category_theory.bicategory.locally_discrete

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

c9c9fa15

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

10bf4f82

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Yuma Mizuno. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yuma Mizuno
 -/
-import Mathbin.CategoryTheory.DiscreteCategory
-import Mathbin.CategoryTheory.Bicategory.Functor
-import Mathbin.CategoryTheory.Bicategory.Strict
+import CategoryTheory.DiscreteCategory
+import CategoryTheory.Bicategory.Functor
+import CategoryTheory.Bicategory.Strict
 
 #align_import category_theory.bicategory.locally_discrete from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"

10bf4f82

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Yuma Mizuno. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yuma Mizuno
-
-! This file was ported from Lean 3 source module category_theory.bicategory.locally_discrete
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.DiscreteCategory
 import Mathbin.CategoryTheory.Bicategory.Functor
 import Mathbin.CategoryTheory.Bicategory.Strict
 
+#align_import category_theory.bicategory.locally_discrete from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
 /-!
 # Locally discrete bicategories

10bf4f82

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -96,9 +96,9 @@ instance locallyDiscreteBicategory : Bicategory (LocallyDiscrete C)
 /-- A locally discrete bicategory is strict. -/
 instance locallyDiscreteBicategory.strict : Strict (LocallyDiscrete C)
     where
-  id_comp' := by intros ; ext1; unfold_projs; apply category.id_comp
-  comp_id' := by intros ; ext1; unfold_projs; apply category.comp_id
-  assoc' := by intros ; ext1; unfold_projs; apply category.assoc
+  id_comp' := by intros; ext1; unfold_projs; apply category.id_comp
+  comp_id' := by intros; ext1; unfold_projs; apply category.comp_id
+  assoc' := by intros; ext1; unfold_projs; apply category.assoc
 #align category_theory.locally_discrete_bicategory.strict CategoryTheory.locallyDiscreteBicategory.strict
 -/

10bf4f82

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -30,7 +30,7 @@ namespace CategoryTheory
 
 open Bicategory Discrete
 
-open Bicategory
+open scoped Bicategory
 
 universe w₂ v v₁ v₂ u u₁ u₂

10bf4f82

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -86,18 +86,9 @@ instance locallyDiscreteBicategory : Bicategory (LocallyDiscrete C)
     where
   whiskerLeft X Y Z f g h η := eqToHom (congr_arg₂ (· ≫ ·) rfl (LocallyDiscrete.eq_of_hom η))
   whiskerRight X Y Z f g η h := eqToHom (congr_arg₂ (· ≫ ·) (LocallyDiscrete.eq_of_hom η) rfl)
-  associator W X Y Z f g h :=
-    eqToIso <| by
-      unfold_projs
-      simp only [category.assoc]
-  leftUnitor X Y f :=
-    eqToIso <| by
-      unfold_projs
-      simp only [category.id_comp, mk_as]
-  rightUnitor X Y f :=
-    eqToIso <| by
-      unfold_projs
-      simp only [category.comp_id, mk_as]
+  associator W X Y Z f g h := eqToIso <| by unfold_projs; simp only [category.assoc]
+  leftUnitor X Y f := eqToIso <| by unfold_projs; simp only [category.id_comp, mk_as]
+  rightUnitor X Y f := eqToIso <| by unfold_projs; simp only [category.comp_id, mk_as]
 #align category_theory.locally_discrete_bicategory CategoryTheory.locallyDiscreteBicategory
 -/
 
@@ -105,21 +96,9 @@ instance locallyDiscreteBicategory : Bicategory (LocallyDiscrete C)
 /-- A locally discrete bicategory is strict. -/
 instance locallyDiscreteBicategory.strict : Strict (LocallyDiscrete C)
     where
-  id_comp' := by
-    intros
-    ext1
-    unfold_projs
-    apply category.id_comp
-  comp_id' := by
-    intros
-    ext1
-    unfold_projs
-    apply category.comp_id
-  assoc' := by
-    intros
-    ext1
-    unfold_projs
-    apply category.assoc
+  id_comp' := by intros ; ext1; unfold_projs; apply category.id_comp
+  comp_id' := by intros ; ext1; unfold_projs; apply category.comp_id
+  assoc' := by intros ; ext1; unfold_projs; apply category.assoc
 #align category_theory.locally_discrete_bicategory.strict CategoryTheory.locallyDiscreteBicategory.strict
 -/

