category_theory.category.Bipointed
⟷
Mathlib.CategoryTheory.Category.Bipointed
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
@@ -3,7 +3,7 @@ Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
-import Mathbin.CategoryTheory.Category.Pointed
+import CategoryTheory.Category.Pointed
#align_import category_theory.category.Bipointed from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -56,7 +56,7 @@ theorem coe_of {X : Type _} (to_prod : X × X) : ↥(of to_prod) = X :=
#align Bipointed.coe_of Bipointed.coe_of
-/
-alias of ← _root_.prod.Bipointed
+alias _root_.prod.Bipointed := of
#align prod.Bipointed Prod.Bipointed
instance : Inhabited Bipointed :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module category_theory.category.Bipointed
-! leanprover-community/mathlib commit 932872382355f00112641d305ba0619305dc8642
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Category.Pointed
+#align_import category_theory.category.Bipointed from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"
+
/-!
# The category of bipointed types
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -130,6 +130,7 @@ def swap : Bipointed ⥤ Bipointed where
#align Bipointed.swap Bipointed.swap
-/
+#print Bipointed.swapEquiv /-
/-- The equivalence between `Bipointed` and itself induced by `prod.swap` both ways. -/
@[simps]
def swapEquiv : Bipointed ≌ Bipointed :=
@@ -145,11 +146,14 @@ def swapEquiv : Bipointed ≌ Bipointed :=
inv := ⟨id, rfl, rfl⟩ })
fun X Y f => rfl)
#align Bipointed.swap_equiv Bipointed.swapEquiv
+-/
+#print Bipointed.swapEquiv_symm /-
@[simp]
theorem swapEquiv_symm : swapEquiv.symm = swapEquiv :=
rfl
#align Bipointed.swap_equiv_symm Bipointed.swapEquiv_symm
+-/
end Bipointed
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -130,12 +130,6 @@ def swap : Bipointed ⥤ Bipointed where
#align Bipointed.swap Bipointed.swap
-/
-/- warning: Bipointed.swap_equiv -> Bipointed.swapEquiv is a dubious translation:
-lean 3 declaration is
- CategoryTheory.Equivalence.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1}
-but is expected to have type
- CategoryTheory.Equivalence.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.largeCategory.{u1}
-Case conversion may be inaccurate. Consider using '#align Bipointed.swap_equiv Bipointed.swapEquivₓ'. -/
/-- The equivalence between `Bipointed` and itself induced by `prod.swap` both ways. -/
@[simps]
def swapEquiv : Bipointed ≌ Bipointed :=
@@ -152,12 +146,6 @@ def swapEquiv : Bipointed ≌ Bipointed :=
fun X Y f => rfl)
#align Bipointed.swap_equiv Bipointed.swapEquiv
-/- warning: Bipointed.swap_equiv_symm -> Bipointed.swapEquiv_symm is a dubious translation:
-lean 3 declaration is
- Eq.{succ (succ u1)} (CategoryTheory.Equivalence.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1}) (CategoryTheory.Equivalence.symm.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.swapEquiv.{u1}) Bipointed.swapEquiv.{u1}
-but is expected to have type
- Eq.{succ (succ u1)} (CategoryTheory.Equivalence.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.largeCategory.{u1}) (CategoryTheory.Equivalence.symm.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.swapEquiv.{u1}) Bipointed.swapEquiv.{u1}
-Case conversion may be inaccurate. Consider using '#align Bipointed.swap_equiv_symm Bipointed.swapEquiv_symmₓ'. -/
@[simp]
theorem swapEquiv_symm : swapEquiv.symm = swapEquiv :=
rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -297,16 +297,9 @@ def pointedToBipointedFstBipointedToPointedFstAdjunction :
