category_theory.category.Quiv
⟷
Mathlib.CategoryTheory.Category.Quiv
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,9 +3,9 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathbin.CategoryTheory.Adjunction.Basic
-import Mathbin.CategoryTheory.Category.Cat
-import Mathbin.CategoryTheory.PathCategory
+import CategoryTheory.Adjunction.Basic
+import CategoryTheory.Category.Cat
+import CategoryTheory.PathCategory
#align_import category_theory.category.Quiv from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
@@ -24,38 +24,38 @@ universe v u
namespace CategoryTheory
-#print CategoryTheory.QuivCat /-
+#print CategoryTheory.Quiv /-
-- intended to be used with explicit universe parameters
/-- Category of quivers. -/
@[nolint check_univs]
-def QuivCat :=
+def Quiv :=
Bundled Quiver.{v + 1, u}
-#align category_theory.Quiv CategoryTheory.QuivCat
+#align category_theory.Quiv CategoryTheory.Quiv
-/
namespace Quiv
-instance : CoeSort QuivCat (Type u) where coe := Bundled.α
+instance : CoeSort Quiv (Type u) where coe := Bundled.α
-#print CategoryTheory.QuivCat.str' /-
-instance str' (C : QuivCat.{v, u}) : Quiver.{v + 1, u} C :=
+#print CategoryTheory.Quiv.str' /-
+instance str' (C : Quiv.{v, u}) : Quiver.{v + 1, u} C :=
C.str
-#align category_theory.Quiv.str CategoryTheory.QuivCat.str'
+#align category_theory.Quiv.str CategoryTheory.Quiv.str'
-/
-#print CategoryTheory.QuivCat.of /-
+#print CategoryTheory.Quiv.of /-
/-- Construct a bundled `Quiv` from the underlying type and the typeclass. -/
-def of (C : Type u) [Quiver.{v + 1} C] : QuivCat.{v, u} :=
+def of (C : Type u) [Quiver.{v + 1} C] : Quiv.{v, u} :=
Bundled.of C
-#align category_theory.Quiv.of CategoryTheory.QuivCat.of
+#align category_theory.Quiv.of CategoryTheory.Quiv.of
-/
-instance : Inhabited QuivCat :=
- ⟨QuivCat.of (Quiver.Empty PEmpty)⟩
+instance : Inhabited Quiv :=
+ ⟨Quiv.of (Quiver.Empty PEmpty)⟩
-#print CategoryTheory.QuivCat.category /-
+#print CategoryTheory.Quiv.category /-
/-- Category structure on `Quiv` -/
-instance category : LargeCategory.{max v u} QuivCat.{v, u}
+instance category : LargeCategory.{max v u} Quiv.{v, u}
where
Hom C D := Prefunctor C D
id C := Prefunctor.id C
@@ -63,17 +63,17 @@ instance category : LargeCategory.{max v u} QuivCat.{v, u}
id_comp' C D F := by cases F <;> rfl
comp_id' C D F := by cases F <;> rfl
assoc' := by intros <;> rfl
-#align category_theory.Quiv.category CategoryTheory.QuivCat.category
+#align category_theory.Quiv.category CategoryTheory.Quiv.category
-/
-#print CategoryTheory.QuivCat.forget /-
+#print CategoryTheory.Quiv.forget /-
/-- The forgetful functor from categories to quivers. -/
@[simps]
-def forget : Cat.{v, u} ⥤ QuivCat.{v, u}
+def forget : Cat.{v, u} ⥤ Quiv.{v, u}
where
- obj C := QuivCat.of C
+ obj C := Quiv.of C
map C D F := F.toPrefunctor
-#align category_theory.Quiv.forget CategoryTheory.QuivCat.forget
+#align category_theory.Quiv.forget CategoryTheory.Quiv.forget
-/
end Quiv
@@ -83,7 +83,7 @@ namespace Cat
#print CategoryTheory.Cat.free /-
/-- The functor sending each quiver to its path category. -/
@[simps]
-def free : QuivCat.{v, u} ⥤ Cat.{max u v, u}
+def free : Quiv.{v, u} ⥤ Cat.{max u v, u}
where
obj V := Cat.of (Paths V)
map V W F :=
@@ -99,24 +99,24 @@ end Cat
namespace Quiv
-#print CategoryTheory.QuivCat.lift /-
+#print CategoryTheory.Quiv.lift /-
/-- Any prefunctor into a category lifts to a functor from the path category. -/
@[simps]
def lift {V : Type u} [Quiver.{v + 1} V] {C : Type _} [Category C] (F : Prefunctor V C) :
Paths V ⥤ C where
obj X := F.obj X
map X Y f := composePath (F.mapPath f)
-#align category_theory.Quiv.lift CategoryTheory.QuivCat.lift
+#align category_theory.Quiv.lift CategoryTheory.Quiv.lift
-/
-#print CategoryTheory.QuivCat.adj /-
+#print CategoryTheory.Quiv.adj /-
-- We might construct `of_lift_iso_self : paths.of ⋙ lift F ≅ F`
-- (and then show that `lift F` is initial amongst such functors)
-- but it would require lifting quite a bit of machinery to quivers!
