C _inst_1 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_2 C _inst_1 F j) (CategoryTheory.Limits.colimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_3) (CategoryTheory.Limits.colimit.ι.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_3 j))
+but is expected to have type
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u2, u4} C] {J : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} J] {j : J}, (CategoryTheory.Limits.IsTerminal.{u1, u3} J _inst_2 j) -> (forall (F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_2 C _inst_1) [_inst_3 : CategoryTheory.Limits.HasColimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F], CategoryTheory.IsIso.{u2, u4} C _inst_1 (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) j) (CategoryTheory.Limits.colimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_3) (CategoryTheory.Limits.colimit.ι.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_3 j))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_iso_ι_of_is_terminal CategoryTheory.Limits.isIso_ι_of_isTerminalₓ'. -/
 /-- If `j` is terminal in the index category, then the map `colimit.ι F j` is an isomorphism.
 -/
 theorem isIso_ι_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasColimit F] :
@@ -748,10 +1024,22 @@ theorem isIso_ι_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasColi
         simp⟩⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_terminal CategoryTheory.Limits.isIso_ι_of_isTerminal
 
+/- warning: category_theory.limits.is_iso_ι_terminal -> CategoryTheory.Limits.isIso_ι_terminal is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u2, u4} C] {J : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} J] [_inst_3 : CategoryTheory.Limits.HasTerminal.{u1, u3} J _inst_2] (F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_2 C _inst_1) [_inst_4 : CategoryTheory.Limits.HasColimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F], CategoryTheory.IsIso.{u2, u4} C _inst_1 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_2 C _inst_1 F (CategoryTheory.Limits.terminal.{u1, u3} J _inst_2 _inst_3)) (CategoryTheory.Limits.colimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4) (CategoryTheory.Limits.colimit.ι.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4 (CategoryTheory.Limits.terminal.{u1, u3} J _inst_2 _inst_3))
+but is expected to have type
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u2, u4} C] {J : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} J] [_inst_3 : CategoryTheory.Limits.HasTerminal.{u1, u3} J _inst_2] (F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_2 C _inst_1) [_inst_4 : CategoryTheory.Limits.HasColimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F], CategoryTheory.IsIso.{u2, u4} C _inst_1 (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) (CategoryTheory.Limits.terminal.{u1, u3} J _inst_2 _inst_3)) (CategoryTheory.Limits.colimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4) (CategoryTheory.Limits.colimit.ι.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4 (CategoryTheory.Limits.terminal.{u1, u3} J _inst_2 _inst_3))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_iso_ι_terminal CategoryTheory.Limits.isIso_ι_terminalₓ'. -/
 instance isIso_ι_terminal [HasTerminal J] (F : J ⥤ C) [HasColimit F] : IsIso (colimit.ι F (⊤_ J)) :=
   isIso_ι_of_isTerminal terminalIsTerminal F
 #align category_theory.limits.is_iso_ι_terminal CategoryTheory.Limits.isIso_ι_terminal
 
+/- warning: category_theory.limits.is_iso_ι_of_is_initial -> CategoryTheory.Limits.isIso_ι_of_isInitial is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u2, u4} C] {J : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} J] {j : J}, (CategoryTheory.Limits.IsInitial.{u1, u3} J _inst_2 j) -> (forall (F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_2 C _inst_1) [_inst_3 : CategoryTheory.Limits.HasColimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F] [_inst_4 : forall (i : J) (j : J) (f : Quiver.Hom.{succ u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) i j), CategoryTheory.IsIso.{u2, u4} C _inst_1 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_2 C _inst_1 F i) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_2 C _inst_1 F j) (CategoryTheory.Functor.map.{u1, u2, u3, u4} J _inst_2 C _inst_1 F i j f)], CategoryTheory.IsIso.{u2, u4} C _inst_1 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_2 C _inst_1 F j) (CategoryTheory.Limits.colimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_3) (CategoryTheory.Limits.colimit.ι.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_3 j))
+but is expected to have type
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u2, u4} C] {J : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} J] {j : J}, (CategoryTheory.Limits.IsInitial.{u1, u3} J _inst_2 j) -> (forall (F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_2 C _inst_1) [_inst_3 : CategoryTheory.Limits.HasColimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F] [_inst_4 : forall (i : J) (j : J) (f : Quiver.Hom.{succ u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) i j), CategoryTheory.IsIso.{u2, u4} C _inst_1 (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) j) (Prefunctor.map.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) i j f)], CategoryTheory.IsIso.{u2, u4} C _inst_1 (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) j) (CategoryTheory.Limits.colimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_3) (CategoryTheory.Limits.colimit.ι.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_3 j))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_iso_ι_of_is_initial CategoryTheory.Limits.isIso_ι_of_isInitialₓ'. -/
 theorem isIso_ι_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasColimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (colimit.ι F j) :=
   ⟨⟨colimit.desc _ (coconeOfDiagramInitial I F),
@@ -760,6 +1048,12 @@ theorem isIso_ι_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasColimi
         simp⟩⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_initial CategoryTheory.Limits.isIso_ι_of_isInitial
 
+/- warning: category_theory.limits.is_iso_ι_initial -> CategoryTheory.Limits.isIso_ι_initial is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u2, u4} C] {J : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} J] [_inst_3 : CategoryTheory.Limits.HasInitial.{u1, u3} J _inst_2] (F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_2 C _inst_1) [_inst_4 : CategoryTheory.Limits.HasColimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F] [_inst_5 : forall (i : J) (j : J) (f : Quiver.Hom.{succ u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) i j), CategoryTheory.IsIso.{u2, u4} C _inst_1 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_2 C _inst_1 F i) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_2 C _inst_1 F j) (CategoryTheory.Functor.map.{u1, u2, u3, u4} J _inst_2 C _inst_1 F i j f)], CategoryTheory.IsIso.{u2, u4} C _inst_1 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} J _inst_2 C _inst_1 F (CategoryTheory.Limits.initial.{u1, u3} J _inst_2 _inst_3)) (CategoryTheory.Limits.colimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4) (CategoryTheory.Limits.colimit.ι.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4 (CategoryTheory.Limits.initial.{u1, u3} J _inst_2 _inst_3))
+but is expected to have type
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u2, u4} C] {J : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u1, u3} J] [_inst_3 : CategoryTheory.Limits.HasInitial.{u1, u3} J _inst_2] (F : CategoryTheory.Functor.{u1, u2, u3, u4} J _inst_2 C _inst_1) [_inst_4 : CategoryTheory.Limits.HasColimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F] [_inst_5 : forall (i : J) (j : J) (f : Quiver.Hom.{succ u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) i j), CategoryTheory.IsIso.{u2, u4} C _inst_1 (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) i) (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) j) (Prefunctor.map.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) i j f)], CategoryTheory.IsIso.{u2, u4} C _inst_1 (Prefunctor.obj.{succ u1, succ u2, u3, u4} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} J (CategoryTheory.Category.toCategoryStruct.{u1, u3} J _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} C (CategoryTheory.Category.toCategoryStruct.{u2, u4} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} J _inst_2 C _inst_1 F) (CategoryTheory.Limits.initial.{u1, u3} J _inst_2 _inst_3)) (CategoryTheory.Limits.colimit.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4) (CategoryTheory.Limits.colimit.ι.{u1, u3, u2, u4} J _inst_2 C _inst_1 F _inst_4 (CategoryTheory.Limits.initial.{u1, u3} J _inst_2 _inst_3))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.is_iso_ι_initial CategoryTheory.Limits.isIso_ι_initialₓ'. -/
 instance isIso_ι_initial [HasInitial J] (F : J ⥤ C) [HasColimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (colimit.ι F (⊥_ J)) :=
   isIso_ι_of_isInitial initialIsInitial F

239d882c

bump to nightly-2023-02-28-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

1fb1623f

Diff

@@ -36,14 +36,14 @@ attribute [local tidy] tactic.discrete_cases
 /-- Construct a cone for the empty diagram given an object. -/
 @[simps]
 def asEmptyCone (X : C) : Cone (Functor.empty.{0} C) :=
-  { x
+  { pt
     π := by tidy }
 #align category_theory.limits.as_empty_cone CategoryTheory.Limits.asEmptyCone
 
 /-- Construct a cocone for the empty diagram given an object. -/
 @[simps]
 def asEmptyCocone (X : C) : Cocone (Functor.empty.{0} C) :=
-  { x
+  { pt
     ι := by tidy }
 #align category_theory.limits.as_empty_cocone CategoryTheory.Limits.asEmptyCocone
 
@@ -65,8 +65,8 @@ def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
     { default := t.lift ⟨X, by tidy⟩
       uniq := fun f => t.uniq ⟨X, by tidy⟩ f (by tidy) }
   invFun u :=
-    { lift := fun s => (u s.x).default
-      uniq := fun s _ _ => (u s.x).2 _ }
+    { lift := fun s => (u s.pt).default
+      uniq := fun s _ _ => (u s.pt).2 _ }
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_terminal_equiv_unique CategoryTheory.Limits.isTerminalEquivUnique
@@ -74,7 +74,7 @@ def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
 /-- An object `Y` is terminal if for every `X` there is a unique morphism `X ⟶ Y`
     (as an instance). -/
 def IsTerminal.ofUnique (Y : C) [h : ∀ X : C, Unique (X ⟶ Y)] : IsTerminal Y
-    where lift s := (h s.x).default
+    where lift s := (h s.pt).default
 #align category_theory.limits.is_terminal.of_unique CategoryTheory.Limits.IsTerminal.ofUnique
 
 /-- If `α` is a preorder with top, then `⊤` is a terminal object. -/
@@ -97,8 +97,8 @@ def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :
     { default := t.desc ⟨X, by tidy⟩
       uniq := fun f => t.uniq ⟨X, by tidy⟩ f (by tidy) }
   invFun u :=
-    { desc := fun s => (u s.x).default
-      uniq := fun s _ _ => (u s.x).2 _ }
+    { desc := fun s => (u s.pt).default
+      uniq := fun s _ _ => (u s.pt).2 _ }
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_initial_equiv_unique CategoryTheory.Limits.isInitialEquivUnique
@@ -106,7 +106,7 @@ def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :
 /-- An object `X` is initial if for every `Y` there is a unique morphism `X ⟶ Y`
     (as an instance). -/
 def IsInitial.ofUnique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : IsInitial X
-    where desc s := (h s.x).default
+    where desc s := (h s.pt).default
 #align category_theory.limits.is_initial.of_unique CategoryTheory.Limits.IsInitial.ofUnique
 
 /-- If `α` is a preorder with bot, then `⊥` is an initial object. -/
@@ -220,9 +220,9 @@ variable (X : C) {F₁ : Discrete.{w} PEmpty ⥤ C} {F₂ : Discrete.{w'} PEmpty
 
 /-- Being terminal is independent of the empty diagram, its universe, and the cone over it,
     as long as the cone points are isomorphic. -/
-def isLimitChangeEmptyCone {c₁ : Cone F₁} (hl : IsLimit c₁) (c₂ : Cone F₂) (hi : c₁.x ≅ c₂.x) :
+def isLimitChangeEmptyCone {c₁ : Cone F₁} (hl : IsLimit c₁) (c₂ : Cone F₂) (hi : c₁.pt ≅ c₂.pt) :
     IsLimit c₂ where
-  lift c := hl.lift ⟨c.x, by tidy⟩ ≫ hi.Hom
+  lift c := hl.lift ⟨c.pt, by tidy⟩ ≫ hi.Hom
   fac _ j := j.as.elim
   uniq c f _ := by
     erw [← hl.uniq ⟨c.X, by tidy⟩ (f ≫ hi.inv) fun j => j.as.elim]
@@ -231,7 +231,8 @@ def isLimitChangeEmptyCone {c₁ : Cone F₁} (hl : IsLimit c₁) (c₂ : Cone F
 
 /-- Replacing an empty cone in `is_limit` by another with the same cone point
     is an equivalence. -/
-def isLimitEmptyConeEquiv (c₁ : Cone F₁) (c₂ : Cone F₂) (h : c₁.x ≅ c₂.x) : IsLimit c₁ ≃ IsLimit c₂
+def isLimitEmptyConeEquiv (c₁ : Cone F₁) (c₂ : Cone F₂) (h : c₁.pt ≅ c₂.pt) :
+    IsLimit c₁ ≃ IsLimit c₂
     where
   toFun hl := isLimitChangeEmptyCone C hl c₂ h
   invFun hl := isLimitChangeEmptyCone C hl c₁ h.symm
@@ -255,9 +256,9 @@ theorem has_terminal_change_universe [h : HasLimitsOfShape (Discrete.{w} PEmpty)
 /-- Being initial is independent of the empty diagram, its universe, and the cocone over it,
     as long as the cocone points are isomorphic. -/
 def isColimitChangeEmptyCocone {c₁ : Cocone F₁} (hl : IsColimit c₁) (c₂ : Cocone F₂)
-    (hi : c₁.x ≅ c₂.x) : IsColimit c₂
+    (hi : c₁.pt ≅ c₂.pt) : IsColimit c₂
     where
-  desc c := hi.inv ≫ hl.desc ⟨c.x, by tidy⟩
+  desc c := hi.inv ≫ hl.desc ⟨c.pt, by tidy⟩
   fac _ j := j.as.elim
   uniq c f _ := by
     erw [← hl.uniq ⟨c.X, by tidy⟩ (hi.hom ≫ f) fun j => j.as.elim]
@@ -266,7 +267,7 @@ def isColimitChangeEmptyCocone {c₁ : Cocone F₁} (hl : IsColimit c₁) (c₂
 
