category_theory.monoidal.CommMon_
⟷
Mathlib.CategoryTheory.Monoidal.CommMon_
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/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -76,7 +76,7 @@ variable (C)
/-- The forgetful functor from commutative monoid objects to monoid objects. -/
def forget₂Mon_ : CommMon_ C ⥤ Mon_ C :=
inducedFunctor CommMon_.toMon_
-deriving Full, Faithful
+deriving CategoryTheory.Functor.Full, CategoryTheory.Functor.Faithful
#align CommMon_.forget₂_Mon_ CommMon_.forget₂Mon_
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import CategoryTheory.Monoidal.Braided
+import CategoryTheory.Monoidal.Braided.Basic
import CategoryTheory.Monoidal.Mon_
#align_import category_theory.monoidal.CommMon_ from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -158,17 +158,17 @@ open CategoryTheory.LaxBraidedFunctor
namespace EquivLaxBraidedFunctorPunit
-#print CommMon_.EquivLaxBraidedFunctorPunit.laxBraidedToCommMon /-
+#print CommMon_.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon /-
/-- Implementation of `CommMon_.equiv_lax_braided_functor_punit`. -/
@[simps]
def laxBraidedToCommMon : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ⥤ CommMon_ C
where
obj F := (F.mapCommMon : CommMon_ _ ⥤ CommMon_ C).obj (trivial (Discrete PUnit))
map F G α := ((mapCommMonFunctor (Discrete PUnit) C).map α).app _
-#align CommMon_.equiv_lax_braided_functor_punit.lax_braided_to_CommMon CommMon_.EquivLaxBraidedFunctorPunit.laxBraidedToCommMon
+#align CommMon_.equiv_lax_braided_functor_punit.lax_braided_to_CommMon CommMon_.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon
-/
-#print CommMon_.EquivLaxBraidedFunctorPunit.commMonToLaxBraided /-
+#print CommMon_.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided /-
/-- Implementation of `CommMon_.equiv_lax_braided_functor_punit`. -/
@[simps]
def commMonToLaxBraided : CommMon_ C ⥤ LaxBraidedFunctor (Discrete PUnit.{u + 1}) C
@@ -185,14 +185,14 @@ def commMonToLaxBraided : CommMon_ C ⥤ LaxBraidedFunctor (Discrete PUnit.{u +
naturality' := fun _ _ _ => by dsimp; rw [category.id_comp, category.comp_id]
unit' := f.OneHom
tensor' := fun _ _ => f.MulHom }
-#align CommMon_.equiv_lax_braided_functor_punit.CommMon_to_lax_braided CommMon_.EquivLaxBraidedFunctorPunit.commMonToLaxBraided
+#align CommMon_.equiv_lax_braided_functor_punit.CommMon_to_lax_braided CommMon_.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided
-/
attribute [local tidy] tactic.discrete_cases
attribute [local simp] eq_to_iso_map
-#print CommMon_.EquivLaxBraidedFunctorPunit.unitIso /-
+#print CommMon_.EquivLaxBraidedFunctorPUnit.unitIso /-
/-- Implementation of `CommMon_.equiv_lax_braided_functor_punit`. -/
@[simps]
def unitIso :
@@ -205,10 +205,10 @@ def unitIso :
(fun _ => F.toLaxMonoidalFunctor.toFunctor.mapIso (eqToIso (by ext))) (by tidy) (by tidy)
(by tidy)))
(by tidy)
-#align CommMon_.equiv_lax_braided_functor_punit.unit_iso CommMon_.EquivLaxBraidedFunctorPunit.unitIso
+#align CommMon_.equiv_lax_braided_functor_punit.unit_iso CommMon_.EquivLaxBraidedFunctorPUnit.unitIso
-/