10bf4f82

bump to nightly-2023-03-16-03

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

8ae28b0b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yuma Mizuno
 
 ! This file was ported from Lean 3 source module category_theory.bicategory.locally_discrete
-! leanprover-community/mathlib commit c9c9fa15fec7ca18e9ec97306fb8764bfe988a7e
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Bicategory.Strict
 /-!
 # Locally discrete bicategories
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A category `C` can be promoted to a strict bicategory `locally_discrete C`. The objects and the
 1-morphisms in `locally_discrete C` are the same as the objects and the morphisms, respectively,
 in `C`, and the 2-morphisms in `locally_discrete C` are the equalities between 1-morphisms. In

c9c9fa15

bump to nightly-2023-03-13-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

66e1e587

Diff

@@ -33,12 +33,14 @@ universe w₂ v v₁ v₂ u u₁ u₂
 
 variable {C : Type u}
 
+#print CategoryTheory.LocallyDiscrete /-
 /-- A type synonym for promoting any type to a category,
 with the only morphisms being equalities.
 -/
 def LocallyDiscrete (C : Type u) :=
   C
 #align category_theory.locally_discrete CategoryTheory.LocallyDiscrete
+-/
 
 namespace LocallyDiscrete
 
@@ -53,21 +55,26 @@ instance [CategoryStruct.{v} C] : CategoryStruct (LocallyDiscrete C)
 
 variable {C} [CategoryStruct.{v} C]
 
+#print CategoryTheory.LocallyDiscrete.homSmallCategory /-
 instance (priority := 900) homSmallCategory (X Y : LocallyDiscrete C) : SmallCategory (X ⟶ Y) :=
   CategoryTheory.discreteCategory (X ⟶ Y)
 #align category_theory.locally_discrete.hom_small_category CategoryTheory.LocallyDiscrete.homSmallCategory
+-/
 
+#print CategoryTheory.LocallyDiscrete.eq_of_hom /-
 /-- Extract the equation from a 2-morphism in a locally discrete 2-category. -/
 theorem eq_of_hom {X Y : LocallyDiscrete C} {f g : X ⟶ Y} (η : f ⟶ g) : f = g :=
   by
   have : discrete.mk f.as = discrete.mk g.as := congr_arg discrete.mk (eq_of_hom η)
   simpa using this
 #align category_theory.locally_discrete.eq_of_hom CategoryTheory.LocallyDiscrete.eq_of_hom
+-/
 
 end LocallyDiscrete
 
 variable (C) [Category.{v} C]
 
+#print CategoryTheory.locallyDiscreteBicategory /-
 /-- The locally discrete bicategory on a category is a bicategory in which the objects and the
 1-morphisms are the same as those in the underlying category, and the 2-morphisms are the
 equalities between 1-morphisms.
@@ -89,7 +96,9 @@ instance locallyDiscreteBicategory : Bicategory (LocallyDiscrete C)
       unfold_projs
       simp only [category.comp_id, mk_as]
 #align category_theory.locally_discrete_bicategory CategoryTheory.locallyDiscreteBicategory
+-/
 
+#print CategoryTheory.locallyDiscreteBicategory.strict /-
 /-- A locally discrete bicategory is strict. -/
 instance locallyDiscreteBicategory.strict : Strict (LocallyDiscrete C)
     where
@@ -109,9 +118,11 @@ instance locallyDiscreteBicategory.strict : Strict (LocallyDiscrete C)
     unfold_projs
     apply category.assoc
 #align category_theory.locally_discrete_bicategory.strict CategoryTheory.locallyDiscreteBicategory.strict
+-/
 
 variable {I : Type u₁} [Category.{v₁} I] {B : Type u₂} [Bicategory.{w₂, v₂} B] [Strict B]
 