 /-- Replacing an empty cocone in `is_colimit` by another with the same cocone point
     is an equivalence. -/
-def isColimitEmptyCoconeEquiv (c₁ : Cocone F₁) (c₂ : Cocone F₂) (h : c₁.x ≅ c₂.x) :
+def isColimitEmptyCoconeEquiv (c₁ : Cocone F₁) (c₂ : Cocone F₂) (h : c₁.pt ≅ c₂.pt) :
     IsColimit c₁ ≃ IsColimit c₂
     where
   toFun hl := isColimitChangeEmptyCocone C hl c₂ h
@@ -399,28 +400,28 @@ instance initial.isSplitEpi_to {Y : C} [HasInitial C] (f : Y ⟶ ⊥_ C) : IsSpl
 /-- An initial object is terminal in the opposite category. -/
 def terminalOpOfInitial {X : C} (t : IsInitial X) : IsTerminal (Opposite.op X)
     where
-  lift s := (t.to s.x.unop).op
+  lift s := (t.to s.pt.unop).op
   uniq s m w := Quiver.Hom.unop_inj (t.hom_ext _ _)
 #align category_theory.limits.terminal_op_of_initial CategoryTheory.Limits.terminalOpOfInitial
 
 /-- An initial object in the opposite category is terminal in the original category. -/
 def terminalUnopOfInitial {X : Cᵒᵖ} (t : IsInitial X) : IsTerminal X.unop
     where
-  lift s := (t.to (Opposite.op s.x)).unop
+  lift s := (t.to (Opposite.op s.pt)).unop
   uniq s m w := Quiver.Hom.op_inj (t.hom_ext _ _)
 #align category_theory.limits.terminal_unop_of_initial CategoryTheory.Limits.terminalUnopOfInitial
 
 /-- A terminal object is initial in the opposite category. -/
 def initialOpOfTerminal {X : C} (t : IsTerminal X) : IsInitial (Opposite.op X)
     where
-  desc s := (t.from s.x.unop).op
+  desc s := (t.from s.pt.unop).op
   uniq s m w := Quiver.Hom.unop_inj (t.hom_ext _ _)
 #align category_theory.limits.initial_op_of_terminal CategoryTheory.Limits.initialOpOfTerminal
 
 /-- A terminal object in the opposite category is initial in the original category. -/
 def initialUnopOfTerminal {X : Cᵒᵖ} (t : IsTerminal X) : IsInitial X.unop
     where
-  desc s := (t.from (Opposite.op s.x)).unop
+  desc s := (t.from (Opposite.op s.pt)).unop
   uniq s m w := Quiver.Hom.op_inj (t.hom_ext _ _)
 #align category_theory.limits.initial_unop_of_terminal CategoryTheory.Limits.initialUnopOfTerminal
 
@@ -444,7 +445,7 @@ instance {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C] :
     HasLimit ((CategoryTheory.Functor.const J).obj (⊤_ C)) :=
   HasLimit.mk
     { Cone :=
-        { x := ⊤_ C
+        { pt := ⊤_ C
           π := { app := fun _ => terminal.from _ } }
       IsLimit := { lift := fun s => terminal.from _ } }
 
@@ -456,7 +457,7 @@ def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasT
   Hom := terminal.from _
   inv :=
     limit.lift ((CategoryTheory.Functor.const J).obj (⊤_ C))
-      { x := ⊤_ C
+      { pt := ⊤_ C
         π := { app := fun j => terminal.from _ } }
 #align category_theory.limits.limit_const_terminal CategoryTheory.Limits.limitConstTerminal
 
@@ -472,7 +473,7 @@ instance {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
     HasColimit ((CategoryTheory.Functor.const J).obj (⊥_ C)) :=
   HasColimit.mk
     { Cocone :=
-        { x := ⊥_ C
+        { pt := ⊥_ C
           ι := { app := fun _ => initial.to _ } }
       IsColimit := { desc := fun s => initial.to _ } }
 
@@ -483,7 +484,7 @@ def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [Has
     where
   Hom :=
     colimit.desc ((CategoryTheory.Functor.const J).obj (⊥_ C))
-      { x := ⊥_ C
+      { pt := ⊥_ C
         ι := { app := fun j => initial.to _ } }
   inv := initial.to _
 #align category_theory.limits.colimit_const_initial CategoryTheory.Limits.colimitConstInitial
@@ -582,7 +583,7 @@ In `limit_of_diagram_initial` we show it is a limit cone. -/
 @[simps]
 def coneOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) : Cone F
     where
-  x := F.obj X
+  pt := F.obj X
   π :=
     { app := fun j => F.map (tX.to j)
       naturality' := fun j j' k => by
@@ -617,7 +618,7 @@ In `limit_of_diagram_terminal` we show it is a limit cone. -/
 def coneOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : Cone F
     where
-  x := F.obj X
+  pt := F.obj X
   π :=
     { app := fun i => inv (F.map (hX.from _))
       naturality' := by
@@ -648,7 +649,7 @@ In `colimit_of_diagram_terminal` we show it is a colimit cocone. -/
 @[simps]
 def coconeOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) : Cocone F
     where
-  x := F.obj X
+  pt := F.obj X
   ι :=
     { app := fun j => F.map (tX.from j)
       naturality' := fun j j' k => by
@@ -684,7 +685,7 @@ In `colimit_of_diagram_initial` we show it is a colimit cocone. -/
 def coconeOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : Cocone F
     where
-  x := F.obj X
+  pt := F.obj X
   ι :=
     { app := fun i => inv (F.map (hX.to _))
       naturality' := by

239d882c

bump to nightly-2023-02-27-08

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

91d8c210

Diff

@@ -66,7 +66,7 @@ def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
       uniq := fun f => t.uniq ⟨X, by tidy⟩ f (by tidy) }
   invFun u :=
     { lift := fun s => (u s.x).default
-      uniq' := fun s _ _ => (u s.x).2 _ }
+      uniq := fun s _ _ => (u s.x).2 _ }
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_terminal_equiv_unique CategoryTheory.Limits.isTerminalEquivUnique
@@ -98,7 +98,7 @@ def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :
       uniq := fun f => t.uniq ⟨X, by tidy⟩ f (by tidy) }
   invFun u :=
     { desc := fun s => (u s.x).default
-      uniq' := fun s _ _ => (u s.x).2 _ }
+      uniq := fun s _ _ => (u s.x).2 _ }
   left_inv := by tidy
   right_inv := by tidy
 #align category_theory.limits.is_initial_equiv_unique CategoryTheory.Limits.isInitialEquivUnique
@@ -223,8 +223,8 @@ variable (X : C) {F₁ : Discrete.{w} PEmpty ⥤ C} {F₂ : Discrete.{w'} PEmpty
 def isLimitChangeEmptyCone {c₁ : Cone F₁} (hl : IsLimit c₁) (c₂ : Cone F₂) (hi : c₁.x ≅ c₂.x) :
     IsLimit c₂ where
   lift c := hl.lift ⟨c.x, by tidy⟩ ≫ hi.Hom
-  fac' _ j := j.as.elim
-  uniq' c f _ := by
+  fac _ j := j.as.elim
+  uniq c f _ := by
     erw [← hl.uniq ⟨c.X, by tidy⟩ (f ≫ hi.inv) fun j => j.as.elim]
     simp
 #align category_theory.limits.is_limit_change_empty_cone CategoryTheory.Limits.isLimitChangeEmptyCone
@@ -239,18 +239,18 @@ def isLimitEmptyConeEquiv (c₁ : Cone F₁) (c₂ : Cone F₂) (h : c₁.x ≅
   right_inv := by tidy
 #align category_theory.limits.is_limit_empty_cone_equiv CategoryTheory.Limits.isLimitEmptyConeEquiv
 
-theorem hasTerminalChangeDiagram (h : HasLimit F₁) : HasLimit F₂ :=
+theorem has_terminal_change_diagram (h : HasLimit F₁) : HasLimit F₂ :=
   ⟨⟨⟨⟨limit F₁, by tidy⟩, isLimitChangeEmptyCone C (limit.isLimit F₁) _ (eqToIso rfl)⟩⟩⟩
-#align category_theory.limits.has_terminal_change_diagram CategoryTheory.Limits.hasTerminalChangeDiagram
+#align category_theory.limits.has_terminal_change_diagram CategoryTheory.Limits.has_terminal_change_diagram
 
-theorem hasTerminalChangeUniverse [h : HasLimitsOfShape (Discrete.{w} PEmpty) C] :
+theorem has_terminal_change_universe [h : HasLimitsOfShape (Discrete.{w} PEmpty) C] :
     HasLimitsOfShape (Discrete.{w'} PEmpty) C :=
   {
     HasLimit := fun J =>
-      hasTerminalChangeDiagram C
+      has_terminal_change_diagram C
         (let f := h.1
         f (Functor.empty C)) }
-#align category_theory.limits.has_terminal_change_universe CategoryTheory.Limits.hasTerminalChangeUniverse
+#align category_theory.limits.has_terminal_change_universe CategoryTheory.Limits.has_terminal_change_universe
 
 /-- Being initial is independent of the empty diagram, its universe, and the cocone over it,
     as long as the cocone points are isomorphic. -/
@@ -258,8 +258,8 @@ def isColimitChangeEmptyCocone {c₁ : Cocone F₁} (hl : IsColimit c₁) (c₂
     (hi : c₁.x ≅ c₂.x) : IsColimit c₂
     where
   desc c := hi.inv ≫ hl.desc ⟨c.x, by tidy⟩
-  fac' _ j := j.as.elim
-  uniq' c f _ := by
+  fac _ j := j.as.elim
+  uniq c f _ := by
     erw [← hl.uniq ⟨c.X, by tidy⟩ (hi.hom ≫ f) fun j => j.as.elim]
     simp
 #align category_theory.limits.is_colimit_change_empty_cocone CategoryTheory.Limits.isColimitChangeEmptyCocone
@@ -275,18 +275,18 @@ def isColimitEmptyCoconeEquiv (c₁ : Cocone F₁) (c₂ : Cocone F₂) (h : c
   right_inv := by tidy
 #align category_theory.limits.is_colimit_empty_cocone_equiv CategoryTheory.Limits.isColimitEmptyCoconeEquiv
 
-theorem hasInitialChangeDiagram (h : HasColimit F₁) : HasColimit F₂ :=
+theorem has_initial_change_diagram (h : HasColimit F₁) : HasColimit F₂ :=
   ⟨⟨⟨⟨colimit F₁, by tidy⟩, isColimitChangeEmptyCocone C (colimit.isColimit F₁) _ (eqToIso rfl)⟩⟩⟩
-#align category_theory.limits.has_initial_change_diagram CategoryTheory.Limits.hasInitialChangeDiagram
+#align category_theory.limits.has_initial_change_diagram CategoryTheory.Limits.has_initial_change_diagram
 
-theorem hasInitialChangeUniverse [h : HasColimitsOfShape (Discrete.{w} PEmpty) C] :
+theorem has_initial_change_universe [h : HasColimitsOfShape (Discrete.{w} PEmpty) C] :
     HasColimitsOfShape (Discrete.{w'} PEmpty) C :=
   {
     HasColimit := fun J =>
-      hasInitialChangeDiagram C
+      has_initial_change_diagram C
         (let f := h.1
         f (Functor.empty C)) }
-#align category_theory.limits.has_initial_change_universe CategoryTheory.Limits.hasInitialChangeUniverse
+#align category_theory.limits.has_initial_change_universe CategoryTheory.Limits.has_initial_change_universe
 
 end Univ
 
@@ -400,28 +400,28 @@ instance initial.isSplitEpi_to {Y : C} [HasInitial C] (f : Y ⟶ ⊥_ C) : IsSpl
 def terminalOpOfInitial {X : C} (t : IsInitial X) : IsTerminal (Opposite.op X)
     where
   lift s := (t.to s.x.unop).op
-  uniq' s m w := Quiver.Hom.unop_inj (t.hom_ext _ _)
+  uniq s m w := Quiver.Hom.unop_inj (t.hom_ext _ _)
 #align category_theory.limits.terminal_op_of_initial CategoryTheory.Limits.terminalOpOfInitial
 
 /-- An initial object in the opposite category is terminal in the original category. -/
 def terminalUnopOfInitial {X : Cᵒᵖ} (t : IsInitial X) : IsTerminal X.unop
     where
   lift s := (t.to (Opposite.op s.x)).unop
-  uniq' s m w := Quiver.Hom.op_inj (t.hom_ext _ _)
+  uniq s m w := Quiver.Hom.op_inj (t.hom_ext _ _)
 #align category_theory.limits.terminal_unop_of_initial CategoryTheory.Limits.terminalUnopOfInitial
 
 /-- A terminal object is initial in the opposite category. -/
 def initialOpOfTerminal {X : C} (t : IsTerminal X) : IsInitial (Opposite.op X)
     where
   desc s := (t.from s.x.unop).op
-  uniq' s m w := Quiver.Hom.unop_inj (t.hom_ext _ _)
+  uniq s m w := Quiver.Hom.unop_inj (t.hom_ext _ _)
 #align category_theory.limits.initial_op_of_terminal CategoryTheory.Limits.initialOpOfTerminal
 