/--
The adjunction between forming the free category on a quiver, and forgetting a category to a quiver.
-/
-def adj : Cat.free ⊣ QuivCat.forget :=
+def adj : Cat.free ⊣ Quiv.forget :=
Adjunction.mkOfHomEquiv
{ homEquiv := fun V C =>
{ toFun := fun F => Paths.of.comp F.toPrefunctor
@@ -131,7 +131,7 @@ def adj : Cat.free ⊣ QuivCat.forget :=
exact category.id_comp _ }
homEquiv_naturality_left_symm := fun V W C f g => by change (show paths V ⥤ _ from _) = _;
ext; apply eq_conj_eq_to_hom; rfl }
-#align category_theory.Quiv.adj CategoryTheory.QuivCat.adj
+#align category_theory.Quiv.adj CategoryTheory.Quiv.adj
-/
end Quiv
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.category.Quiv
-! 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.Adjunction.Basic
import Mathbin.CategoryTheory.Category.Cat
import Mathbin.CategoryTheory.PathCategory
+#align_import category_theory.category.Quiv from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
/-!
# The category of quivers
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -130,7 +130,7 @@ def adj : Cat.free ⊣ QuivCat.forget :=
rintro ⟨obj, map⟩
dsimp only [Prefunctor.comp]
congr
- ext (X Y f)
+ ext X Y f
exact category.id_comp _ }
homEquiv_naturality_left_symm := fun V W C f g => by change (show paths V ⥤ _ from _) = _;
ext; apply eq_conj_eq_to_hom; rfl }
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -112,6 +112,7 @@ def lift {V : Type u} [Quiver.{v + 1} V] {C : Type _} [Category C] (F : Prefunct
#align category_theory.Quiv.lift CategoryTheory.QuivCat.lift
-/
+#print CategoryTheory.QuivCat.adj /-
-- We might construct `of_lift_iso_self : paths.of ⋙ lift F ≅ F`
-- (and then show that `lift F` is initial amongst such functors)
-- but it would require lifting quite a bit of machinery to quivers!
@@ -134,6 +135,7 @@ def adj : Cat.free ⊣ QuivCat.forget :=
homEquiv_naturality_left_symm := fun V W C f g => by change (show paths V ⥤ _ from _) = _;
ext; apply eq_conj_eq_to_hom; rfl }
#align category_theory.Quiv.adj CategoryTheory.QuivCat.adj
+-/
end Quiv
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -112,12 +112,6 @@ def lift {V : Type u} [Quiver.{v + 1} V] {C : Type _} [Category C] (F : Prefunct
#align category_theory.Quiv.lift CategoryTheory.QuivCat.lift
-/
-/- warning: category_theory.Quiv.adj -> CategoryTheory.QuivCat.adj is a dubious translation:
-lean 3 declaration is
- CategoryTheory.Adjunction.{max u1 u2, max u1 u2, max (succ u1) u1 (succ (max u1 u2)), max (succ u1) u1 (succ (max u1 u2))} CategoryTheory.QuivCat.{max u1 u2, u1} CategoryTheory.QuivCat.category.{max u1 u2, u1} CategoryTheory.Cat.{max u1 u2, u1} CategoryTheory.Cat.category.{max u1 u2, u1} CategoryTheory.Cat.free.{max u1 u2, u1} CategoryTheory.QuivCat.forget.{max u1 u2, u1}
-but is expected to have type
- CategoryTheory.Adjunction.{max u1 u2, max u1 u2, max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} CategoryTheory.QuivCat.{max u1 u2, u2} CategoryTheory.QuivCat.category.{max u1 u2, u2} CategoryTheory.Cat.{max u1 u2, u2} CategoryTheory.Cat.category.{max u1 u2, u2} CategoryTheory.Cat.free.{max u1 u2, u2} CategoryTheory.QuivCat.forget.{max u1 u2, u2}
-Case conversion may be inaccurate. Consider using '#align category_theory.Quiv.adj CategoryTheory.QuivCat.adjₓ'. -/
-- We might construct `of_lift_iso_self : paths.of ⋙ lift F ≅ F`
-- (and then show that `lift F` is initial amongst such functors)
-- but it would require lifting quite a bit of machinery to quivers!