+#print CategoryTheory.Functor.toOplaxFunctor /-
 /--
 If `B` is a strict bicategory and `I` is a (1-)category, any functor (of 1-categories) `I ⥤ B` can
 be promoted to an oplax functor from `locally_discrete I` to `B`.
@@ -125,6 +136,7 @@ def Functor.toOplaxFunctor (F : I ⥤ B) : OplaxFunctor (LocallyDiscrete I) B
   map_id i := eqToHom (F.map_id i)
   map_comp i j k f g := eqToHom (F.map_comp f.as g.as)
 #align category_theory.functor.to_oplax_functor CategoryTheory.Functor.toOplaxFunctor
+-/
 
 end CategoryTheory

c9c9fa15

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

c9c9fa15

feat(CategoryTheory/Bicategory/LocallyDiscrete): Make LocallyDiscrete a structure (#12383)

Made LocallyDiscrete a structure, similar to Discrete, and added some basic API. Coherence.lean was also adjusted because of these changes. This should make it easier to move between a given type C and LocallyDiscrete C.

bdc67338

Diff

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2022 Yuma Mizuno. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Yuma Mizuno
+Authors: Yuma Mizuno, Calle Sönne
 -/
 import Mathlib.CategoryTheory.DiscreteCategory
 import Mathlib.CategoryTheory.Bicategory.Functor
@@ -19,49 +19,69 @@ other words, the category consisting of the 1-morphisms between each pair of obj
 in `LocallyDiscrete C` is defined as the discrete category associated with the type `X ⟶ Y`.
 -/
 
-
 namespace CategoryTheory
 
 open Bicategory Discrete
 
 open Bicategory
 
+
 universe w₂ v v₁ v₂ u u₁ u₂
 
 variable {C : Type u}
 
-/-- A type synonym for promoting any type to a category,
-with the only morphisms being equalities.
+/-- A wrapper for promoting any category to a bicategory,
+with the only 2-morphisms being equalities.
 -/
-def LocallyDiscrete (C : Type u) :=
-  C
-#align category_theory.locally_discrete CategoryTheory.LocallyDiscrete
+@[ext]
+structure LocallyDiscrete (C : Type u) where
+  /-- A wrapper for promoting any category to a bicategory,
+  with the only 2-morphisms being equalities.
+  -/
+  as : C
 
 namespace LocallyDiscrete
 
-instance [Inhabited C] : Inhabited (LocallyDiscrete C) := ⟨(default : C)⟩
+@[simp]
+theorem mk_as (a : LocallyDiscrete C) : mk a.as = a := rfl
+
+/-- `LocallyDiscrete C` is equivalent to the original type `C`. -/
+@[simps]
+def locallyDiscreteEquiv : LocallyDiscrete C ≃ C where
+  toFun := LocallyDiscrete.as
+  invFun := LocallyDiscrete.mk
+  left_inv := by aesop_cat
+  right_inv := by aesop_cat
 
-instance [CategoryStruct.{v} C] : CategoryStruct (LocallyDiscrete C)
+instance [DecidableEq C] : DecidableEq (LocallyDiscrete C) :=
+  locallyDiscreteEquiv.decidableEq
+
+instance [Inhabited C] : Inhabited (LocallyDiscrete C) :=
+  ⟨⟨default⟩⟩
+
+instance categoryStruct [CategoryStruct.{v} C] : CategoryStruct (LocallyDiscrete C)
     where
-  Hom := fun X Y : C => Discrete (X ⟶ Y)
-  id := fun X : C => ⟨𝟙 X⟩
+  Hom := fun a b => Discrete (a.as ⟶ b.as)
+  id := fun a => ⟨𝟙 a.as⟩
   comp f g := ⟨f.as ≫ g.as⟩
 
 variable [CategoryStruct.{v} C]
 