 /-- A terminal object in the opposite category is initial in the original category. -/
 def initialUnopOfTerminal {X : Cᵒᵖ} (t : IsTerminal X) : IsInitial X.unop
     where
   desc s := (t.from (Opposite.op s.x)).unop
-  uniq' s m w := Quiver.Hom.op_inj (t.hom_ext _ _)
+  uniq s m w := Quiver.Hom.op_inj (t.hom_ext _ _)
 #align category_theory.limits.initial_unop_of_terminal CategoryTheory.Limits.initialUnopOfTerminal
 
 instance hasInitial_op_of_hasTerminal [HasTerminal C] : HasInitial Cᵒᵖ :=
@@ -596,8 +596,7 @@ def limitOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) :
     IsLimit (coneOfDiagramInitial tX F)
     where
   lift s := s.π.app X
-  uniq' s m w :=
-    by
+  uniq s m w := by
     rw [← w X, cone_of_diagram_initial_π_app, tX.hom_ext (tX.to X) (𝟙 _)]
     dsimp; simp
 #align category_theory.limits.limit_of_diagram_initial CategoryTheory.Limits.limitOfDiagramInitial
@@ -663,7 +662,7 @@ def colimitOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) :
     IsColimit (coconeOfDiagramTerminal tX F)
     where
   desc s := s.ι.app X
-  uniq' s m w :=
+  uniq s m w :=
     by
     rw [← w X, cocone_of_diagram_terminal_ι_app, tX.hom_ext (tX.from X) (𝟙 _)]
     simp

239d882c

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

239d882c

feat(CategoryTheory): the left Kan extension functor (#12168)

Given a functor F : C ⥤ D, we define the left Kan extension functor F.lan : (C ⥤ E) ⥤ (D ⥤ E) which sends a functor G : C ⥤ E to its left Kan extension along F. (This is a step towards the refactor of Lan/Ran in mathlib using the new API for Kan extensions of functors #10425.)

32f9bf1b

Diff

@@ -681,6 +681,12 @@ def colimitOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) :
 instance hasColimit_of_domain_hasTerminal [HasTerminal J] {F : J ⥤ C} : HasColimit F :=
   HasColimit.mk { cocone := _, isColimit := colimitOfDiagramTerminal (terminalIsTerminal) F }
 
+lemma IsColimit.isIso_ι_app_of_isTerminal {F : J ⥤ C} {c : Cocone F} (hc : IsColimit c)
+    (X : J) (hX : IsTerminal X) :
+    IsIso (c.ι.app X) := by
+  change IsIso (coconePointUniqueUpToIso (colimitOfDiagramTerminal hX F) hc).hom
+  infer_instance
+
 -- This is reducible to allow usage of lemmas about `cocone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has a terminal object then the image of it is isomorphic
 to the colimit of `F`. -/
@@ -717,6 +723,12 @@ instance hasColimit_of_domain_hasInitial [HasInitial J] {F : J ⥤ C}
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : HasColimit F :=
   HasColimit.mk { cocone := _, isColimit := colimitOfDiagramInitial (initialIsInitial) F }
 
+lemma IsLimit.isIso_π_app_of_isInitial {F : J ⥤ C} {c : Cone F} (hc : IsLimit c)
+    (X : J) (hX : IsInitial X) :
+    IsIso (c.π.app X) := by
+  change IsIso (conePointUniqueUpToIso hc (limitOfDiagramInitial hX F)).hom
+  infer_instance
+
 -- This is reducible to allow usage of lemmas about `cocone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has an initial object and all the morphisms in the diagram
 are isomorphisms, then the image of the initial object is isomorphic to the colimit of `F`. -/

239d882c

chore: remove tactics (#11365)

More tactics that are not used, found using the linter at #11308.

The PR consists of tactic removals, whitespace changes and replacing a porting note by an explanation.

c33c2724

Diff

@@ -252,7 +252,7 @@ def isLimitEmptyConeEquiv (c₁ : Cone F₁) (c₂ : Cone F₂) (h : c₁.pt ≅
   invFun hl := isLimitChangeEmptyCone C hl c₁ h.symm
   left_inv := by dsimp [Function.LeftInverse]; intro; simp only [eq_iff_true_of_subsingleton]
   right_inv := by
-    dsimp [Function.LeftInverse,Function.RightInverse]; intro; funext
+    dsimp [Function.LeftInverse,Function.RightInverse]; intro
     simp only [eq_iff_true_of_subsingleton]
 #align category_theory.limits.is_limit_empty_cone_equiv CategoryTheory.Limits.isLimitEmptyConeEquiv
 
@@ -286,7 +286,7 @@ def isColimitEmptyCoconeEquiv (c₁ : Cocone F₁) (c₂ : Cocone F₂) (h : c
   invFun hl := isColimitChangeEmptyCocone C hl c₁ h.symm
   left_inv := by dsimp [Function.LeftInverse]; intro; simp only [eq_iff_true_of_subsingleton]
   right_inv := by
-    dsimp [Function.LeftInverse,Function.RightInverse]; intro; funext
+    dsimp [Function.LeftInverse,Function.RightInverse]; intro
     simp only [eq_iff_true_of_subsingleton]
 #align category_theory.limits.is_colimit_empty_cocone_equiv CategoryTheory.Limits.isColimitEmptyCoconeEquiv
 
@@ -604,7 +604,7 @@ def limitOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) :
   uniq s m w := by
     conv_lhs => dsimp
     simp_rw [← w X, coneOfDiagramInitial_π_app, tX.hom_ext (tX.to X) (𝟙 _)]
-    dsimp; simp
+    simp
 #align category_theory.limits.limit_of_diagram_initial CategoryTheory.Limits.limitOfDiagramInitial
 
 instance hasLimit_of_domain_hasInitial [HasInitial J] {F : J ⥤ C} : HasLimit F :=

239d882c

fix: attribute [simp] ... in -> attribute [local simp] ... in (#7678)

Mathlib.Logic.Unique contains the line attribute [simp] eq_iff_true_of_subsingleton in ...:

https://github.com/leanprover-community/mathlib4/blob/96a11c7aac574c00370c2b3dab483cb676405c5d/Mathlib/Logic/Unique.lean#L255-L256

Despite what the in part may imply, this adds the lemma to the simp set "globally", including for downstream files; it is likely that attribute [local simp] eq_iff_true_of_subsingleton in ... was meant instead (or maybe scoped simp, but I think "scoped" refers to the current namespace). Indeed, the relevant lemma is not marked with @[simp] for possible slowness: https://github.com/leanprover/std4/blob/846e9e1d6bb534774d1acd2dc430e70987da3c18/Std/Logic.lean#L749. Adding it to the simp set causes the example at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Regression.20in.20simp to slow down.

This PR changes this and fixes the relevant downstream simps. There was also one ocurrence of attribute [simp] FullSubcategory.comp_def FullSubcategory.id_def in in Mathlib.CategoryTheory.Monoidal.Subcategory but that was much easier to fix.

https://github.com/leanprover-community/mathlib4/blob/bc49eb9ba756a233370b4b68bcdedd60402f71ed/Mathlib/CategoryTheory/Monoidal/Subcategory.lean#L118-L119

1fe87718

Diff

@@ -380,12 +380,13 @@ instance uniqueFromInitial [HasInitial C] (P : C) : Unique (⊥_ C ⟶ P) :=
 
 @[simp]
 theorem terminal.comp_from [HasTerminal C] {P Q : C} (f : P ⟶ Q) :
-    f ≫ terminal.from Q = terminal.from P := by aesop
+    f ≫ terminal.from Q = terminal.from P := by
+  simp [eq_iff_true_of_subsingleton]
 #align category_theory.limits.terminal.comp_from CategoryTheory.Limits.terminal.comp_from
 
 @[simp]
 theorem initial.to_comp [HasInitial C] {P Q : C} (f : P ⟶ Q) : initial.to P ≫ f = initial.to Q := by
-  aesop
+  simp [eq_iff_true_of_subsingleton]
 #align category_theory.limits.initial.to_comp CategoryTheory.Limits.initial.to_comp
 
 /-- The (unique) isomorphism between the chosen initial object and any other initial object. -/

239d882c

chore(CategoryTheory/Limits/Shapes/Terminal): remove some unnecessary HasLimit and HasColimit hypotheses (#8068)

e3bc933a

Diff

@@ -606,12 +606,15 @@ def limitOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) :
     dsimp; simp
 #align category_theory.limits.limit_of_diagram_initial CategoryTheory.Limits.limitOfDiagramInitial
 
+instance hasLimit_of_domain_hasInitial [HasInitial J] {F : J ⥤ C} : HasLimit F :=
+  HasLimit.mk { cone := _, isLimit := limitOfDiagramInitial (initialIsInitial) F }
+
 -- See note [dsimp, simp]
 -- This is reducible to allow usage of lemmas about `cone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has an initial object then the image of it is isomorphic
 to the limit of `F`. -/
 @[reducible]
-def limitOfInitial (F : J ⥤ C) [HasInitial J] [HasLimit F] : limit F ≅ F.obj (⊥_ J) :=
+def limitOfInitial (F : J ⥤ C) [HasInitial J] : limit F ≅ F.obj (⊥_ J) :=
   IsLimit.conePointUniqueUpToIso (limit.isLimit _) (limitOfDiagramInitial initialIsInitial F)
 #align category_theory.limits.limit_of_initial CategoryTheory.Limits.limitOfInitial
 
@@ -638,12 +641,16 @@ def limitOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
   lift S := S.π.app _
 #align category_theory.limits.limit_of_diagram_terminal CategoryTheory.Limits.limitOfDiagramTerminal
 
+instance hasLimit_of_domain_hasTerminal [HasTerminal J] {F : J ⥤ C}
+    [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : HasLimit F :=
+  HasLimit.mk { cone := _, isLimit := limitOfDiagramTerminal (terminalIsTerminal) F }
+
 -- This is reducible to allow usage of lemmas about `cone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has a terminal object and all the morphisms in the diagram
 are isomorphisms, then the image of the terminal object is isomorphic to the limit of `F`. -/
 @[reducible]
-def limitOfTerminal (F : J ⥤ C) [HasTerminal J] [HasLimit F]
-    [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : limit F ≅ F.obj (⊤_ J) :=
+def limitOfTerminal (F : J ⥤ C) [HasTerminal J] [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] :
+    limit F ≅ F.obj (⊤_ J) :=
   IsLimit.conePointUniqueUpToIso (limit.isLimit _) (limitOfDiagramTerminal terminalIsTerminal F)
 #align category_theory.limits.limit_of_terminal CategoryTheory.Limits.limitOfTerminal
 
@@ -670,11 +677,14 @@ def colimitOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) :
     simp
 #align category_theory.limits.colimit_of_diagram_terminal CategoryTheory.Limits.colimitOfDiagramTerminal
 
+instance hasColimit_of_domain_hasTerminal [HasTerminal J] {F : J ⥤ C} : HasColimit F :=
+  HasColimit.mk { cocone := _, isColimit := colimitOfDiagramTerminal (terminalIsTerminal) F }
+
 -- This is reducible to allow usage of lemmas about `cocone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has a terminal object then the image of it is isomorphic
 to the colimit of `F`. -/
 @[reducible]
-def colimitOfTerminal (F : J ⥤ C) [HasTerminal J] [HasColimit F] : colimit F ≅ F.obj (⊤_ J) :=
+def colimitOfTerminal (F : J ⥤ C) [HasTerminal J] : colimit F ≅ F.obj (⊤_ J) :=
   IsColimit.coconePointUniqueUpToIso (colimit.isColimit _)
     (colimitOfDiagramTerminal terminalIsTerminal F)
 #align category_theory.limits.colimit_of_terminal CategoryTheory.Limits.colimitOfTerminal
@@ -702,12 +712,16 @@ def colimitOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
   desc S := S.ι.app _
 #align category_theory.limits.colimit_of_diagram_initial CategoryTheory.Limits.colimitOfDiagramInitial
 
+instance hasColimit_of_domain_hasInitial [HasInitial J] {F : J ⥤ C}
+    [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : HasColimit F :=
+  HasColimit.mk { cocone := _, isColimit := colimitOfDiagramInitial (initialIsInitial) F }
+
 -- This is reducible to allow usage of lemmas about `cocone_point_unique_up_to_iso`.
 /-- For a functor `F : J ⥤ C`, if `J` has an initial object and all the morphisms in the diagram
 are isomorphisms, then the image of the initial object is isomorphic to the colimit of `F`. -/
 @[reducible]
-def colimitOfInitial (F : J ⥤ C) [HasInitial J] [HasColimit F]
-    [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : colimit F ≅ F.obj (⊥_ J) :=
+def colimitOfInitial (F : J ⥤ C) [HasInitial J] [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] :
+    colimit F ≅ F.obj (⊥_ J) :=
   IsColimit.coconePointUniqueUpToIso (colimit.isColimit _)
     (colimitOfDiagramInitial initialIsInitial _)
 #align category_theory.limits.colimit_of_initial CategoryTheory.Limits.colimitOfInitial
@@ -719,7 +733,7 @@ theorem isIso_π_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasLimit
   ⟨⟨limit.lift _ (coneOfDiagramInitial I F), ⟨by ext; simp, by simp⟩⟩⟩
 #align category_theory.limits.is_iso_π_of_is_initial CategoryTheory.Limits.isIso_π_of_isInitial
 