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -93,16 +93,8 @@ def free : QuivCat.{v, u} ⥤ Cat.{max u v, u}
{ obj := fun X => F.obj X
map := fun X Y f => F.mapPath f
map_comp' := fun X Y Z f g => F.mapPath_comp f g }
- map_id' V := by
- change (show paths V ⥤ _ from _) = _
- ext
- apply eq_conj_eq_to_hom
- rfl
- map_comp' U V W F G := by
- change (show paths U ⥤ _ from _) = _
- ext
- apply eq_conj_eq_to_hom
- rfl
+ map_id' V := by change (show paths V ⥤ _ from _) = _; ext; apply eq_conj_eq_to_hom; rfl
+ map_comp' U V W F G := by change (show paths U ⥤ _ from _) = _; ext; apply eq_conj_eq_to_hom; rfl
#align category_theory.Cat.free CategoryTheory.Cat.free
-/
@@ -137,10 +129,7 @@ def adj : Cat.free ⊣ QuivCat.forget :=
{ homEquiv := fun V C =>
{ toFun := fun F => Paths.of.comp F.toPrefunctor
invFun := fun F => lift F
- left_inv := fun F => by
- ext
- · erw [(eq_conj_eq_to_hom _).symm]
- apply category.id_comp
+ left_inv := fun F => by ext; · erw [(eq_conj_eq_to_hom _).symm]; apply category.id_comp;
rfl
right_inv := by
rintro ⟨obj, map⟩
@@ -148,12 +137,8 @@ def adj : Cat.free ⊣ QuivCat.forget :=
congr
ext (X Y f)
exact category.id_comp _ }
- homEquiv_naturality_left_symm := fun V W C f g =>
- by
- change (show paths V ⥤ _ from _) = _
- ext
- apply eq_conj_eq_to_hom
- rfl }
+ homEquiv_naturality_left_symm := fun V W C f g => by change (show paths V ⥤ _ from _) = _;
+ ext; apply eq_conj_eq_to_hom; rfl }
#align category_theory.Quiv.adj CategoryTheory.QuivCat.adj
end Quiv
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
! This file was ported from Lean 3 source module category_theory.category.Quiv
-! leanprover-community/mathlib commit 350a381705199e9a070f84e98e803c3c25a97a4c
+! 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.PathCategory
/-!
# The category of quivers
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
The category of (bundled) quivers, and the free/forgetful adjunction between `Cat` and `Quiv`.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2
@@ -24,31 +24,38 @@ universe v u
namespace CategoryTheory
+#print CategoryTheory.QuivCat /-
-- intended to be used with explicit universe parameters
/-- Category of quivers. -/
@[nolint check_univs]
-def Quiv :=
+def QuivCat :=
Bundled Quiver.{v + 1, u}
-#align category_theory.Quiv CategoryTheory.Quiv
+#align category_theory.Quiv CategoryTheory.QuivCat
+-/
namespace Quiv
-instance : CoeSort Quiv (Type u) where coe := Bundled.α
+instance : CoeSort QuivCat (Type u) where coe := Bundled.α
-instance str (C : Quiv.{v, u}) : Quiver.{v + 1, u} C :=
+#print CategoryTheory.QuivCat.str' /-
+instance str' (C : QuivCat.{v, u}) : Quiver.{v + 1, u} C :=
C.str
-#align category_theory.Quiv.str CategoryTheory.Quiv.str
+#align category_theory.Quiv.str CategoryTheory.QuivCat.str'
+-/
+#print CategoryTheory.QuivCat.of /-
/-- Construct a bundled `Quiv` from the underlying type and the typeclass. -/
-def of (C : Type u) [Quiver.{v + 1} C] : Quiv.{v, u} :=
+def of (C : Type u) [Quiver.{v + 1} C] : QuivCat.{v, u} :=
Bundled.of C
-#align category_theory.Quiv.of CategoryTheory.Quiv.of
+#align category_theory.Quiv.of CategoryTheory.QuivCat.of
+-/
-instance : Inhabited Quiv :=
- ⟨Quiv.of (Quiver.Empty PEmpty)⟩