{ homEquiv := fun X Y =>
{ toFun := fun f => ⟨f.toFun ∘ Option.some, f.map_fst⟩
invFun := fun f => ⟨fun o => o.elim Y.toProd.2 f.toFun, f.map_point, rfl⟩
- left_inv := fun f => by
- ext
- cases x
- exact f.map_snd.symm
- rfl
+ left_inv := fun f => by ext; cases x; exact f.map_snd.symm; rfl
right_inv := fun f => Pointed.Hom.ext _ _ rfl }
- homEquiv_naturality_left_symm := fun X' X Y f g =>
- by
- ext
- cases x <;> rfl }
+ homEquiv_naturality_left_symm := fun X' X Y f g => by ext; cases x <;> rfl }
#align Pointed_to_Bipointed_fst_Bipointed_to_Pointed_fst_adjunction pointedToBipointedFstBipointedToPointedFstAdjunction
-/
@@ -319,16 +312,9 @@ def pointedToBipointedSndBipointedToPointedSndAdjunction :
{ homEquiv := fun X Y =>
{ toFun := fun f => ⟨f.toFun ∘ Option.some, f.map_snd⟩
invFun := fun f => ⟨fun o => o.elim Y.toProd.1 f.toFun, rfl, f.map_point⟩
- left_inv := fun f => by
- ext
- cases x
- exact f.map_fst.symm
- rfl
+ left_inv := fun f => by ext; cases x; exact f.map_fst.symm; rfl
right_inv := fun f => Pointed.Hom.ext _ _ rfl }
- homEquiv_naturality_left_symm := fun X' X Y f g =>
- by
- ext
- cases x <;> rfl }
+ homEquiv_naturality_left_symm := fun X' X Y f g => by ext; cases x <;> rfl }
#align Pointed_to_Bipointed_snd_Bipointed_to_Pointed_snd_adjunction pointedToBipointedSndBipointedToPointedSndAdjunction
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/1f4705ccdfe1e557fc54a0ce081a05e33d2e6240
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
! This file was ported from Lean 3 source module category_theory.category.Bipointed
-! leanprover-community/mathlib commit c8ab806ef73c20cab1d87b5157e43a82c205f28e
+! leanprover-community/mathlib commit 932872382355f00112641d305ba0619305dc8642
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.CategoryTheory.Category.Pointed
/-!
# The category of bipointed types
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This defines `Bipointed`, the category of bipointed types.
## TODO
mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559
@@ -27,11 +27,13 @@ universe u
variable {α β : Type _}
+#print Bipointed /-
/-- The category of bipointed types. -/
structure Bipointed : Type (u + 1) where
pt : Type u
toProd : X × X
#align Bipointed Bipointed
+-/
namespace Bipointed
@@ -40,22 +42,27 @@ instance : CoeSort Bipointed (Type _) :=
attribute [protected] Bipointed.X
+#print Bipointed.of /-
/-- Turns a bipointing into a bipointed type. -/
def of {X : Type _} (to_prod : X × X) : Bipointed :=
⟨X, to_prod⟩
#align Bipointed.of Bipointed.of
+-/
+#print Bipointed.coe_of /-
@[simp]
theorem coe_of {X : Type _} (to_prod : X × X) : ↥(of to_prod) = X :=
rfl
#align Bipointed.coe_of Bipointed.coe_of
+-/
alias of ← _root_.prod.Bipointed
-#align prod.Bipointed Prod.bipointed
+#align prod.Bipointed Prod.Bipointed
instance : Inhabited Bipointed :=
⟨of ((), ())⟩
+#print Bipointed.Hom /-
/-- Morphisms in `Bipointed`. -/
@[ext]
protected structure Hom (X Y : Bipointed.{u}) : Type u where
@@ -63,27 +70,33 @@ protected structure Hom (X Y : Bipointed.{u}) : Type u where
map_fst : to_fun X.toProd.1 = Y.toProd.1
map_snd : to_fun X.toProd.2 = Y.toProd.2
#align Bipointed.hom Bipointed.Hom
+-/
namespace Hom
+#print Bipointed.Hom.id /-
/-- The identity morphism of `X : Bipointed`. -/
@[simps]
def id (X : Bipointed) : Hom X X :=
⟨id, rfl, rfl⟩
#align Bipointed.hom.id Bipointed.Hom.id
+-/
instance (X : Bipointed) : Inhabited (Hom X X) :=
⟨id X⟩
+#print Bipointed.Hom.comp /-
/-- Composition of morphisms of `Bipointed`. -/