-instance isIso_π_initial [HasInitial J] (F : J ⥤ C) [HasLimit F] : IsIso (limit.π F (⊥_ J)) :=
+instance isIso_π_initial [HasInitial J] (F : J ⥤ C) : IsIso (limit.π F (⊥_ J)) :=
   isIso_π_of_isInitial initialIsInitial F
 #align category_theory.limits.is_iso_π_initial CategoryTheory.Limits.isIso_π_initial
 
@@ -728,8 +742,8 @@ theorem isIso_π_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasLimi
   ⟨⟨limit.lift _ (coneOfDiagramTerminal I F), by ext; simp, by simp⟩⟩
 #align category_theory.limits.is_iso_π_of_is_terminal CategoryTheory.Limits.isIso_π_of_isTerminal
 
-instance isIso_π_terminal [HasTerminal J] (F : J ⥤ C) [HasLimit F]
-    [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (limit.π F (⊤_ J)) :=
+instance isIso_π_terminal [HasTerminal J] (F : J ⥤ C) [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] :
+    IsIso (limit.π F (⊤_ J)) :=
   isIso_π_of_isTerminal terminalIsTerminal F
 #align category_theory.limits.is_iso_π_terminal CategoryTheory.Limits.isIso_π_terminal
 
@@ -740,7 +754,7 @@ theorem isIso_ι_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasColi
   ⟨⟨colimit.desc _ (coconeOfDiagramTerminal I F), ⟨by simp, by ext; simp⟩⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_terminal CategoryTheory.Limits.isIso_ι_of_isTerminal
 
-instance isIso_ι_terminal [HasTerminal J] (F : J ⥤ C) [HasColimit F] : IsIso (colimit.ι F (⊤_ J)) :=
+instance isIso_ι_terminal [HasTerminal J] (F : J ⥤ C) : IsIso (colimit.ι F (⊤_ J)) :=
   isIso_ι_of_isTerminal terminalIsTerminal F
 #align category_theory.limits.is_iso_ι_terminal CategoryTheory.Limits.isIso_ι_terminal
 
@@ -755,8 +769,8 @@ theorem isIso_ι_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasColimi
   ⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_initial CategoryTheory.Limits.isIso_ι_of_isInitial
 
-instance isIso_ι_initial [HasInitial J] (F : J ⥤ C) [HasColimit F]
-    [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (colimit.ι F (⊥_ J)) :=
+instance isIso_ι_initial [HasInitial J] (F : J ⥤ C) [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] :
+    IsIso (colimit.ι F (⊥_ J)) :=
   isIso_ι_of_isInitial initialIsInitial F
 #align category_theory.limits.is_iso_ι_initial CategoryTheory.Limits.isIso_ι_initial

239d882c

chore: replace ConeMorphism.Hom by ConeMorphism.hom (#7176)

3e44bb07

Diff

@@ -92,8 +92,8 @@ def isTerminalTop {α : Type*} [Preorder α] [OrderTop α] : IsTerminal (⊤ : 
 /-- Transport a term of type `IsTerminal` across an isomorphism. -/
 def IsTerminal.ofIso {Y Z : C} (hY : IsTerminal Y) (i : Y ≅ Z) : IsTerminal Z :=
   IsLimit.ofIsoLimit hY
-    { hom := { Hom := i.hom }
-      inv := { Hom := i.inv } }
+    { hom := { hom := i.hom }
+      inv := { hom := i.inv } }
 #align category_theory.limits.is_terminal.of_iso CategoryTheory.Limits.IsTerminal.ofIso
 
 /-- An object `X` is initial iff for every `Y` there is a unique morphism `X ⟶ Y`. -/
@@ -133,8 +133,8 @@ def isInitialBot {α : Type*} [Preorder α] [OrderBot α] : IsInitial (⊥ : α)
 /-- Transport a term of type `is_initial` across an isomorphism. -/
 def IsInitial.ofIso {X Y : C} (hX : IsInitial X) (i : X ≅ Y) : IsInitial Y :=
   IsColimit.ofIsoColimit hX
-    { hom := { Hom := i.hom }
-      inv := { Hom := i.inv } }
+    { hom := { hom := i.hom }
+      inv := { hom := i.inv } }
 #align category_theory.limits.is_initial.of_iso CategoryTheory.Limits.IsInitial.ofIso
 
 /-- Give the morphism to a terminal object from any other. -/

239d882c

feat(CategoryTheory/Bicategory): define left Kan extensions (#6552)

The basic design follows the API for colimits in the category theory library.

The dictionary looks like: Current PR LeftExtension <-> Limits.Cocone LeftExtension.IsKan <-> Limits.IsColimit Future PR LeftExtension.HasKan <-> Limits.HasColimit lan <-> Limits.colimit

The diagrams in the docs are far from ideal, but I hope it helps for the time being. I would be very happy to have a graphical visualization by e.g. the widgets.

f8d81046

Diff

@@ -77,6 +77,13 @@ def IsTerminal.ofUnique (Y : C) [h : ∀ X : C, Unique (X ⟶ Y)] : IsTerminal Y
   fac := fun _ ⟨j⟩ => j.elim
 #align category_theory.limits.is_terminal.of_unique CategoryTheory.Limits.IsTerminal.ofUnique
 
+/-- An object `Y` is terminal if for every `X` there is a unique morphism `X ⟶ Y`
+    (as explicit arguments). -/
+def IsTerminal.ofUniqueHom {Y : C} (h : ∀ X : C, X ⟶ Y) (uniq : ∀ (X : C) (m : X ⟶ Y), m = h X) :
+    IsTerminal Y :=
+  have : ∀ X : C, Unique (X ⟶ Y) := fun X ↦ ⟨⟨h X⟩, uniq X⟩
+  IsTerminal.ofUnique Y
+
 /-- If `α` is a preorder with top, then `⊤` is a terminal object. -/
 def isTerminalTop {α : Type*} [Preorder α] [OrderTop α] : IsTerminal (⊤ : α) :=
   IsTerminal.ofUnique _
@@ -111,6 +118,13 @@ def IsInitial.ofUnique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : IsInitial X w
   fac := fun _ ⟨j⟩ => j.elim
 #align category_theory.limits.is_initial.of_unique CategoryTheory.Limits.IsInitial.ofUnique
 
+/-- An object `X` is initial if for every `Y` there is a unique morphism `X ⟶ Y`
+    (as explicit arguments). -/
+def IsInitial.ofUniqueHom {X : C} (h : ∀ Y : C, X ⟶ Y) (uniq : ∀ (Y : C) (m : X ⟶ Y), m = h Y) :
+    IsInitial X :=
+  have : ∀ Y : C, Unique (X ⟶ Y) := fun Y ↦ ⟨⟨h Y⟩, uniq Y⟩
+  IsInitial.ofUnique X
+
 /-- If `α` is a preorder with bot, then `⊥` is an initial object. -/
 def isInitialBot {α : Type*} [Preorder α] [OrderBot α] : IsInitial (⊥ : α) :=
   IsInitial.ofUnique _

239d882c

chore: remove unused simps (#6632)

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

916c75c1

Diff

@@ -518,7 +518,6 @@ every morphism out of it is a monomorphism. -/
 theorem InitialMonoClass.of_isInitial {I : C} (hI : IsInitial I) (h : ∀ X, Mono (hI.to X)) :
     InitialMonoClass C where
   isInitial_mono_from {I'} X hI' := by
-    dsimp
     rw [hI'.hom_ext (hI'.to X) ((hI'.uniqueUpToIso hI).hom ≫ hI.to X)]
     apply mono_comp
 #align category_theory.limits.initial_mono_class.of_is_initial CategoryTheory.Limits.InitialMonoClass.of_isInitial

239d882c

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

@@ -78,7 +78,7 @@ def IsTerminal.ofUnique (Y : C) [h : ∀ X : C, Unique (X ⟶ Y)] : IsTerminal Y
 #align category_theory.limits.is_terminal.of_unique CategoryTheory.Limits.IsTerminal.ofUnique
 
 /-- If `α` is a preorder with top, then `⊤` is a terminal object. -/
-def isTerminalTop {α : Type _} [Preorder α] [OrderTop α] : IsTerminal (⊤ : α) :=
+def isTerminalTop {α : Type*} [Preorder α] [OrderTop α] : IsTerminal (⊤ : α) :=
   IsTerminal.ofUnique _
 #align category_theory.limits.is_terminal_top CategoryTheory.Limits.isTerminalTop
 
@@ -112,7 +112,7 @@ def IsInitial.ofUnique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : IsInitial X w
 #align category_theory.limits.is_initial.of_unique CategoryTheory.Limits.IsInitial.ofUnique
 
 /-- If `α` is a preorder with bot, then `⊥` is an initial object. -/
-def isInitialBot {α : Type _} [Preorder α] [OrderBot α] : IsInitial (⊥ : α) :=
+def isInitialBot {α : Type*} [Preorder α] [OrderBot α] : IsInitial (⊥ : α) :=
   IsInitial.ofUnique _
 #align category_theory.limits.is_initial_bot CategoryTheory.Limits.isInitialBot
 
@@ -436,7 +436,7 @@ theorem hasInitial_of_hasTerminal_op [HasTerminal Cᵒᵖ] : HasInitial C :=
   (initialUnopOfTerminal terminalIsTerminal).hasInitial
 #align category_theory.limits.has_initial_of_has_terminal_op CategoryTheory.Limits.hasInitial_of_hasTerminal_op
 
-instance {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C] :
+instance {J : Type*} [Category J] {C : Type*} [Category C] [HasTerminal C] :
     HasLimit ((CategoryTheory.Functor.const J).obj (⊤_ C)) :=
   HasLimit.mk
     { cone :=
@@ -446,7 +446,7 @@ instance {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C] :
 
 /-- The limit of the constant `⊤_ C` functor is `⊤_ C`. -/
 @[simps hom]
-def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C] :
+def limitConstTerminal {J : Type*} [Category J] {C : Type*} [Category C] [HasTerminal C] :
     limit ((CategoryTheory.Functor.const J).obj (⊤_ C)) ≅ ⊤_ C where
   hom := terminal.from _
   inv :=
@@ -456,13 +456,13 @@ def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasT
 #align category_theory.limits.limit_const_terminal CategoryTheory.Limits.limitConstTerminal
 
 @[reassoc (attr := simp)]
-theorem limitConstTerminal_inv_π {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C]
+theorem limitConstTerminal_inv_π {J : Type*} [Category J] {C : Type*} [Category C] [HasTerminal C]
     {j : J} :
     limitConstTerminal.inv ≫ limit.π ((CategoryTheory.Functor.const J).obj (⊤_ C)) j =
       terminal.from _ := by aesop_cat
 #align category_theory.limits.limit_const_terminal_inv_π CategoryTheory.Limits.limitConstTerminal_inv_π
 
-instance {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
+instance {J : Type*} [Category J] {C : Type*} [Category C] [HasInitial C] :
     HasColimit ((CategoryTheory.Functor.const J).obj (⊥_ C)) :=
   HasColimit.mk
     { cocone :=
@@ -472,7 +472,7 @@ instance {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
 
 /-- The colimit of the constant `⊥_ C` functor is `⊥_ C`. -/
 @[simps inv]
-def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
+def colimitConstInitial {J : Type*} [Category J] {C : Type*} [Category C] [HasInitial C] :
     colimit ((CategoryTheory.Functor.const J).obj (⊥_ C)) ≅ ⊥_ C where
   hom :=
     colimit.desc ((CategoryTheory.Functor.const J).obj (⊥_ C))
@@ -482,7 +482,7 @@ def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [Has
 #align category_theory.limits.colimit_const_initial CategoryTheory.Limits.colimitConstInitial
 
 @[reassoc (attr := simp)]
-theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C]
+theorem ι_colimitConstInitial_hom {J : Type*} [Category J] {C : Type*} [Category C] [HasInitial C]
     {j : J} :
     colimit.ι ((CategoryTheory.Functor.const J).obj (⊥_ C)) j ≫ colimitConstInitial.hom =
       initial.to _ := by aesop_cat

239d882c

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

@@ -2,17 +2,14 @@
 Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.limits.shapes.terminal
-! leanprover-community/mathlib commit 239d882c4fb58361ee8b3b39fb2091320edef10a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.PEmpty
 import Mathlib.CategoryTheory.Limits.HasLimits
 import Mathlib.CategoryTheory.EpiMono
 import Mathlib.CategoryTheory.Category.Preorder
 
+#align_import category_theory.limits.shapes.terminal from "leanprover-community/mathlib"@"239d882c4fb58361ee8b3b39fb2091320edef10a"
+
 /-!
 # Initial and terminal objects in a category.