+instance : Inhabited QuivCat :=
+ ⟨QuivCat.of (Quiver.Empty PEmpty)⟩
+#print CategoryTheory.QuivCat.category /-
/-- Category structure on `Quiv` -/
-instance category : LargeCategory.{max v u} Quiv.{v, u}
+instance category : LargeCategory.{max v u} QuivCat.{v, u}
where
Hom C D := Prefunctor C D
id C := Prefunctor.id C
@@ -56,23 +63,27 @@ instance category : LargeCategory.{max v u} Quiv.{v, u}
id_comp' C D F := by cases F <;> rfl
comp_id' C D F := by cases F <;> rfl
assoc' := by intros <;> rfl
-#align category_theory.Quiv.category CategoryTheory.Quiv.category
+#align category_theory.Quiv.category CategoryTheory.QuivCat.category
+-/
+#print CategoryTheory.QuivCat.forget /-
/-- The forgetful functor from categories to quivers. -/
@[simps]
-def forget : Cat.{v, u} ⥤ Quiv.{v, u}
+def forget : Cat.{v, u} ⥤ QuivCat.{v, u}
where
- obj C := Quiv.of C
+ obj C := QuivCat.of C
map C D F := F.toPrefunctor
-#align category_theory.Quiv.forget CategoryTheory.Quiv.forget
+#align category_theory.Quiv.forget CategoryTheory.QuivCat.forget
+-/
end Quiv
namespace Cat
+#print CategoryTheory.Cat.free /-
/-- The functor sending each quiver to its path category. -/
@[simps]
-def free : Quiv.{v, u} ⥤ Cat.{max u v, u}
+def free : QuivCat.{v, u} ⥤ Cat.{max u v, u}
where
obj V := Cat.of (Paths V)
map V W F :=
@@ -90,26 +101,35 @@ def free : Quiv.{v, u} ⥤ Cat.{max u v, u}
apply eq_conj_eq_to_hom
rfl
#align category_theory.Cat.free CategoryTheory.Cat.free
+-/
end Cat
namespace Quiv
+#print CategoryTheory.QuivCat.lift /-
/-- Any prefunctor into a category lifts to a functor from the path category. -/
@[simps]
def lift {V : Type u} [Quiver.{v + 1} V] {C : Type _} [Category C] (F : Prefunctor V C) :
Paths V ⥤ C where
obj X := F.obj X
map X Y f := composePath (F.mapPath f)
-#align category_theory.Quiv.lift CategoryTheory.Quiv.lift
+#align category_theory.Quiv.lift CategoryTheory.QuivCat.lift
+-/
+/- warning: category_theory.Quiv.adj -> CategoryTheory.QuivCat.adj is a dubious translation:
+lean 3 declaration is
+ CategoryTheory.Adjunction.{max u1 u2, max u1 u2, max (succ u1) u1 (succ (max u1 u2)), max (succ u1) u1 (succ (max u1 u2))} CategoryTheory.QuivCat.{max u1 u2, u1} CategoryTheory.QuivCat.category.{max u1 u2, u1} CategoryTheory.Cat.{max u1 u2, u1} CategoryTheory.Cat.category.{max u1 u2, u1} CategoryTheory.Cat.free.{max u1 u2, u1} CategoryTheory.QuivCat.forget.{max u1 u2, u1}
+but is expected to have type
+ CategoryTheory.Adjunction.{max u1 u2, max u1 u2, max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} CategoryTheory.QuivCat.{max u1 u2, u2} CategoryTheory.QuivCat.category.{max u1 u2, u2} CategoryTheory.Cat.{max u1 u2, u2} CategoryTheory.Cat.category.{max u1 u2, u2} CategoryTheory.Cat.free.{max u1 u2, u2} CategoryTheory.QuivCat.forget.{max u1 u2, u2}
+Case conversion may be inaccurate. Consider using '#align category_theory.Quiv.adj CategoryTheory.QuivCat.adjₓ'. -/
-- We might construct `of_lift_iso_self : paths.of ⋙ lift F ≅ F`
-- (and then show that `lift F` is initial amongst such functors)
-- but it would require lifting quite a bit of machinery to quivers!
/--
The adjunction between forming the free category on a quiver, and forgetting a category to a quiver.