@[simps]
def comp {X Y Z : Bipointed.{u}} (f : Hom X Y) (g : Hom Y Z) : Hom X Z :=
⟨g.toFun ∘ f.toFun, by rw [Function.comp_apply, f.map_fst, g.map_fst], by
rw [Function.comp_apply, f.map_snd, g.map_snd]⟩
#align Bipointed.hom.comp Bipointed.Hom.comp
+-/
end Hom
+#print Bipointed.largeCategory /-
instance largeCategory : LargeCategory Bipointed
where
Hom := Hom
@@ -93,7 +106,9 @@ instance largeCategory : LargeCategory Bipointed
comp_id' _ _ _ := Hom.ext _ _ rfl
assoc' _ _ _ _ _ _ _ := Hom.ext _ _ rfl
#align Bipointed.large_category Bipointed.largeCategory
+-/
+#print Bipointed.concreteCategory /-
instance concreteCategory : ConcreteCategory Bipointed
where
forget :=
@@ -101,14 +116,23 @@ instance concreteCategory : ConcreteCategory Bipointed
map := @Hom.toFun }
forget_faithful := ⟨@Hom.ext⟩
#align Bipointed.concrete_category Bipointed.concreteCategory
+-/
+#print Bipointed.swap /-
/-- Swaps the pointed elements of a bipointed type. `prod.swap` as a functor. -/
@[simps]
def swap : Bipointed ⥤ Bipointed where
obj X := ⟨X, X.toProd.symm⟩
map X Y f := ⟨f.toFun, f.map_snd, f.map_fst⟩
#align Bipointed.swap Bipointed.swap
+-/
+/- warning: Bipointed.swap_equiv -> Bipointed.swapEquiv is a dubious translation:
+lean 3 declaration is
+ CategoryTheory.Equivalence.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1}
+but is expected to have type
+ CategoryTheory.Equivalence.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.largeCategory.{u1}
+Case conversion may be inaccurate. Consider using '#align Bipointed.swap_equiv Bipointed.swapEquivₓ'. -/
/-- The equivalence between `Bipointed` and itself induced by `prod.swap` both ways. -/
@[simps]
def swapEquiv : Bipointed ≌ Bipointed :=
@@ -125,6 +149,12 @@ def swapEquiv : Bipointed ≌ Bipointed :=
fun X Y f => rfl)
#align Bipointed.swap_equiv Bipointed.swapEquiv
+/- warning: Bipointed.swap_equiv_symm -> Bipointed.swapEquiv_symm is a dubious translation:
+lean 3 declaration is
+ Eq.{succ (succ u1)} (CategoryTheory.Equivalence.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1}) (CategoryTheory.Equivalence.symm.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.swapEquiv.{u1}) Bipointed.swapEquiv.{u1}
+but is expected to have type
+ Eq.{succ (succ u1)} (CategoryTheory.Equivalence.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.largeCategory.{u1}) (CategoryTheory.Equivalence.symm.{u1, u1, succ u1, succ u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.{u1} Bipointed.largeCategory.{u1} Bipointed.swapEquiv.{u1}) Bipointed.swapEquiv.{u1}
+Case conversion may be inaccurate. Consider using '#align Bipointed.swap_equiv_symm Bipointed.swapEquiv_symmₓ'. -/
@[simp]
theorem swapEquiv_symm : swapEquiv.symm = swapEquiv :=
rfl
@@ -132,51 +162,66 @@ theorem swapEquiv_symm : swapEquiv.symm = swapEquiv :=
end Bipointed
+#print bipointedToPointedFst /-
/-- The forgetful functor from `Bipointed` to `Pointed` which forgets about the second point. -/
def bipointedToPointedFst : Bipointed ⥤ Pointed
where
obj X := ⟨X, X.toProd.1⟩
map X Y f := ⟨f.toFun, f.map_fst⟩
#align Bipointed_to_Pointed_fst bipointedToPointedFst
+-/
+#print bipointedToPointedSnd /-
/-- The forgetful functor from `Bipointed` to `Pointed` which forgets about the first point. -/
def bipointedToPointedSnd : Bipointed ⥤ Pointed
where
obj X := ⟨X, X.toProd.2⟩
map X Y f := ⟨f.toFun, f.map_snd⟩
#align Bipointed_to_Pointed_snd bipointedToPointedSnd
+-/
+#print bipointedToPointedFst_comp_forget /-
@[simp]