-instance (priority := 900) homSmallCategory (X Y : LocallyDiscrete C) : SmallCategory (X ⟶ Y) :=
-  let X' : C := X
-  let Y' : C := Y
-  CategoryTheory.discreteCategory (X' ⟶ Y')
+@[simp]
+lemma id_as (a : LocallyDiscrete C) : (𝟙 a : Discrete (a.as ⟶ a.as)).as = 𝟙 a.as :=
+  rfl
+
+@[simp]
+lemma comp_as {a b c : LocallyDiscrete C} (f : a ⟶ b) (g : b ⟶ c) : (f ≫ g).as = f.as ≫ g.as :=
+  rfl
+
+instance (priority := 900) homSmallCategory (a b : LocallyDiscrete C) : SmallCategory (a ⟶ b) :=
+  CategoryTheory.discreteCategory (a.as ⟶ b.as)
 #align category_theory.locally_discrete.hom_small_category CategoryTheory.LocallyDiscrete.homSmallCategory
 
 -- Porting note: Manually adding this instance (inferInstance doesn't work)
-instance subsingleton2Hom {X Y : LocallyDiscrete C} (f g : X ⟶ Y) : Subsingleton (f ⟶ g) :=
-  let X' : C := X
-  let Y' : C := Y
-  let f' : Discrete (X' ⟶ Y') := f
-  let g' : Discrete (X' ⟶ Y') := g
-  show Subsingleton (f' ⟶ g') from inferInstance
+instance subsingleton2Hom {a b : LocallyDiscrete C} (f g : a ⟶ b) : Subsingleton (f ⟶ g) :=
+  instSubsingletonDiscreteHom f g
 
 /-- Extract the equation from a 2-morphism in a locally discrete 2-category. -/
 theorem eq_of_hom {X Y : LocallyDiscrete C} {f g : X ⟶ Y} (η : f ⟶ g) : f = g :=
@@ -70,7 +90,8 @@ theorem eq_of_hom {X Y : LocallyDiscrete C} {f g : X ⟶ Y} (η : f ⟶ g) : f =
 
 end LocallyDiscrete
 
-variable (C) [Category.{v} C]
+variable (C)
+variable [Category.{v} C]
 
 /-- The locally discrete bicategory on a category is a bicategory in which the objects and the
 1-morphisms are the same as those in the underlying category, and the 2-morphisms are the
@@ -80,42 +101,33 @@ instance locallyDiscreteBicategory : Bicategory (LocallyDiscrete C)
     where
   whiskerLeft f g h η := eqToHom (congr_arg₂ (· ≫ ·) rfl (LocallyDiscrete.eq_of_hom η))
   whiskerRight η h := eqToHom (congr_arg₂ (· ≫ ·) (LocallyDiscrete.eq_of_hom η) rfl)
-  associator f g h :=
-    eqToIso <| by
-      apply Discrete.ext
-      change (f.as ≫ g.as) ≫ h.as = f.as ≫ (g.as ≫ h.as)
-      rw [Category.assoc]
-  leftUnitor f :=
-    eqToIso <| by
-      apply Discrete.ext
-      change 𝟙 _ ≫ _ = _
-      rw [Category.id_comp]
-  rightUnitor f :=
-    eqToIso <| by
-      apply Discrete.ext
-      change _ ≫ 𝟙 _ = _
-      rw [Category.comp_id]
+  associator f g h := eqToIso <| by apply Discrete.ext; simp
+  leftUnitor f := eqToIso <| by apply Discrete.ext; simp
+  rightUnitor f := eqToIso <| by apply Discrete.ext; simp
 #align category_theory.locally_discrete_bicategory CategoryTheory.locallyDiscreteBicategory
 
 /-- A locally discrete bicategory is strict. -/
-instance locallyDiscreteBicategory.strict : Strict (LocallyDiscrete C)
-    where
-  id_comp := by
-    intros
-    apply Discrete.ext
-    apply Category.id_comp
-  comp_id := by
-    intros
-    apply Discrete.ext
-    apply Category.comp_id
-  assoc := by
-    intros
-    apply Discrete.ext
-    apply Category.assoc
+instance locallyDiscreteBicategory.strict : Strict (LocallyDiscrete C) where
+  id_comp f := Discrete.ext _ _ (Category.id_comp _)
+  comp_id f := Discrete.ext _ _ (Category.comp_id _)
+  assoc f g h := Discrete.ext _ _ (Category.assoc _ _ _)
 #align category_theory.locally_discrete_bicategory.strict CategoryTheory.locallyDiscreteBicategory.strict
 
 variable {I : Type u₁} [Category.{v₁} I] {B : Type u₂} [Bicategory.{w₂, v₂} B] [Strict B]
 