239d882c

feat: add Aesop rules for Discrete category (#2519)

Adds a global Aesop cases rule for the Discrete category. This rule was previously added locally in several places.

ecb36a8f

Diff

@@ -31,8 +31,6 @@ namespace CategoryTheory.Limits
 
 variable {C : Type u₁} [Category.{v₁} C]
 
-attribute [local aesop safe cases (rule_sets [CategoryTheory])] Discrete
-
 /-- Construct a cone for the empty diagram given an object. -/
 @[simps]
 def asEmptyCone (X : C) : Cone (Functor.empty.{0} C) :=

239d882c

feat: more consistent use of ext, and updating porting notes. (#5242)

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

dbae2f17

Diff

@@ -464,8 +464,7 @@ def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasT
 theorem limitConstTerminal_inv_π {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C]
     {j : J} :
     limitConstTerminal.inv ≫ limit.π ((CategoryTheory.Functor.const J).obj (⊤_ C)) j =
-      terminal.from _ := by
-  apply Limits.limit.hom_ext; aesop_cat
+      terminal.from _ := by aesop_cat
 #align category_theory.limits.limit_const_terminal_inv_π CategoryTheory.Limits.limitConstTerminal_inv_π
 
 instance {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
@@ -491,7 +490,7 @@ def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [Has
 theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C]
     {j : J} :
     colimit.ι ((CategoryTheory.Functor.const J).obj (⊥_ C)) j ≫ colimitConstInitial.hom =
-      initial.to _ := by apply Limits.colimit.hom_ext; aesop_cat
+      initial.to _ := by aesop_cat
 #align category_theory.limits.ι_colimit_const_initial_hom CategoryTheory.Limits.ι_colimitConstInitial_hom
 
 /-- A category is an `InitialMonoClass` if the canonical morphism of an initial object is a

239d882c

chore: fix grammar 2/3 (#5002)

Part 2 of #5001

9e80ae3b

Diff

@@ -494,7 +494,7 @@ theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Categ
       initial.to _ := by apply Limits.colimit.hom_ext; aesop_cat
 #align category_theory.limits.ι_colimit_const_initial_hom CategoryTheory.Limits.ι_colimitConstInitial_hom
 
-/-- A category is a `InitialMonoClass` if the canonical morphism of an initial object is a
+/-- A category is an `InitialMonoClass` if the canonical morphism of an initial object is a
 monomorphism.  In practice, this is most useful when given an arbitrary morphism out of the chosen
 initial object, see `initial.mono_from`.
 Given a terminal object, this is equivalent to the assumption that the unique morphism from initial
@@ -519,7 +519,7 @@ instance (priority := 100) initial.mono_from [HasInitial C] [InitialMonoClass C]
   initialIsInitial.mono_from f
 #align category_theory.limits.initial.mono_from CategoryTheory.Limits.initial.mono_from
 
-/-- To show a category is a `InitialMonoClass` it suffices to give an initial object such that
+/-- To show a category is an `InitialMonoClass` it suffices to give an initial object such that
 every morphism out of it is a monomorphism. -/
 theorem InitialMonoClass.of_isInitial {I : C} (hI : IsInitial I) (h : ∀ X, Mono (hI.to X)) :
     InitialMonoClass C where
@@ -529,21 +529,21 @@ theorem InitialMonoClass.of_isInitial {I : C} (hI : IsInitial I) (h : ∀ X, Mon
     apply mono_comp
 #align category_theory.limits.initial_mono_class.of_is_initial CategoryTheory.Limits.InitialMonoClass.of_isInitial
 
-/-- To show a category is a `InitialMonoClass` it suffices to show every morphism out of the
+/-- To show a category is an `InitialMonoClass` it suffices to show every morphism out of the
 initial object is a monomorphism. -/
 theorem InitialMonoClass.of_initial [HasInitial C] (h : ∀ X : C, Mono (initial.to X)) :
     InitialMonoClass C :=
   InitialMonoClass.of_isInitial initialIsInitial h
 #align category_theory.limits.initial_mono_class.of_initial CategoryTheory.Limits.InitialMonoClass.of_initial
 
-/-- To show a category is a `InitialMonoClass` it suffices to show the unique morphism from an
+/-- To show a category is an `InitialMonoClass` it suffices to show the unique morphism from an
 initial object to a terminal object is a monomorphism. -/
 theorem InitialMonoClass.of_isTerminal {I T : C} (hI : IsInitial I) (hT : IsTerminal T)
     (_ : Mono (hI.to T)) : InitialMonoClass C :=
   InitialMonoClass.of_isInitial hI fun X => mono_of_mono_fac (hI.hom_ext (_ ≫ hT.from X) (hI.to T))
 #align category_theory.limits.initial_mono_class.of_is_terminal CategoryTheory.Limits.InitialMonoClass.of_isTerminal
 
-/-- To show a category is a `InitialMonoClass` it suffices to show the unique morphism from the
+/-- To show a category is an `InitialMonoClass` it suffices to show the unique morphism from the
 initial object to a terminal object is a monomorphism. -/
 theorem InitialMonoClass.of_terminal [HasInitial C] [HasTerminal C] (h : Mono (initial.to (⊤_ C))) :
     InitialMonoClass C :=

239d882c

chore: cleanup Discrete porting notes (#4780)

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

86ade6e9

Diff

@@ -31,22 +31,14 @@ namespace CategoryTheory.Limits
 
 variable {C : Type u₁} [Category.{v₁} C]
 
--- attribute [local tidy] tactic.discrete_cases -- Porting note: no tidy
-open Lean Elab Meta Tactic in
-/- Porting note: adding a lightweight macro intended to serve the narrow use case of casing on
-`Discrete PEmpty`. -/
-/-- A local tactic replacing the use of discrete cases on `PEmpty` in Lean 3.
-`dee` is short for `discrete_empty_elim`. -/
-scoped elab (name := discrete_empty_elim) "dee" : tactic => withMainContext do
-  evalTactic (← `(tactic| iterate (try {constructor}; try {intro ⟨a⟩; cases a} <;> intro )))
+attribute [local aesop safe cases (rule_sets [CategoryTheory])] Discrete
 
 /-- Construct a cone for the empty diagram given an object. -/
 @[simps]
 def asEmptyCone (X : C) : Cone (Functor.empty.{0} C) :=
   { pt := X
     π :=
-    { app := by dee
-      naturality := by dee } }
+    { app := by aesop_cat } }
 #align category_theory.limits.as_empty_cone CategoryTheory.Limits.asEmptyCone
 
 /-- Construct a cocone for the empty diagram given an object. -/
@@ -54,8 +46,7 @@ def asEmptyCone (X : C) : Cone (Functor.empty.{0} C) :=
 def asEmptyCocone (X : C) : Cocone (Functor.empty.{0} C) :=
   { pt := X
     ι :=
-    { app := by dee
-      naturality := by dee } }
+    { app := by aesop_cat } }
 #align category_theory.limits.as_empty_cocone CategoryTheory.Limits.asEmptyCocone
 
 /-- `X` is terminal if the cone it induces on the empty diagram is limiting. -/
@@ -70,15 +61,13 @@ abbrev IsInitial (X : C) :=
 
 /-- An object `Y` is terminal iff for every `X` there is a unique morphism `X ⟶ Y`. -/
 def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
-    IsLimit (⟨Y, (by dee), (by dee)⟩ :
-    Cone F) ≃ ∀ X : C, Unique (X ⟶ Y) where
+    IsLimit (⟨Y, by aesop_cat, by aesop_cat⟩ : Cone F) ≃ ∀ X : C, Unique (X ⟶ Y) where
   toFun t X :=
-    { default := t.lift ⟨X, ⟨(by dee),(by dee)⟩⟩
+    { default := t.lift ⟨X, ⟨by aesop_cat, by aesop_cat⟩⟩
       uniq := fun f =>
-        t.uniq ⟨X, ⟨by dee, by dee⟩⟩ f (by dee) }
+        t.uniq ⟨X, ⟨by aesop_cat, by aesop_cat⟩⟩ f (by aesop_cat) }
   invFun u :=
     { lift := fun s => (u s.pt).default
-      fac := by dee
       uniq := fun s _ _ => (u s.pt).2 _ }
   left_inv := by dsimp [Function.LeftInverse]; intro x; simp only [eq_iff_true_of_subsingleton]
   right_inv := by
@@ -101,19 +90,18 @@ def isTerminalTop {α : Type _} [Preorder α] [OrderTop α] : IsTerminal (⊤ :
 /-- Transport a term of type `IsTerminal` across an isomorphism. -/
 def IsTerminal.ofIso {Y Z : C} (hY : IsTerminal Y) (i : Y ≅ Z) : IsTerminal Z :=
   IsLimit.ofIsoLimit hY
-    { hom := { Hom := i.hom, w := by dee }
-      inv := { Hom := i.inv, w := by dee } }
+    { hom := { Hom := i.hom }
+      inv := { Hom := i.inv } }
 #align category_theory.limits.is_terminal.of_iso CategoryTheory.Limits.IsTerminal.ofIso
 
 /-- An object `X` is initial iff for every `Y` there is a unique morphism `X ⟶ Y`. -/
 def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :
-    IsColimit (⟨X, ⟨by dee,by dee⟩⟩ : Cocone F) ≃ ∀ Y : C, Unique (X ⟶ Y) where
+    IsColimit (⟨X, ⟨by aesop_cat, by aesop_cat⟩⟩ : Cocone F) ≃ ∀ Y : C, Unique (X ⟶ Y) where
   toFun t X :=
-    { default := t.desc ⟨X,⟨by dee,by dee⟩⟩
-      uniq := fun f => t.uniq ⟨X, ⟨by dee, by dee⟩⟩ f (by dee) }
+    { default := t.desc ⟨X, ⟨by aesop_cat, by aesop_cat⟩⟩
+      uniq := fun f => t.uniq ⟨X, ⟨by aesop_cat, by aesop_cat⟩⟩ f (by aesop_cat) }
   invFun u :=
     { desc := fun s => (u s.pt).default
-      fac := by dee
       uniq := fun s _ _ => (u s.pt).2 _ }
   left_inv := by dsimp [Function.LeftInverse]; intro; simp only [eq_iff_true_of_subsingleton]
   right_inv := by
@@ -136,8 +124,8 @@ def isInitialBot {α : Type _} [Preorder α] [OrderBot α] : IsInitial (⊥ : α
 /-- Transport a term of type `is_initial` across an isomorphism. -/
 def IsInitial.ofIso {X Y : C} (hX : IsInitial X) (i : X ≅ Y) : IsInitial Y :=
   IsColimit.ofIsoColimit hX
-    { hom := { Hom := i.hom, w := by dee }
-      inv := { Hom := i.inv, w := by dee } }
+    { hom := { Hom := i.hom }
+      inv := { Hom := i.inv } }
 #align category_theory.limits.is_initial.of_iso CategoryTheory.Limits.IsInitial.ofIso
 
 /-- Give the morphism to a terminal object from any other. -/
@@ -147,7 +135,7 @@ def IsTerminal.from {X : C} (t : IsTerminal X) (Y : C) : Y ⟶ X :=
 
 /-- Any two morphisms to a terminal object are equal. -/
 theorem IsTerminal.hom_ext {X Y : C} (t : IsTerminal X) (f g : Y ⟶ X) : f = g :=
-  IsLimit.hom_ext t (by dee)
+  IsLimit.hom_ext t (by aesop_cat)
 #align category_theory.limits.is_terminal.hom_ext CategoryTheory.Limits.IsTerminal.hom_ext
 
 @[simp]
@@ -168,7 +156,7 @@ def IsInitial.to {X : C} (t : IsInitial X) (Y : C) : X ⟶ Y :=
 
 /-- Any two morphisms from an initial object are equal. -/
 theorem IsInitial.hom_ext {X Y : C} (t : IsInitial X) (f g : X ⟶ Y) : f = g :=
-  IsColimit.hom_ext t (by dee)
+  IsColimit.hom_ext t (by aesop_cat)
 #align category_theory.limits.is_initial.hom_ext CategoryTheory.Limits.IsInitial.hom_ext
 
 @[simp]
@@ -239,13 +227,12 @@ variable (X : C) {F₁ : Discrete.{w} PEmpty ⥤ C} {F₂ : Discrete.{w'} PEmpty
     as long as the cone points are isomorphic. -/
 def isLimitChangeEmptyCone {c₁ : Cone F₁} (hl : IsLimit c₁) (c₂ : Cone F₂) (hi : c₁.pt ≅ c₂.pt) :
     IsLimit c₂ where
-  lift c := hl.lift ⟨c.pt, by dee, by dee⟩ ≫ hi.hom
-  fac _ j := j.as.elim
+  lift c := hl.lift ⟨c.pt, by aesop_cat, by aesop_cat⟩ ≫ hi.hom
   uniq c f _ := by
     dsimp
     rw [← hl.uniq _ (f ≫ hi.inv) _]
     · simp only [Category.assoc, Iso.inv_hom_id, Category.comp_id]
-    · dee
+    · aesop_cat
 #align category_theory.limits.is_limit_change_empty_cone CategoryTheory.Limits.isLimitChangeEmptyCone
 