theorem bipointedToPointedFst_comp_forget :
bipointedToPointedFst ⋙ forget Pointed = forget Bipointed :=
rfl
#align Bipointed_to_Pointed_fst_comp_forget bipointedToPointedFst_comp_forget
+-/
+#print bipointedToPointedSnd_comp_forget /-
@[simp]
theorem bipointedToPointedSnd_comp_forget :
bipointedToPointedSnd ⋙ forget Pointed = forget Bipointed :=
rfl
#align Bipointed_to_Pointed_snd_comp_forget bipointedToPointedSnd_comp_forget
+-/
+#print swap_comp_bipointedToPointedFst /-
@[simp]
theorem swap_comp_bipointedToPointedFst :
Bipointed.swap ⋙ bipointedToPointedFst = bipointedToPointedSnd :=
rfl
#align swap_comp_Bipointed_to_Pointed_fst swap_comp_bipointedToPointedFst
+-/
+#print swap_comp_bipointedToPointedSnd /-
@[simp]
theorem swap_comp_bipointedToPointedSnd :
Bipointed.swap ⋙ bipointedToPointedSnd = bipointedToPointedFst :=
rfl
#align swap_comp_Bipointed_to_Pointed_snd swap_comp_bipointedToPointedSnd
+-/
+#print pointedToBipointed /-
/-- The functor from `Pointed` to `Bipointed` which bipoints the point. -/
def pointedToBipointed : Pointed.{u} ⥤ Bipointed
where
obj X := ⟨X, X.point, X.point⟩
map X Y f := ⟨f.toFun, f.map_point, f.map_point⟩
#align Pointed_to_Bipointed pointedToBipointed
+-/
+#print pointedToBipointedFst /-
/-- The functor from `Pointed` to `Bipointed` which adds a second point. -/
def pointedToBipointedFst : Pointed.{u} ⥤ Bipointed
where
@@ -185,7 +230,9 @@ def pointedToBipointedFst : Pointed.{u} ⥤ Bipointed
map_id' X := Bipointed.Hom.ext _ _ Option.map_id
map_comp' X Y Z f g := Bipointed.Hom.ext _ _ (Option.map_comp_map _ _).symm
#align Pointed_to_Bipointed_fst pointedToBipointedFst
+-/
+#print pointedToBipointedSnd /-
/-- The functor from `Pointed` to `Bipointed` which adds a first point. -/
def pointedToBipointedSnd : Pointed.{u} ⥤ Bipointed
where
@@ -194,19 +241,25 @@ def pointedToBipointedSnd : Pointed.{u} ⥤ Bipointed
map_id' X := Bipointed.Hom.ext _ _ Option.map_id
map_comp' X Y Z f g := Bipointed.Hom.ext _ _ (Option.map_comp_map _ _).symm
#align Pointed_to_Bipointed_snd pointedToBipointedSnd
+-/
+#print pointedToBipointedFst_comp_swap /-
@[simp]
theorem pointedToBipointedFst_comp_swap :
pointedToBipointedFst ⋙ Bipointed.swap = pointedToBipointedSnd :=
rfl
#align Pointed_to_Bipointed_fst_comp_swap pointedToBipointedFst_comp_swap
+-/
+#print pointedToBipointedSnd_comp_swap /-
@[simp]
theorem pointedToBipointedSnd_comp_swap :
pointedToBipointedSnd ⋙ Bipointed.swap = pointedToBipointedFst :=
rfl
#align Pointed_to_Bipointed_snd_comp_swap pointedToBipointedSnd_comp_swap
+-/
+#print pointedToBipointedCompBipointedToPointedFst /-
/-- `Bipointed_to_Pointed_fst` is inverse to `Pointed_to_Bipointed`. -/
@[simps]
def pointedToBipointedCompBipointedToPointedFst :
@@ -217,7 +270,9 @@ def pointedToBipointedCompBipointedToPointedFst :
inv := ⟨id, rfl⟩ })
fun X Y f => rfl
#align Pointed_to_Bipointed_comp_Bipointed_to_Pointed_fst pointedToBipointedCompBipointedToPointedFst
+-/
+#print pointedToBipointedCompBipointedToPointedSnd /-
/-- `Bipointed_to_Pointed_snd` is inverse to `Pointed_to_Bipointed`. -/
@[simps]
def pointedToBipointedCompBipointedToPointedSnd :
@@ -228,7 +283,9 @@ def pointedToBipointedCompBipointedToPointedSnd :
inv := ⟨id, rfl⟩ })
fun X Y f => rfl
#align Pointed_to_Bipointed_comp_Bipointed_to_Pointed_snd pointedToBipointedCompBipointedToPointedSnd
+-/
+#print pointedToBipointedFstBipointedToPointedFstAdjunction /-
/-- The free/forgetful adjunction between `Pointed_to_Bipointed_fst` and `Bipointed_to_Pointed_fst`.