-/
-def adj : Cat.free ⊣ Quiv.forget :=
+def adj : Cat.free ⊣ QuivCat.forget :=
Adjunction.mkOfHomEquiv
{ homEquiv := fun V C =>
{ toFun := fun F => Paths.of.comp F.toPrefunctor
@@ -131,7 +151,7 @@ def adj : Cat.free ⊣ Quiv.forget :=
ext
apply eq_conj_eq_to_hom
rfl }
-#align category_theory.Quiv.adj CategoryTheory.Quiv.adj
+#align category_theory.Quiv.adj CategoryTheory.QuivCat.adj
end Quiv
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -81,13 +81,13 @@ def free : Quiv.{v, u} ⥤ Cat.{max u v, u}
map_id V := by
change (show Paths V ⥤ _ from _) = _
ext; swap
- apply eq_conj_eqToHom
- rfl
+ · apply eq_conj_eqToHom
+ · rfl
map_comp {U _ _} F G := by
change (show Paths U ⥤ _ from _) = _
ext; swap
- apply eq_conj_eqToHom
- rfl
+ · apply eq_conj_eqToHom
+ · rfl
set_option linter.uppercaseLean3 false in
#align category_theory.Cat.free CategoryTheory.Cat.free
@@ -125,8 +125,8 @@ def adj : Cat.free ⊣ Quiv.forget :=
homEquiv_naturality_left_symm := fun {V _ _} f g => by
change (show Paths V ⥤ _ from _) = _
ext; swap
- apply eq_conj_eqToHom
- rfl }
+ · apply eq_conj_eqToHom
+ · rfl }
set_option linter.uppercaseLean3 false in
#align category_theory.Quiv.adj CategoryTheory.Quiv.adj
@@ -12,7 +12,7 @@ import Mathlib.CategoryTheory.PathCategory
/-!
# The category of quivers
-The category of (bundled) quivers, and the free/forgetful adjunction between `Cat` and `QuivCat`.
+The category of (bundled) quivers, and the free/forgetful adjunction between `Cat` and `Quiv`.
-/
@@ -24,54 +24,55 @@ namespace CategoryTheory
-- intended to be used with explicit universe parameters
/-- Category of quivers. -/
@[nolint checkUnivs]
-def QuivCat :=
+def Quiv :=
Bundled Quiver.{v + 1, u}
set_option linter.uppercaseLean3 false in
-#align category_theory.Quiv CategoryTheory.QuivCat
+#align category_theory.Quiv CategoryTheory.Quiv
-namespace QuivCat
+namespace Quiv
-instance : CoeSort QuivCat (Type u) where coe := Bundled.α
+instance : CoeSort Quiv (Type u) where coe := Bundled.α
-instance str' (C : QuivCat.{v, u}) : Quiver.{v + 1, u} C :=
+instance str' (C : Quiv.{v, u}) : Quiver.{v + 1, u} C :=
C.str
set_option linter.uppercaseLean3 false in
-#align category_theory.Quiv.str CategoryTheory.QuivCat.str'
+#align category_theory.Quiv.str CategoryTheory.Quiv.str'
-/-- Construct a bundled `QuivCat` from the underlying type and the typeclass. -/
-def of (C : Type u) [Quiver.{v + 1} C] : QuivCat.{v, u} :=
+/-- Construct a bundled `Quiv` from the underlying type and the typeclass. -/
+def of (C : Type u) [Quiver.{v + 1} C] : Quiv.{v, u} :=
Bundled.of C
set_option linter.uppercaseLean3 false in
-#align category_theory.Quiv.of CategoryTheory.QuivCat.of
+#align category_theory.Quiv.of CategoryTheory.Quiv.of
-instance : Inhabited QuivCat :=
- ⟨QuivCat.of (Quiver.Empty PEmpty)⟩
+instance : Inhabited Quiv :=
+ ⟨Quiv.of (Quiver.Empty PEmpty)⟩
-/-- Category structure on `QuivCat` -/
-instance category : LargeCategory.{max v u} QuivCat.{v, u}
+/-- Category structure on `Quiv` -/
+instance category : LargeCategory.{max v u} Quiv.{v, u}
where
Hom C D := Prefunctor C D
id C := Prefunctor.id C
comp F G := Prefunctor.comp F G
set_option linter.uppercaseLean3 false in
-#align category_theory.Quiv.category CategoryTheory.QuivCat.category
+#align category_theory.Quiv.category CategoryTheory.Quiv.category
/-- The forgetful functor from categories to quivers. -/
@[simps]
-def forget : Cat.{v, u} ⥤ QuivCat.{v, u}
+def forget : Cat.{v, u} ⥤ Quiv.{v, u}
where
- obj C := QuivCat.of C
+ obj C := Quiv.of C
map F := F.toPrefunctor
set_option linter.uppercaseLean3 false in