-#print CommMon_.EquivLaxBraidedFunctorPunit.counitIso /-
+#print CommMon_.EquivLaxBraidedFunctorPUnit.counitIso /-
/-- Implementation of `CommMon_.equiv_lax_braided_functor_punit`. -/
@[simps]
def counitIso : commMonToLaxBraided C ⋙ laxBraidedToCommMon C ≅ 𝟭 (CommMon_ C) :=
@@ -217,7 +217,7 @@ def counitIso : commMonToLaxBraided C ⋙ laxBraidedToCommMon C ≅ 𝟭 (CommMo
{ Hom := { Hom := 𝟙 _ }
inv := { Hom := 𝟙 _ } })
(by tidy)
-#align CommMon_.equiv_lax_braided_functor_punit.counit_iso CommMon_.EquivLaxBraidedFunctorPunit.counitIso
+#align CommMon_.equiv_lax_braided_functor_punit.counit_iso CommMon_.EquivLaxBraidedFunctorPUnit.counitIso
-/
end EquivLaxBraidedFunctorPunit
@@ -226,18 +226,18 @@ open EquivLaxBraidedFunctorPunit
attribute [local simp] eq_to_iso_map
-#print CommMon_.equivLaxBraidedFunctorPunit /-
+#print CommMon_.equivLaxBraidedFunctorPUnit /-
/-- Commutative monoid objects in `C` are "just" braided lax monoidal functors from the trivial
braided monoidal category to `C`.
-/
@[simps]
-def equivLaxBraidedFunctorPunit : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ≌ CommMon_ C
+def equivLaxBraidedFunctorPUnit : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ≌ CommMon_ C
where
Functor := laxBraidedToCommMon C
inverse := commMonToLaxBraided C
unitIso := unitIso C
counitIso := counitIso C
-#align CommMon_.equiv_lax_braided_functor_punit CommMon_.equivLaxBraidedFunctorPunit
+#align CommMon_.equiv_lax_braided_functor_punit CommMon_.equivLaxBraidedFunctorPUnit
-/
end CommMon_
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathbin.CategoryTheory.Monoidal.Braided
-import Mathbin.CategoryTheory.Monoidal.Mon_
+import CategoryTheory.Monoidal.Braided
+import CategoryTheory.Monoidal.Mon_
#align_import category_theory.monoidal.CommMon_ from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d
@@ -32,8 +32,6 @@ structure CommMon_ extends Mon_ C where
#align CommMon_ CommMon_
-/
-restate_axiom CommMon_.mul_comm'
-
attribute [simp, reassoc] CommMon_.mul_comm
namespace CommMon_
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 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.monoidal.CommMon_
-! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Monoidal.Braided
import Mathbin.CategoryTheory.Monoidal.Mon_
+#align_import category_theory.monoidal.CommMon_ from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
+
/-!
# The category of commutative monoids in a braided monoidal category.
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -27,11 +27,13 @@ open CategoryTheory.MonoidalCategory
variable (C : Type u₁) [Category.{v₁} C] [MonoidalCategory.{v₁} C] [BraidedCategory.{v₁} C]
+#print CommMon_ /-
/-- A commutative monoid object internal to a monoidal category.
-/
structure CommMon_ extends Mon_ C where
mul_comm' : (β_ _ _).Hom ≫ mul = mul := by obviously
#align CommMon_ CommMon_
+-/
restate_axiom CommMon_.mul_comm'
@@ -39,12 +41,14 @@ attribute [simp, reassoc] CommMon_.mul_comm
namespace CommMon_
+#print CommMon_.trivial /-
/-- The trivial commutative monoid object. We later show this is initial in `CommMon_ C`.