 /-- Replacing an empty cone in `IsLimit` by another with the same cone point
@@ -261,7 +248,8 @@ def isLimitEmptyConeEquiv (c₁ : Cone F₁) (c₂ : Cone F₂) (h : c₁.pt ≅
 #align category_theory.limits.is_limit_empty_cone_equiv CategoryTheory.Limits.isLimitEmptyConeEquiv
 
 theorem hasTerminalChangeDiagram (h : HasLimit F₁) : HasLimit F₂ :=
-  ⟨⟨⟨⟨limit F₁, by dee, by dee⟩, isLimitChangeEmptyCone C (limit.isLimit F₁) _ (eqToIso rfl)⟩⟩⟩
+  ⟨⟨⟨⟨limit F₁, by aesop_cat, by aesop_cat⟩,
+    isLimitChangeEmptyCone C (limit.isLimit F₁) _ (eqToIso rfl)⟩⟩⟩
 #align category_theory.limits.has_terminal_change_diagram CategoryTheory.Limits.hasTerminalChangeDiagram
 
 theorem hasTerminalChangeUniverse [h : HasLimitsOfShape (Discrete.{w} PEmpty) C] :
@@ -273,13 +261,12 @@ theorem hasTerminalChangeUniverse [h : HasLimitsOfShape (Discrete.{w} PEmpty) C]
     as long as the cocone points are isomorphic. -/
 def isColimitChangeEmptyCocone {c₁ : Cocone F₁} (hl : IsColimit c₁) (c₂ : Cocone F₂)
     (hi : c₁.pt ≅ c₂.pt) : IsColimit c₂ where
-  desc c := hi.inv ≫ hl.desc ⟨c.pt, by dee, by dee⟩
-  fac _ j := j.as.elim
+  desc c := hi.inv ≫ hl.desc ⟨c.pt, by aesop_cat, by aesop_cat⟩
   uniq c f _ := by
     dsimp
     rw [← hl.uniq _ (hi.hom ≫ f) _]
     · simp only [Iso.inv_hom_id_assoc]
-    · dee
+    · aesop_cat
 #align category_theory.limits.is_colimit_change_empty_cocone CategoryTheory.Limits.isColimitChangeEmptyCocone
 
 /-- Replacing an empty cocone in `IsColimit` by another with the same cocone point
@@ -295,7 +282,7 @@ def isColimitEmptyCoconeEquiv (c₁ : Cocone F₁) (c₂ : Cocone F₂) (h : c
 #align category_theory.limits.is_colimit_empty_cocone_equiv CategoryTheory.Limits.isColimitEmptyCoconeEquiv
 
 theorem hasInitialChangeDiagram (h : HasColimit F₁) : HasColimit F₂ :=
-  ⟨⟨⟨⟨colimit F₁, by dee, by dee⟩,
+  ⟨⟨⟨⟨colimit F₁, by aesop_cat, by aesop_cat⟩,
     isColimitChangeEmptyCocone C (colimit.isColimit F₁) _ (eqToIso rfl)⟩⟩⟩
 #align category_theory.limits.has_initial_change_diagram CategoryTheory.Limits.hasInitialChangeDiagram
 
@@ -339,7 +326,7 @@ theorem hasTerminal_of_unique (X : C) [h : ∀ Y : C, Unique (Y ⟶ X)] : HasTer
 #align category_theory.limits.has_terminal_of_unique CategoryTheory.Limits.hasTerminal_of_unique
 
 theorem IsTerminal.hasTerminal {X : C} (h : IsTerminal X) : HasTerminal C :=
-  { has_limit := fun F => HasLimit.mk ⟨⟨X, by dee, by dee⟩,
+  { has_limit := fun F => HasLimit.mk ⟨⟨X, by aesop_cat, by aesop_cat⟩,
     isLimitChangeEmptyCone _ h _ (Iso.refl _)⟩ }
 #align category_theory.limits.is_terminal.has_terminal CategoryTheory.Limits.IsTerminal.hasTerminal
 
@@ -351,7 +338,7 @@ theorem hasInitial_of_unique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : HasInit
 
 theorem IsInitial.hasInitial {X : C} (h : IsInitial X) : HasInitial C where
   has_colimit F :=
-    HasColimit.mk ⟨⟨X, by dee, by dee⟩, isColimitChangeEmptyCocone _ h _ (Iso.refl _)⟩
+    HasColimit.mk ⟨⟨X, by aesop_cat, by aesop_cat⟩, isColimitChangeEmptyCocone _ h _ (Iso.refl _)⟩
 #align category_theory.limits.is_initial.has_initial CategoryTheory.Limits.IsInitial.hasInitial
 
 /-- The map from an object to the terminal object. -/
@@ -367,15 +354,11 @@ abbrev initial.to [HasInitial C] (P : C) : ⊥_ C ⟶ P :=
 /-- A terminal object is terminal. -/
 def terminalIsTerminal [HasTerminal C] : IsTerminal (⊤_ C) where
   lift s := terminal.from _
-  fac := by dee
-  uniq := by intro _ _ _; dsimp; ext ⟨j⟩; dsimp; cases j
 #align category_theory.limits.terminal_is_terminal CategoryTheory.Limits.terminalIsTerminal
 
 /-- An initial object is initial. -/
 def initialIsInitial [HasInitial C] : IsInitial (⊥_ C) where
   desc s := initial.to _
-  fac := by dee
-  uniq := by intro _ _ _; dsimp; ext ⟨j⟩; dsimp; cases j
 #align category_theory.limits.initial_is_initial CategoryTheory.Limits.initialIsInitial
 
 instance uniqueToTerminal [HasTerminal C] (P : C) : Unique (P ⟶ ⊤_ C) :=
@@ -421,28 +404,24 @@ instance initial.isSplitEpi_to {Y : C} [HasInitial C] (f : Y ⟶ ⊥_ C) : IsSpl
 /-- An initial object is terminal in the opposite category. -/
 def terminalOpOfInitial {X : C} (t : IsInitial X) : IsTerminal (Opposite.op X) where
   lift s := (t.to s.pt.unop).op
-  fac := by dee
   uniq s m _ := Quiver.Hom.unop_inj (t.hom_ext _ _)
 #align category_theory.limits.terminal_op_of_initial CategoryTheory.Limits.terminalOpOfInitial
 
 /-- An initial object in the opposite category is terminal in the original category. -/
 def terminalUnopOfInitial {X : Cᵒᵖ} (t : IsInitial X) : IsTerminal X.unop where
   lift s := (t.to (Opposite.op s.pt)).unop
-  fac := by dee
   uniq s m _ := Quiver.Hom.op_inj (t.hom_ext _ _)
 #align category_theory.limits.terminal_unop_of_initial CategoryTheory.Limits.terminalUnopOfInitial
 
 /-- A terminal object is initial in the opposite category. -/
 def initialOpOfTerminal {X : C} (t : IsTerminal X) : IsInitial (Opposite.op X) where
   desc s := (t.from s.pt.unop).op
-  fac := by dee
   uniq s m _ := Quiver.Hom.unop_inj (t.hom_ext _ _)
 #align category_theory.limits.initial_op_of_terminal CategoryTheory.Limits.initialOpOfTerminal
 
 /-- A terminal object in the opposite category is initial in the original category. -/
 def initialUnopOfTerminal {X : Cᵒᵖ} (t : IsTerminal X) : IsInitial X.unop where
   desc s := (t.from (Opposite.op s.pt)).unop
-  fac := by dee
   uniq s m _ := Quiver.Hom.op_inj (t.hom_ext _ _)
 #align category_theory.limits.initial_unop_of_terminal CategoryTheory.Limits.initialUnopOfTerminal
 
@@ -486,7 +465,7 @@ theorem limitConstTerminal_inv_π {J : Type _} [Category J] {C : Type _} [Catego
     {j : J} :
     limitConstTerminal.inv ≫ limit.π ((CategoryTheory.Functor.const J).obj (⊤_ C)) j =
       terminal.from _ := by
-  apply Limits.limit.hom_ext; dee
+  apply Limits.limit.hom_ext; aesop_cat
 #align category_theory.limits.limit_const_terminal_inv_π CategoryTheory.Limits.limitConstTerminal_inv_π
 
 instance {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
@@ -512,7 +491,7 @@ def colimitConstInitial {J : Type _} [Category J] {C : Type _} [Category C] [Has
 theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C]
     {j : J} :
     colimit.ι ((CategoryTheory.Functor.const J).obj (⊥_ C)) j ≫ colimitConstInitial.hom =
-      initial.to _ := by apply Limits.colimit.hom_ext; dee
+      initial.to _ := by apply Limits.colimit.hom_ext; aesop_cat
 #align category_theory.limits.ι_colimit_const_initial_hom CategoryTheory.Limits.ι_colimitConstInitial_hom
 
 /-- A category is a `InitialMonoClass` if the canonical morphism of an initial object is a

239d882c

chore: tidy various files (#3584)

3a1848ee

Diff

@@ -225,7 +225,7 @@ abbrev HasTerminal :=
 #align category_theory.limits.has_terminal CategoryTheory.Limits.HasTerminal
 
 /-- A category has an initial object if it has a colimit over the empty diagram.
-Use `has_initial_of_unique` to construct instances.
+Use `hasInitial_of_unique` to construct instances.
 -/
 abbrev HasInitial :=
   HasColimitsOfShape (Discrete.{0} PEmpty) C
@@ -265,12 +265,8 @@ theorem hasTerminalChangeDiagram (h : HasLimit F₁) : HasLimit F₂ :=
 #align category_theory.limits.has_terminal_change_diagram CategoryTheory.Limits.hasTerminalChangeDiagram
 
 theorem hasTerminalChangeUniverse [h : HasLimitsOfShape (Discrete.{w} PEmpty) C] :
-    HasLimitsOfShape (Discrete.{w'} PEmpty) C :=
-  {
-    has_limit := fun _ =>
-      hasTerminalChangeDiagram C
-        (let f := h.1
-        f (Functor.empty C)) }
+    HasLimitsOfShape (Discrete.{w'} PEmpty) C where
+  has_limit _ := hasTerminalChangeDiagram C (h.1 (Functor.empty C))
 #align category_theory.limits.has_terminal_change_universe CategoryTheory.Limits.hasTerminalChangeUniverse
 
 /-- Being initial is independent of the empty diagram, its universe, and the cocone over it,
@@ -304,12 +300,8 @@ theorem hasInitialChangeDiagram (h : HasColimit F₁) : HasColimit F₂ :=
 #align category_theory.limits.has_initial_change_diagram CategoryTheory.Limits.hasInitialChangeDiagram
 
 theorem hasInitialChangeUniverse [h : HasColimitsOfShape (Discrete.{w} PEmpty) C] :
-    HasColimitsOfShape (Discrete.{w'} PEmpty) C :=
-  {
-    has_colimit := fun _ =>
-      hasInitialChangeDiagram C
-        (let f := h.1
-        f (Functor.empty C)) }
+    HasColimitsOfShape (Discrete.{w'} PEmpty) C where
+  has_colimit _ := hasInitialChangeDiagram C (h.1 (Functor.empty C))
 #align category_theory.limits.has_initial_change_universe CategoryTheory.Limits.hasInitialChangeUniverse
 
 end Univ
@@ -357,10 +349,9 @@ theorem hasInitial_of_unique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : HasInit
   { has_colimit := fun F => HasColimit.mk ⟨_, (isInitialEquivUnique F X).invFun h⟩ }
 #align category_theory.limits.has_initial_of_unique CategoryTheory.Limits.hasInitial_of_unique
 
-theorem IsInitial.hasInitial {X : C} (h : IsInitial X) : HasInitial C :=
-  {
-    has_colimit := fun F =>
-      HasColimit.mk ⟨⟨X, by dee, by dee⟩, isColimitChangeEmptyCocone _ h _ (Iso.refl _)⟩ }
+theorem IsInitial.hasInitial {X : C} (h : IsInitial X) : HasInitial C where
+  has_colimit F :=
+    HasColimit.mk ⟨⟨X, by dee, by dee⟩, isColimitChangeEmptyCocone _ h _ (Iso.refl _)⟩
 #align category_theory.limits.is_initial.has_initial CategoryTheory.Limits.IsInitial.hasInitial
 
 /-- The map from an object to the terminal object. -/
@@ -495,7 +486,7 @@ theorem limitConstTerminal_inv_π {J : Type _} [Category J] {C : Type _} [Catego
     {j : J} :
     limitConstTerminal.inv ≫ limit.π ((CategoryTheory.Functor.const J).obj (⊤_ C)) j =
       terminal.from _ := by
-        apply Limits.limit.hom_ext; dee
+  apply Limits.limit.hom_ext; dee
 #align category_theory.limits.limit_const_terminal_inv_π CategoryTheory.Limits.limitConstTerminal_inv_π
 
 instance {J : Type _} [Category J] {C : Type _} [Category C] [HasInitial C] :
@@ -524,7 +515,7 @@ theorem ι_colimitConstInitial_hom {J : Type _} [Category J] {C : Type _} [Categ
       initial.to _ := by apply Limits.colimit.hom_ext; dee
 #align category_theory.limits.ι_colimit_const_initial_hom CategoryTheory.Limits.ι_colimitConstInitial_hom
 
-/-- A category is a `initial_mono_class` if the canonical morphism of an initial object is a
+/-- A category is a `InitialMonoClass` if the canonical morphism of an initial object is a
 monomorphism.  In practice, this is most useful when given an arbitrary morphism out of the chosen
 initial object, see `initial.mono_from`.
 Given a terminal object, this is equivalent to the assumption that the unique morphism from initial
@@ -549,32 +540,31 @@ instance (priority := 100) initial.mono_from [HasInitial C] [InitialMonoClass C]
   initialIsInitial.mono_from f
 #align category_theory.limits.initial.mono_from CategoryTheory.Limits.initial.mono_from
 