-/
def pointedToBipointedFstBipointedToPointedFstAdjunction :
@@ -248,7 +305,9 @@ def pointedToBipointedFstBipointedToPointedFstAdjunction :
ext
cases x <;> rfl }
#align Pointed_to_Bipointed_fst_Bipointed_to_Pointed_fst_adjunction pointedToBipointedFstBipointedToPointedFstAdjunction
+-/
+#print pointedToBipointedSndBipointedToPointedSndAdjunction /-
/-- The free/forgetful adjunction between `Pointed_to_Bipointed_snd` and `Bipointed_to_Pointed_snd`.
-/
def pointedToBipointedSndBipointedToPointedSndAdjunction :
@@ -268,4 +327,5 @@ def pointedToBipointedSndBipointedToPointedSndAdjunction :
ext
cases x <;> rfl }
#align Pointed_to_Bipointed_snd_Bipointed_to_Pointed_snd_adjunction pointedToBipointedSndBipointedToPointedSndAdjunction
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -29,7 +29,7 @@ variable {α β : Type _}
/-- The category of bipointed types. -/
structure Bipointed : Type (u + 1) where
- x : Type u
+ pt : Type u
toProd : X × X
#align Bipointed Bipointed
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@[inherit_doc]
on notations (#9942)
Make all the notations that unambiguously should inherit the docstring of their definition actually inherit it.
Also write a few docstrings by hand. I only wrote the ones I was competent to write and which I was sure of. Some docstrings come from mathlib3 as they were lost during the early port.
This PR is only intended as a first pass There are many more docstrings to add.
@@ -28,17 +28,15 @@ set_option linter.uppercaseLean3 false
/-- The category of bipointed types. -/
structure Bipointed : Type (u + 1) where
- X : Type u
+ /-- The underlying type of a bipointed type. -/
+ protected X : Type u
+ /-- The two points of a bipointed type, bundled together as a pair. -/
toProd : X × X
#align Bipointed Bipointed
namespace Bipointed
-instance : CoeSort Bipointed (Type*) :=
- ⟨X⟩
-
--- porting note: protected attribute does not work
--- attribute [protected] Bipointed.X
+instance : CoeSort Bipointed Type* := ⟨Bipointed.X⟩
/-- Turns a bipointing into a bipointed type. -/
def of {X : Type*} (to_prod : X × X) : Bipointed :=
@@ -59,6 +57,7 @@ instance : Inhabited Bipointed :=
/-- Morphisms in `Bipointed`. -/
@[ext]
protected structure Hom (X Y : Bipointed.{u}) : Type u where
+ /-- The underlying function of a morphism of bipointed types. -/
toFun : X → Y
map_fst : toFun X.toProd.1 = Y.toProd.1
map_snd : toFun X.toProd.2 = Y.toProd.2
@@ -50,7 +50,7 @@ theorem coe_of {X : Type*} (to_prod : X × X) : ↥(of to_prod) = X :=
rfl
#align Bipointed.coe_of Bipointed.coe_of
-alias of ← _root_.Prod.Bipointed
+alias _root_.Prod.Bipointed := of
#align prod.Bipointed Prod.Bipointed
instance : Inhabited Bipointed :=
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -22,7 +22,7 @@ open CategoryTheory
universe u
-variable {α β : Type _}
+variable {α β : Type*}
set_option linter.uppercaseLean3 false
@@ -34,19 +34,19 @@ structure Bipointed : Type (u + 1) where
namespace Bipointed
-instance : CoeSort Bipointed (Type _) :=
+instance : CoeSort Bipointed (Type*) :=
⟨X⟩
-- porting note: protected attribute does not work
-- attribute [protected] Bipointed.X
/-- Turns a bipointing into a bipointed type. -/
-def of {X : Type _} (to_prod : X × X) : Bipointed :=
+def of {X : Type*} (to_prod : X × X) : Bipointed :=
⟨X, to_prod⟩
#align Bipointed.of Bipointed.of
@[simp]
-theorem coe_of {X : Type _} (to_prod : X × X) : ↥(of to_prod) = X :=
+theorem coe_of {X : Type*} (to_prod : X × X) : ↥(of to_prod) = X :=
rfl
#align Bipointed.coe_of Bipointed.coe_of
@@ -2,14 +2,11 @@
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module category_theory.category.Bipointed
-! leanprover-community/mathlib commit c8ab806ef73c20cab1d87b5157e43a82c205f28e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Category.Pointed
+#align_import category_theory.category.Bipointed from "leanprover-community/mathlib"@"c8ab806ef73c20cab1d87b5157e43a82c205f28e"
+
/-!