-/
@[simps]
def trivial : CommMon_ C :=
{ Mon_.trivial C with mul_comm' := by dsimp; rw [braiding_left_unitor, unitors_equal] }
#align CommMon_.trivial CommMon_.trivial
+-/
instance : Inhabited (CommMon_ C) :=
⟨trivial C⟩
@@ -54,47 +58,61 @@ variable {C} {M : CommMon_ C}
instance : Category (CommMon_ C) :=
InducedCategory.category CommMon_.toMon_
+#print CommMon_.id_hom /-
@[simp]
theorem id_hom (A : CommMon_ C) : Mon_.Hom.hom (𝟙 A) = 𝟙 A.pt :=
rfl
#align CommMon_.id_hom CommMon_.id_hom
+-/
+#print CommMon_.comp_hom /-
@[simp]
theorem comp_hom {R S T : CommMon_ C} (f : R ⟶ S) (g : S ⟶ T) :
Mon_.Hom.hom (f ≫ g) = f.Hom ≫ g.Hom :=
rfl
#align CommMon_.comp_hom CommMon_.comp_hom
+-/
section
variable (C)
+#print CommMon_.forget₂Mon_ /-
/-- The forgetful functor from commutative monoid objects to monoid objects. -/
def forget₂Mon_ : CommMon_ C ⥤ Mon_ C :=
inducedFunctor CommMon_.toMon_
deriving Full, Faithful
#align CommMon_.forget₂_Mon_ CommMon_.forget₂Mon_
+-/
+#print CommMon_.forget₂_Mon_obj_one /-
@[simp]
theorem forget₂_Mon_obj_one (A : CommMon_ C) : ((forget₂Mon_ C).obj A).one = A.one :=
rfl
#align CommMon_.forget₂_Mon_obj_one CommMon_.forget₂_Mon_obj_one
+-/
+#print CommMon_.forget₂_Mon_obj_mul /-
@[simp]
theorem forget₂_Mon_obj_mul (A : CommMon_ C) : ((forget₂Mon_ C).obj A).mul = A.mul :=
rfl
#align CommMon_.forget₂_Mon_obj_mul CommMon_.forget₂_Mon_obj_mul
+-/
+#print CommMon_.forget₂_Mon_map_hom /-
@[simp]
theorem forget₂_Mon_map_hom {A B : CommMon_ C} (f : A ⟶ B) : ((forget₂Mon_ C).map f).Hom = f.Hom :=
rfl
#align CommMon_.forget₂_Mon_map_hom CommMon_.forget₂_Mon_map_hom
+-/
end
+#print CommMon_.uniqueHomFromTrivial /-
instance uniqueHomFromTrivial (A : CommMon_ C) : Unique (trivial C ⟶ A) :=
Mon_.uniqueHomFromTrivial A.toMon_
#align CommMon_.unique_hom_from_trivial CommMon_.uniqueHomFromTrivial
+-/
open CategoryTheory.Limits
@@ -107,6 +125,7 @@ namespace CategoryTheory.LaxBraidedFunctor
variable {C} {D : Type u₂} [Category.{v₂} D] [MonoidalCategory.{v₂} D] [BraidedCategory.{v₂} D]
+#print CategoryTheory.LaxBraidedFunctor.mapCommMon /-
/-- A lax braided functor takes commutative monoid objects to commutative monoid objects.
That is, a lax braided functor `F : C ⥤ D` induces a functor `CommMon_ C ⥤ CommMon_ D`.