-/-- To show a category is a `initial_mono_class` it suffices to give an initial object such that
+/-- To show a category is a `InitialMonoClass` it suffices to give an initial object such that
 every morphism out of it is a monomorphism. -/
 theorem InitialMonoClass.of_isInitial {I : C} (hI : IsInitial I) (h : ∀ X, Mono (hI.to X)) :
-    InitialMonoClass C :=
-  {
-    isInitial_mono_from := fun {I'} X hI' => by
-      dsimp
-      rw [hI'.hom_ext (hI'.to X) ((hI'.uniqueUpToIso hI).hom ≫ hI.to X)]
-      apply mono_comp }
+    InitialMonoClass C where
+  isInitial_mono_from {I'} X hI' := by
+    dsimp
+    rw [hI'.hom_ext (hI'.to X) ((hI'.uniqueUpToIso hI).hom ≫ hI.to X)]
+    apply mono_comp
 #align category_theory.limits.initial_mono_class.of_is_initial CategoryTheory.Limits.InitialMonoClass.of_isInitial
 
-/-- To show a category is a `initial_mono_class` it suffices to show every morphism out of the
+/-- To show a category is a `InitialMonoClass` it suffices to show every morphism out of the
 initial object is a monomorphism. -/
 theorem InitialMonoClass.of_initial [HasInitial C] (h : ∀ X : C, Mono (initial.to X)) :
     InitialMonoClass C :=
   InitialMonoClass.of_isInitial initialIsInitial h
 #align category_theory.limits.initial_mono_class.of_initial CategoryTheory.Limits.InitialMonoClass.of_initial
 
-/-- To show a category is a `initial_mono_class` it suffices to show the unique morphism from an
+/-- To show a category is a `InitialMonoClass` it suffices to show the unique morphism from an
 initial object to a terminal object is a monomorphism. -/
 theorem InitialMonoClass.of_isTerminal {I T : C} (hI : IsInitial I) (hT : IsTerminal T)
     (_ : Mono (hI.to T)) : InitialMonoClass C :=
   InitialMonoClass.of_isInitial hI fun X => mono_of_mono_fac (hI.hom_ext (_ ≫ hT.from X) (hI.to T))
 #align category_theory.limits.initial_mono_class.of_is_terminal CategoryTheory.Limits.InitialMonoClass.of_isTerminal
 
-/-- To show a category is a `initial_mono_class` it suffices to show the unique morphism from the
+/-- To show a category is a `InitialMonoClass` it suffices to show the unique morphism from the
 initial object to a terminal object is a monomorphism. -/
 theorem InitialMonoClass.of_terminal [HasInitial C] [HasTerminal C] (h : Mono (initial.to (⊤_ C))) :
     InitialMonoClass C :=
@@ -588,7 +578,7 @@ variable {D : Type u₂} [Category.{v₂} D] (G : C ⥤ D)
 /-- The comparison morphism from the image of a terminal object to the terminal object in the target
 category.
 This is an isomorphism iff `G` preserves terminal objects, see
-`category_theory.limits.preserves_terminal.of_iso_comparison`.
+`CategoryTheory.Limits.PreservesTerminal.ofIsoComparison`.
 -/
 def terminalComparison [HasTerminal C] [HasTerminal D] : G.obj (⊤_ C) ⟶ ⊤_ D :=
   terminal.from _
@@ -608,7 +598,7 @@ end Comparison
 variable {J : Type u} [Category.{v} J]
 
 /-- From a functor `F : J ⥤ C`, given an initial object of `J`, construct a cone for `J`.
-In `limit_of_diagram_initial` we show it is a limit cone. -/
+In `limitOfDiagramInitial` we show it is a limit cone. -/
 @[simps]
 def coneOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) : Cone F where
   pt := F.obj X
@@ -620,7 +610,7 @@ def coneOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) : Cone F where
 #align category_theory.limits.cone_of_diagram_initial CategoryTheory.Limits.coneOfDiagramInitial
 
 /-- From a functor `F : J ⥤ C`, given an initial object of `J`, show the cone
-`cone_of_diagram_initial` is a limit. -/
+`coneOfDiagramInitial` is a limit. -/
 def limitOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) :
     IsLimit (coneOfDiagramInitial tX F) where
   lift s := s.π.app X
@@ -641,7 +631,7 @@ def limitOfInitial (F : J ⥤ C) [HasInitial J] [HasLimit F] : limit F ≅ F.obj
 
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J`, construct a cone for `J`,
 provided that the morphisms in the diagram are isomorphisms.
-In `limit_of_diagram_terminal` we show it is a limit cone. -/
+In `limitOfDiagramTerminal` we show it is a limit cone. -/
 @[simps]
 def coneOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : Cone F where
@@ -656,7 +646,7 @@ def coneOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
 #align category_theory.limits.cone_of_diagram_terminal CategoryTheory.Limits.coneOfDiagramTerminal
 
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J` and that the morphisms in the
-diagram are isomorphisms, show the cone `cone_of_diagram_terminal` is a limit. -/
+diagram are isomorphisms, show the cone `coneOfDiagramTerminal` is a limit. -/
 def limitOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsLimit (coneOfDiagramTerminal hX F) where
   lift S := S.π.app _
@@ -672,7 +662,7 @@ def limitOfTerminal (F : J ⥤ C) [HasTerminal J] [HasLimit F]
 #align category_theory.limits.limit_of_terminal CategoryTheory.Limits.limitOfTerminal
 
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J`, construct a cocone for `J`.
-In `colimit_of_diagram_terminal` we show it is a colimit cocone. -/
+In `colimitOfDiagramTerminal` we show it is a colimit cocone. -/
 @[simps]
 def coconeOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) : Cocone F where
   pt := F.obj X
@@ -684,7 +674,7 @@ def coconeOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) : Cocone F
 #align category_theory.limits.cocone_of_diagram_terminal CategoryTheory.Limits.coconeOfDiagramTerminal
 
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J`, show the cocone
-`cocone_of_diagram_terminal` is a colimit. -/
+`coconeOfDiagramTerminal` is a colimit. -/
 def colimitOfDiagramTerminal {X : J} (tX : IsTerminal X) (F : J ⥤ C) :
     IsColimit (coconeOfDiagramTerminal tX F) where
   desc s := s.ι.app X
@@ -705,7 +695,7 @@ def colimitOfTerminal (F : J ⥤ C) [HasTerminal J] [HasColimit F] : colimit F 
 
 /-- From a functor `F : J ⥤ C`, given an initial object of `J`, construct a cocone for `J`,
 provided that the morphisms in the diagram are isomorphisms.
-In `colimit_of_diagram_initial` we show it is a colimit cocone. -/
+In `colimitOfDiagramInitial` we show it is a colimit cocone. -/
 @[simps]
 def coconeOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : Cocone F where
@@ -720,7 +710,7 @@ def coconeOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
 #align category_theory.limits.cocone_of_diagram_initial CategoryTheory.Limits.coconeOfDiagramInitial
 
 /-- From a functor `F : J ⥤ C`, given an initial object of `J` and that the morphisms in the
-diagram are isomorphisms, show the cone `cocone_of_diagram_initial` is a colimit. -/
+diagram are isomorphisms, show the cone `coconeOfDiagramInitial` is a colimit. -/
 def colimitOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsColimit (coconeOfDiagramInitial hX F) where
   desc S := S.ι.app _
@@ -740,10 +730,7 @@ def colimitOfInitial (F : J ⥤ C) [HasInitial J] [HasColimit F]
 -/
 theorem isIso_π_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasLimit F] :
     IsIso (limit.π F j) :=
-  ⟨⟨limit.lift _ (coneOfDiagramInitial I F),
-      ⟨by
-        ext
-        simp, by simp⟩⟩⟩
+  ⟨⟨limit.lift _ (coneOfDiagramInitial I F), ⟨by ext; simp, by simp⟩⟩⟩
 #align category_theory.limits.is_iso_π_of_is_initial CategoryTheory.Limits.isIso_π_of_isInitial
 
 instance isIso_π_initial [HasInitial J] (F : J ⥤ C) [HasLimit F] : IsIso (limit.π F (⊥_ J)) :=
@@ -752,9 +739,7 @@ instance isIso_π_initial [HasInitial J] (F : J ⥤ C) [HasLimit F] : IsIso (lim
 
 theorem isIso_π_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasLimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (limit.π F j) :=
-  ⟨⟨limit.lift _ (coneOfDiagramTerminal I F), by
-      ext
-      simp, by simp⟩⟩
+  ⟨⟨limit.lift _ (coneOfDiagramTerminal I F), by ext; simp, by simp⟩⟩
 #align category_theory.limits.is_iso_π_of_is_terminal CategoryTheory.Limits.isIso_π_of_isTerminal
 
 instance isIso_π_terminal [HasTerminal J] (F : J ⥤ C) [HasLimit F]
@@ -766,10 +751,7 @@ instance isIso_π_terminal [HasTerminal J] (F : J ⥤ C) [HasLimit F]
 -/
 theorem isIso_ι_of_isTerminal {j : J} (I : IsTerminal j) (F : J ⥤ C) [HasColimit F] :
     IsIso (colimit.ι F j) :=
-  ⟨⟨colimit.desc _ (coconeOfDiagramTerminal I F),
-      ⟨by simp, by
-        ext
-        simp⟩⟩⟩
+  ⟨⟨colimit.desc _ (coconeOfDiagramTerminal I F), ⟨by simp, by ext; simp⟩⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_terminal CategoryTheory.Limits.isIso_ι_of_isTerminal
 
 instance isIso_ι_terminal [HasTerminal J] (F : J ⥤ C) [HasColimit F] : IsIso (colimit.ι F (⊤_ J)) :=

239d882c

chore: strip trailing spaces in lean files (#2828)

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

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

This was done with a regex search in vscode,

6ceb5945

Diff

@@ -32,8 +32,8 @@ namespace CategoryTheory.Limits
 variable {C : Type u₁} [Category.{v₁} C]
 
 -- attribute [local tidy] tactic.discrete_cases -- Porting note: no tidy
-open Lean Elab Meta Tactic in 
-/- Porting note: adding a lightweight macro intended to serve the narrow use case of casing on 
+open Lean Elab Meta Tactic in
+/- Porting note: adding a lightweight macro intended to serve the narrow use case of casing on
 `Discrete PEmpty`. -/
 /-- A local tactic replacing the use of discrete cases on `PEmpty` in Lean 3.
 `dee` is short for `discrete_empty_elim`. -/
@@ -44,7 +44,7 @@ scoped elab (name := discrete_empty_elim) "dee" : tactic => withMainContext do
 @[simps]
 def asEmptyCone (X : C) : Cone (Functor.empty.{0} C) :=
   { pt := X
-    π := 
+    π :=
     { app := by dee
       naturality := by dee } }
 #align category_theory.limits.as_empty_cone CategoryTheory.Limits.asEmptyCone
@@ -53,7 +53,7 @@ def asEmptyCone (X : C) : Cone (Functor.empty.{0} C) :=
 @[simps]
 def asEmptyCocone (X : C) : Cocone (Functor.empty.{0} C) :=
   { pt := X
-    ι := 
+    ι :=
     { app := by dee
       naturality := by dee } }
 #align category_theory.limits.as_empty_cocone CategoryTheory.Limits.asEmptyCocone
@@ -70,27 +70,27 @@ abbrev IsInitial (X : C) :=
 
 /-- An object `Y` is terminal iff for every `X` there is a unique morphism `X ⟶ Y`. -/
 def isTerminalEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (Y : C) :
-    IsLimit (⟨Y, (by dee), (by dee)⟩ : 
+    IsLimit (⟨Y, (by dee), (by dee)⟩ :
     Cone F) ≃ ∀ X : C, Unique (X ⟶ Y) where
   toFun t X :=
-    { default := t.lift ⟨X, ⟨(by dee),(by dee)⟩⟩ 
-      uniq := fun f => 
+    { default := t.lift ⟨X, ⟨(by dee),(by dee)⟩⟩
+      uniq := fun f =>
         t.uniq ⟨X, ⟨by dee, by dee⟩⟩ f (by dee) }
   invFun u :=
     { lift := fun s => (u s.pt).default
       fac := by dee
       uniq := fun s _ _ => (u s.pt).2 _ }
   left_inv := by dsimp [Function.LeftInverse]; intro x; simp only [eq_iff_true_of_subsingleton]
-  right_inv := by 
+  right_inv := by
     dsimp [Function.RightInverse,Function.LeftInverse]
     intro u; funext X; simp only
 #align category_theory.limits.is_terminal_equiv_unique CategoryTheory.Limits.isTerminalEquivUnique
 
 /-- An object `Y` is terminal if for every `X` there is a unique morphism `X ⟶ Y`
     (as an instance). -/
-def IsTerminal.ofUnique (Y : C) [h : ∀ X : C, Unique (X ⟶ Y)] : IsTerminal Y where 
-  lift s := (h s.pt).default 
-  fac := fun _ ⟨j⟩ => j.elim  
+def IsTerminal.ofUnique (Y : C) [h : ∀ X : C, Unique (X ⟶ Y)] : IsTerminal Y where
+  lift s := (h s.pt).default
+  fac := fun _ ⟨j⟩ => j.elim
 #align category_theory.limits.is_terminal.of_unique CategoryTheory.Limits.IsTerminal.ofUnique
 