# The category of bipointed types
@@ -112,16 +112,12 @@ def swap : Bipointed ⥤ Bipointed where
@[simps!]
def swapEquiv : Bipointed ≌ Bipointed :=
CategoryTheory.Equivalence.mk swap swap
- (NatIso.ofComponents
- (fun X =>
+ (NatIso.ofComponents fun X =>
{ hom := ⟨id, rfl, rfl⟩
inv := ⟨id, rfl, rfl⟩ })
- fun f => rfl)
- (NatIso.ofComponents
- (fun X =>
+ (NatIso.ofComponents fun X =>
{ hom := ⟨id, rfl, rfl⟩
inv := ⟨id, rfl, rfl⟩ })
- fun f => rfl)
#align Bipointed.swap_equiv Bipointed.swapEquiv
@[simp]
@@ -205,22 +201,18 @@ theorem pointedToBipointedSnd_comp_swap :
@[simps!]
def pointedToBipointedCompBipointedToPointedFst :
pointedToBipointed ⋙ bipointedToPointedFst ≅ 𝟭 _ :=
- NatIso.ofComponents
- (fun X =>
- { hom := ⟨id, rfl⟩
- inv := ⟨id, rfl⟩ })
- fun f => rfl
+ NatIso.ofComponents fun X =>
+ { hom := ⟨id, rfl⟩
+ inv := ⟨id, rfl⟩ }
#align Pointed_to_Bipointed_comp_Bipointed_to_Pointed_fst pointedToBipointedCompBipointedToPointedFst
/-- `BipointedToPointed_snd` is inverse to `PointedToBipointed`. -/
@[simps!]
def pointedToBipointedCompBipointedToPointedSnd :
pointedToBipointed ⋙ bipointedToPointedSnd ≅ 𝟭 _ :=
- NatIso.ofComponents
- (fun X =>
- { hom := ⟨id, rfl⟩
- inv := ⟨id, rfl⟩ })
- fun f => rfl
+ NatIso.ofComponents fun X =>
+ { hom := ⟨id, rfl⟩
+ inv := ⟨id, rfl⟩ }
#align Pointed_to_Bipointed_comp_Bipointed_to_Pointed_snd pointedToBipointedCompBipointedToPointedSnd
/-- The free/forgetful adjunction between `PointedToBipointed_fst` and `BipointedToPointed_fst`.
I think the ports
didn't quite get things right, and also have some variation between them. This PR tries to straighten things out.
Major changes:
X.\a
, and put attribute @[coe]
on this.lemma Hom.map_mul {X Y : MonCat} (f : X ⟶ Y) (x y : X) : ((forget MonCat).map f) (x * y) = f x * f y
lemma coe_comp {X Y Z : MonCat} {f : X ⟶ Y} {g : Y ⟶ Z} : (f ≫ g : X → Z) = g ∘ f := rfl
Overall I'm pretty happy, and it allows me to unstick the long stuck https://github.com/leanprover-community/mathlib4/pull/3105.
This is not everything I want to do to refactor these files, but once I was satisfied that I can move forward with RingCat, I want to get this merged so we can unblock porting progress. I'll promise to come back to this soon! :-)
Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>
@@ -95,7 +95,7 @@ instance largeCategory : LargeCategory Bipointed where
#align Bipointed.large_category Bipointed.largeCategory
instance concreteCategory : ConcreteCategory Bipointed where
- Forget :=
+ forget :=
{ obj := Bipointed.X
map := @Hom.toFun }
forget_faithful := ⟨@Hom.ext⟩
Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: adamtopaz <github@adamtopaz.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>
All dependencies are ported!