+/--
+If `B` is a strict bicategory and `I` is a (1-)category, any functor (of 1-categories) `I ⥤ B` can
+be promoted to a pseudofunctor from `LocallyDiscrete I` to `B`.
+-/
+@[simps]
+def Functor.toPseudoFunctor (F : I ⥤ B) : Pseudofunctor (LocallyDiscrete I) B
+    where
+  obj i := F.obj i.as
+  map f := F.map f.as
+  map₂ η := eqToHom (congr_arg _ (LocallyDiscrete.eq_of_hom η))
+  mapId i := eqToIso (F.map_id i.as)
+  mapComp f g := eqToIso (F.map_comp f.as g.as)
+
 /--
 If `B` is a strict bicategory and `I` is a (1-)category, any functor (of 1-categories) `I ⥤ B` can
 be promoted to an oplax functor from `LocallyDiscrete I` to `B`.
@@ -123,11 +135,35 @@ be promoted to an oplax functor from `LocallyDiscrete I` to `B`.
 @[simps]
 def Functor.toOplaxFunctor (F : I ⥤ B) : OplaxFunctor (LocallyDiscrete I) B
     where
-  obj := F.obj
+  obj i := F.obj i.as
   map f := F.map f.as
   map₂ η := eqToHom (congr_arg _ (LocallyDiscrete.eq_of_hom η))
-  mapId i := eqToHom (F.map_id i)
+  mapId i := eqToHom (F.map_id i.as)
   mapComp f g := eqToHom (F.map_comp f.as g.as)
 #align category_theory.functor.to_oplax_functor CategoryTheory.Functor.toOplaxFunctor
 
 end CategoryTheory
+
+section Quiver
+
+open CategoryTheory LocallyDiscrete
+
+universe v u
+
+variable {C : Type u} [CategoryStruct.{v} C]
+
+/-- The 1-morphism in `LocallyDiscrete C` associated to a given morphism `f : a ⟶ b` in `C` -/
+@[simps]
+def Quiver.Hom.toLoc {a b : C} (f : a ⟶ b) : LocallyDiscrete.mk a ⟶ LocallyDiscrete.mk b :=
+  ⟨f⟩
+
+@[simp]
+lemma Quiver.Hom.id_toLoc (a : C) : (𝟙 a).toLoc = 𝟙 (LocallyDiscrete.mk a) :=
+  rfl
+
+@[simp]
+lemma Quiver.Hom.comp_toLoc {a b c : C} (f : a ⟶ b) (g : b ⟶ c) :
+    (f ≫ g).toLoc = f.toLoc ≫ g.toLoc :=
+  rfl
+
+end Quiver

c9c9fa15

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Yuma Mizuno. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yuma Mizuno
-
-! This file was ported from Lean 3 source module category_theory.bicategory.locally_discrete
-! leanprover-community/mathlib commit c9c9fa15fec7ca18e9ec97306fb8764bfe988a7e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.DiscreteCategory
 import Mathlib.CategoryTheory.Bicategory.Functor
 import Mathlib.CategoryTheory.Bicategory.Strict
 
+#align_import category_theory.bicategory.locally_discrete from "leanprover-community/mathlib"@"c9c9fa15fec7ca18e9ec97306fb8764bfe988a7e"
+
 /-!
 # Locally discrete bicategories

c9c9fa15

feat: port CategoryTheory.Bicategory.LocallyDiscrete (#2813)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: adamtopaz <github@adamtopaz.com>

baf8d765

`category_theory.bicategory.locally_discrete` ⟷ `Mathlib.CategoryTheory.Bicategory.LocallyDiscrete`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 34

category_theory.bicategory.locally_discrete ⟷ Mathlib.CategoryTheory.Bicategory.LocallyDiscrete

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 34

`category_theory.bicategory.locally_discrete` ⟷ `Mathlib.CategoryTheory.Bicategory.LocallyDiscrete`