 /-- If `α` is a preorder with top, then `⊤` is a terminal object. -/
@@ -113,19 +113,19 @@ def isInitialEquivUnique (F : Discrete.{0} PEmpty.{1} ⥤ C) (X : C) :
       uniq := fun f => t.uniq ⟨X, ⟨by dee, by dee⟩⟩ f (by dee) }
   invFun u :=
     { desc := fun s => (u s.pt).default
-      fac := by dee  
+      fac := by dee
       uniq := fun s _ _ => (u s.pt).2 _ }
   left_inv := by dsimp [Function.LeftInverse]; intro; simp only [eq_iff_true_of_subsingleton]
-  right_inv := by 
+  right_inv := by
     dsimp [Function.RightInverse,Function.LeftInverse]
-    intro; funext; simp only 
+    intro; funext; simp only
 #align category_theory.limits.is_initial_equiv_unique CategoryTheory.Limits.isInitialEquivUnique
 
 /-- An object `X` is initial if for every `Y` there is a unique morphism `X ⟶ Y`
     (as an instance). -/
-def IsInitial.ofUnique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : IsInitial X where 
+def IsInitial.ofUnique (X : C) [h : ∀ Y : C, Unique (X ⟶ Y)] : IsInitial X where
   desc s := (h s.pt).default
-  fac := fun _ ⟨j⟩ => j.elim 
+  fac := fun _ ⟨j⟩ => j.elim
 #align category_theory.limits.is_initial.of_unique CategoryTheory.Limits.IsInitial.ofUnique
 
 /-- If `α` is a preorder with bot, then `⊥` is an initial object. -/
@@ -241,8 +241,8 @@ def isLimitChangeEmptyCone {c₁ : Cone F₁} (hl : IsLimit c₁) (c₂ : Cone F
     IsLimit c₂ where
   lift c := hl.lift ⟨c.pt, by dee, by dee⟩ ≫ hi.hom
   fac _ j := j.as.elim
-  uniq c f _ := by 
-    dsimp 
+  uniq c f _ := by
+    dsimp
     rw [← hl.uniq _ (f ≫ hi.inv) _]
     · simp only [Category.assoc, Iso.inv_hom_id, Category.comp_id]
     · dee
@@ -250,14 +250,14 @@ def isLimitChangeEmptyCone {c₁ : Cone F₁} (hl : IsLimit c₁) (c₂ : Cone F
 
 /-- Replacing an empty cone in `IsLimit` by another with the same cone point
     is an equivalence. -/
-def isLimitEmptyConeEquiv (c₁ : Cone F₁) (c₂ : Cone F₂) (h : c₁.pt ≅ c₂.pt) : 
+def isLimitEmptyConeEquiv (c₁ : Cone F₁) (c₂ : Cone F₂) (h : c₁.pt ≅ c₂.pt) :
     IsLimit c₁ ≃ IsLimit c₂ where
   toFun hl := isLimitChangeEmptyCone C hl c₂ h
   invFun hl := isLimitChangeEmptyCone C hl c₁ h.symm
-  left_inv := by dsimp [Function.LeftInverse]; intro; simp only [eq_iff_true_of_subsingleton] 
-  right_inv := by 
+  left_inv := by dsimp [Function.LeftInverse]; intro; simp only [eq_iff_true_of_subsingleton]
+  right_inv := by
     dsimp [Function.LeftInverse,Function.RightInverse]; intro; funext
-    simp only [eq_iff_true_of_subsingleton] 
+    simp only [eq_iff_true_of_subsingleton]
 #align category_theory.limits.is_limit_empty_cone_equiv CategoryTheory.Limits.isLimitEmptyConeEquiv
 
 theorem hasTerminalChangeDiagram (h : HasLimit F₁) : HasLimit F₂ :=
@@ -281,8 +281,8 @@ def isColimitChangeEmptyCocone {c₁ : Cocone F₁} (hl : IsColimit c₁) (c₂
   fac _ j := j.as.elim
   uniq c f _ := by
     dsimp
-    rw [← hl.uniq _ (hi.hom ≫ f) _] 
-    · simp only [Iso.inv_hom_id_assoc] 
+    rw [← hl.uniq _ (hi.hom ≫ f) _]
+    · simp only [Iso.inv_hom_id_assoc]
     · dee
 #align category_theory.limits.is_colimit_change_empty_cocone CategoryTheory.Limits.isColimitChangeEmptyCocone
 
@@ -292,14 +292,14 @@ def isColimitEmptyCoconeEquiv (c₁ : Cocone F₁) (c₂ : Cocone F₂) (h : c
     IsColimit c₁ ≃ IsColimit c₂ where
   toFun hl := isColimitChangeEmptyCocone C hl c₂ h
   invFun hl := isColimitChangeEmptyCocone C hl c₁ h.symm
-  left_inv := by dsimp [Function.LeftInverse]; intro; simp only [eq_iff_true_of_subsingleton] 
-  right_inv := by 
+  left_inv := by dsimp [Function.LeftInverse]; intro; simp only [eq_iff_true_of_subsingleton]
+  right_inv := by
     dsimp [Function.LeftInverse,Function.RightInverse]; intro; funext
     simp only [eq_iff_true_of_subsingleton]
 #align category_theory.limits.is_colimit_empty_cocone_equiv CategoryTheory.Limits.isColimitEmptyCoconeEquiv
 
 theorem hasInitialChangeDiagram (h : HasColimit F₁) : HasColimit F₂ :=
-  ⟨⟨⟨⟨colimit F₁, by dee, by dee⟩, 
+  ⟨⟨⟨⟨colimit F₁, by dee, by dee⟩,
     isColimitChangeEmptyCocone C (colimit.isColimit F₁) _ (eqToIso rfl)⟩⟩⟩
 #align category_theory.limits.has_initial_change_diagram CategoryTheory.Limits.hasInitialChangeDiagram
 
@@ -347,7 +347,7 @@ theorem hasTerminal_of_unique (X : C) [h : ∀ Y : C, Unique (Y ⟶ X)] : HasTer
 #align category_theory.limits.has_terminal_of_unique CategoryTheory.Limits.hasTerminal_of_unique
 
 theorem IsTerminal.hasTerminal {X : C} (h : IsTerminal X) : HasTerminal C :=
-  { has_limit := fun F => HasLimit.mk ⟨⟨X, by dee, by dee⟩, 
+  { has_limit := fun F => HasLimit.mk ⟨⟨X, by dee, by dee⟩,
     isLimitChangeEmptyCone _ h _ (Iso.refl _)⟩ }
 #align category_theory.limits.is_terminal.has_terminal CategoryTheory.Limits.IsTerminal.hasTerminal
 
@@ -374,16 +374,16 @@ abbrev initial.to [HasInitial C] (P : C) : ⊥_ C ⟶ P :=
 #align category_theory.limits.initial.to CategoryTheory.Limits.initial.to
 
 /-- A terminal object is terminal. -/
-def terminalIsTerminal [HasTerminal C] : IsTerminal (⊤_ C) where 
+def terminalIsTerminal [HasTerminal C] : IsTerminal (⊤_ C) where
   lift s := terminal.from _
-  fac := by dee 
+  fac := by dee
   uniq := by intro _ _ _; dsimp; ext ⟨j⟩; dsimp; cases j
 #align category_theory.limits.terminal_is_terminal CategoryTheory.Limits.terminalIsTerminal
 
 /-- An initial object is initial. -/
-def initialIsInitial [HasInitial C] : IsInitial (⊥_ C) where 
+def initialIsInitial [HasInitial C] : IsInitial (⊥_ C) where
   desc s := initial.to _
-  fac := by dee 
+  fac := by dee
   uniq := by intro _ _ _; dsimp; ext ⟨j⟩; dsimp; cases j
 #align category_theory.limits.initial_is_initial CategoryTheory.Limits.initialIsInitial
 
@@ -494,7 +494,7 @@ def limitConstTerminal {J : Type _} [Category J] {C : Type _} [Category C] [HasT
 theorem limitConstTerminal_inv_π {J : Type _} [Category J] {C : Type _} [Category C] [HasTerminal C]
     {j : J} :
     limitConstTerminal.inv ≫ limit.π ((CategoryTheory.Functor.const J).obj (⊤_ C)) j =
-      terminal.from _ := by 
+      terminal.from _ := by
         apply Limits.limit.hom_ext; dee
 #align category_theory.limits.limit_const_terminal_inv_π CategoryTheory.Limits.limitConstTerminal_inv_π
 
@@ -533,7 +533,7 @@ to terminal is a monomorphism, which is the second of Freyd's axioms for an AT c
 TODO: This is a condition satisfied by categories with zero objects and morphisms.
 -/
 class InitialMonoClass (C : Type u₁) [Category.{v₁} C] : Prop where
-  /-- The map from the (any as stated) initial object to any other object is a 
+  /-- The map from the (any as stated) initial object to any other object is a
     monomorphism -/
   isInitial_mono_from : ∀ {I} (X : C) (hI : IsInitial I), Mono (hI.to X)
 #align category_theory.limits.initial_mono_class CategoryTheory.Limits.InitialMonoClass
@@ -625,7 +625,7 @@ def limitOfDiagramInitial {X : J} (tX : IsInitial X) (F : J ⥤ C) :
     IsLimit (coneOfDiagramInitial tX F) where
   lift s := s.π.app X
   uniq s m w := by
-    conv_lhs => dsimp  
+    conv_lhs => dsimp
     simp_rw [← w X, coneOfDiagramInitial_π_app, tX.hom_ext (tX.to X) (𝟙 _)]
     dsimp; simp
 #align category_theory.limits.limit_of_diagram_initial CategoryTheory.Limits.limitOfDiagramInitial
@@ -658,7 +658,7 @@ def coneOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
 /-- From a functor `F : J ⥤ C`, given a terminal object of `J` and that the morphisms in the
 diagram are isomorphisms, show the cone `cone_of_diagram_terminal` is a limit. -/
 def limitOfDiagramTerminal {X : J} (hX : IsTerminal X) (F : J ⥤ C)
-    [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsLimit (coneOfDiagramTerminal hX F) where 
+    [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsLimit (coneOfDiagramTerminal hX F) where
   lift S := S.π.app _
 #align category_theory.limits.limit_of_diagram_terminal CategoryTheory.Limits.limitOfDiagramTerminal
 
@@ -722,7 +722,7 @@ def coconeOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
 /-- From a functor `F : J ⥤ C`, given an initial object of `J` and that the morphisms in the
 diagram are isomorphisms, show the cone `cocone_of_diagram_initial` is a colimit. -/
 def colimitOfDiagramInitial {X : J} (hX : IsInitial X) (F : J ⥤ C)
-    [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsColimit (coconeOfDiagramInitial hX F) where 
+    [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsColimit (coconeOfDiagramInitial hX F) where
   desc S := S.ι.app _
 #align category_theory.limits.colimit_of_diagram_initial CategoryTheory.Limits.colimitOfDiagramInitial
 
@@ -778,11 +778,11 @@ instance isIso_ι_terminal [HasTerminal J] (F : J ⥤ C) [HasColimit F] : IsIso
 
 theorem isIso_ι_of_isInitial {j : J} (I : IsInitial j) (F : J ⥤ C) [HasColimit F]
     [∀ (i j : J) (f : i ⟶ j), IsIso (F.map f)] : IsIso (colimit.ι F j) :=
-  ⟨⟨colimit.desc _ (coconeOfDiagramInitial I F), by 
+  ⟨⟨colimit.desc _ (coconeOfDiagramInitial I F), by
     refine ⟨?_, by ext; simp⟩
-    dsimp; simp only [colimit.ι_desc, coconeOfDiagramInitial_pt, coconeOfDiagramInitial_ι_app, 
+    dsimp; simp only [colimit.ι_desc, coconeOfDiagramInitial_pt, coconeOfDiagramInitial_ι_app,
       Functor.const_obj_obj, IsInitial.to_self, Functor.map_id]
-    dsimp [inv]; simp only [Category.id_comp, Category.comp_id, and_self] 
+    dsimp [inv]; simp only [Category.id_comp, Category.comp_id, and_self]
     apply @Classical.choose_spec _ (fun x => x = 𝟙 F.obj j) _
   ⟩⟩
 #align category_theory.limits.is_iso_ι_of_is_initial CategoryTheory.Limits.isIso_ι_of_isInitial
@@ -795,4 +795,3 @@ instance isIso_ι_initial [HasInitial J] (F : J ⥤ C) [HasColimit F]
 end
 
 end CategoryTheory.Limits
-

239d882c

feat: port CategoryTheory.Limits.Shapes.Terminal (#2459)

Co-authored-by: Matthew Robert Ballard <100034030+mattrobball@users.noreply.github.com> Co-authored-by: Johan Commelin <johan@commelin.net>

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`category_theory.limits.shapes.terminal` ⟷ `Mathlib.CategoryTheory.Limits.Shapes.Terminal`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 82

category_theory.limits.shapes.terminal ⟷ Mathlib.CategoryTheory.Limits.Shapes.Terminal

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 82

`category_theory.limits.shapes.terminal` ⟷ `Mathlib.CategoryTheory.Limits.Shapes.Terminal`