-#align category_theory.Quiv.forget CategoryTheory.QuivCat.forget
+#align category_theory.Quiv.forget CategoryTheory.Quiv.forget
-end QuivCat
+end Quiv
namespace Cat
/-- The functor sending each quiver to its path category. -/
@[simps]
-def free : QuivCat.{v, u} ⥤ Cat.{max u v, u} where
+def free : Quiv.{v, u} ⥤ Cat.{max u v, u}
+ where
obj V := Cat.of (Paths V)
map F :=
{ obj := fun X => F.obj X
@@ -92,7 +93,7 @@ set_option linter.uppercaseLean3 false in
end Cat
-namespace QuivCat
+namespace Quiv
/-- Any prefunctor into a category lifts to a functor from the path category. -/
@[simps]
@@ -101,7 +102,7 @@ def lift {V : Type u} [Quiver.{v + 1} V] {C : Type*} [Category C] (F : Prefuncto
obj X := F.obj X
map f := composePath (F.mapPath f)
set_option linter.uppercaseLean3 false in
-#align category_theory.Quiv.lift CategoryTheory.QuivCat.lift
+#align category_theory.Quiv.lift CategoryTheory.Quiv.lift
-- We might construct `of_lift_iso_self : Paths.of ⋙ lift F ≅ F`
-- (and then show that `lift F` is initial amongst such functors)
@@ -109,7 +110,7 @@ set_option linter.uppercaseLean3 false in
/--
The adjunction between forming the free category on a quiver, and forgetting a category to a quiver.
-/
-def adj : Cat.free ⊣ QuivCat.forget :=
+def adj : Cat.free ⊣ Quiv.forget :=
Adjunction.mkOfHomEquiv
{ homEquiv := fun V C =>
{ toFun := fun F => Paths.of.comp F.toPrefunctor
@@ -127,8 +128,8 @@ def adj : Cat.free ⊣ QuivCat.forget :=
apply eq_conj_eqToHom
rfl }
set_option linter.uppercaseLean3 false in
-#align category_theory.Quiv.adj CategoryTheory.QuivCat.adj
+#align category_theory.Quiv.adj CategoryTheory.Quiv.adj
-end QuivCat
+end Quiv
end CategoryTheory
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -96,7 +96,7 @@ namespace QuivCat
/-- Any prefunctor into a category lifts to a functor from the path category. -/
@[simps]
-def lift {V : Type u} [Quiver.{v + 1} V] {C : Type _} [Category C] (F : Prefunctor V C) :
+def lift {V : Type u} [Quiver.{v + 1} V] {C : Type*} [Category C] (F : Prefunctor V C) :
Paths V ⥤ C where
obj X := F.obj X
map f := composePath (F.mapPath f)
@@ -2,16 +2,13 @@
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.category.Quiv
-! leanprover-community/mathlib commit 350a381705199e9a070f84e98e803c3c25a97a4c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Adjunction.Basic
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.CategoryTheory.PathCategory
+#align_import category_theory.category.Quiv from "leanprover-community/mathlib"@"350a381705199e9a070f84e98e803c3c25a97a4c"
+
/-!
# The category of quivers
Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>
@@ -74,8 +74,7 @@ namespace Cat
/-- The functor sending each quiver to its path category. -/
@[simps]
-def free : QuivCat.{v, u} ⥤ Cat.{max u v, u}
- where
+def free : QuivCat.{v, u} ⥤ Cat.{max u v, u} where
obj V := Cat.of (Paths V)
map F :=
{ obj := fun X => F.obj X
@@ -83,12 +82,12 @@ def free : QuivCat.{v, u} ⥤ Cat.{max u v, u}
map_comp := fun f g => F.mapPath_comp f g }
map_id V := by
change (show Paths V ⥤ _ from _) = _
- ext
+ ext; swap
apply eq_conj_eqToHom
rfl
map_comp {U _ _} F G := by
change (show Paths U ⥤ _ from _) = _
- ext
+ ext; swap
apply eq_conj_eqToHom
rfl
set_option linter.uppercaseLean3 false in
@@ -127,7 +126,7 @@ def adj : Cat.free ⊣ QuivCat.forget :=
exact Category.id_comp _ }
homEquiv_naturality_left_symm := fun {V _ _} f g => by
change (show Paths V ⥤ _ from _) = _
- ext
+ ext; swap
apply eq_conj_eqToHom
rfl }
set_option linter.uppercaseLean3 false in
All dependencies are ported!