@@ -123,15 +142,18 @@ def mapCommMon (F : LaxBraidedFunctor C D) : CommMon_ C ⥤ CommMon_ D
slice_lhs 2 3 => rw [← CategoryTheory.Functor.map_comp, A.mul_comm] }
map A B f := F.toLaxMonoidalFunctor.mapMon.map f
#align category_theory.lax_braided_functor.map_CommMon CategoryTheory.LaxBraidedFunctor.mapCommMon
+-/
variable (C) (D)
+#print CategoryTheory.LaxBraidedFunctor.mapCommMonFunctor /-
/-- `map_CommMon` is functorial in the lax braided functor. -/
def mapCommMonFunctor : LaxBraidedFunctor C D ⥤ CommMon_ C ⥤ CommMon_ D
where
obj := mapCommMon
map F G α := { app := fun A => { Hom := α.app A.pt } }
#align category_theory.lax_braided_functor.map_CommMon_functor CategoryTheory.LaxBraidedFunctor.mapCommMonFunctor
+-/
end CategoryTheory.LaxBraidedFunctor
@@ -141,6 +163,7 @@ open CategoryTheory.LaxBraidedFunctor
namespace EquivLaxBraidedFunctorPunit
+#print CommMon_.EquivLaxBraidedFunctorPunit.laxBraidedToCommMon /-
/-- Implementation of `CommMon_.equiv_lax_braided_functor_punit`. -/
@[simps]
def laxBraidedToCommMon : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ⥤ CommMon_ C
@@ -148,7 +171,9 @@ def laxBraidedToCommMon : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ⥤ CommM
obj F := (F.mapCommMon : CommMon_ _ ⥤ CommMon_ C).obj (trivial (Discrete PUnit))
map F G α := ((mapCommMonFunctor (Discrete PUnit) C).map α).app _
#align CommMon_.equiv_lax_braided_functor_punit.lax_braided_to_CommMon CommMon_.EquivLaxBraidedFunctorPunit.laxBraidedToCommMon
+-/
+#print CommMon_.EquivLaxBraidedFunctorPunit.commMonToLaxBraided /-
/-- Implementation of `CommMon_.equiv_lax_braided_functor_punit`. -/
@[simps]
def commMonToLaxBraided : CommMon_ C ⥤ LaxBraidedFunctor (Discrete PUnit.{u + 1}) C
@@ -166,11 +191,13 @@ def commMonToLaxBraided : CommMon_ C ⥤ LaxBraidedFunctor (Discrete PUnit.{u +
unit' := f.OneHom
tensor' := fun _ _ => f.MulHom }
#align CommMon_.equiv_lax_braided_functor_punit.CommMon_to_lax_braided CommMon_.EquivLaxBraidedFunctorPunit.commMonToLaxBraided
+-/
attribute [local tidy] tactic.discrete_cases
attribute [local simp] eq_to_iso_map
+#print CommMon_.EquivLaxBraidedFunctorPunit.unitIso /-
/-- Implementation of `CommMon_.equiv_lax_braided_functor_punit`. -/
@[simps]
def unitIso :
@@ -184,7 +211,9 @@ def unitIso :
(by tidy)))
(by tidy)
#align CommMon_.equiv_lax_braided_functor_punit.unit_iso CommMon_.EquivLaxBraidedFunctorPunit.unitIso
+-/
+#print CommMon_.EquivLaxBraidedFunctorPunit.counitIso /-
/-- Implementation of `CommMon_.equiv_lax_braided_functor_punit`. -/
@[simps]
def counitIso : commMonToLaxBraided C ⋙ laxBraidedToCommMon C ≅ 𝟭 (CommMon_ C) :=
@@ -194,6 +223,7 @@ def counitIso : commMonToLaxBraided C ⋙ laxBraidedToCommMon C ≅ 𝟭 (CommMo
inv := { Hom := 𝟙 _ } })
(by tidy)
#align CommMon_.equiv_lax_braided_functor_punit.counit_iso CommMon_.EquivLaxBraidedFunctorPunit.counitIso
+-/
end EquivLaxBraidedFunctorPunit
@@ -201,6 +231,7 @@ open EquivLaxBraidedFunctorPunit
attribute [local simp] eq_to_iso_map
+#print CommMon_.equivLaxBraidedFunctorPunit /-
/-- Commutative monoid objects in `C` are "just" braided lax monoidal functors from the trivial
braided monoidal category to `C`.
-/
@@ -212,6 +243,7 @@ def equivLaxBraidedFunctorPunit : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C
unitIso := unitIso C
counitIso := counitIso C
#align CommMon_.equiv_lax_braided_functor_punit CommMon_.equivLaxBraidedFunctorPunit
+-/
end CommMon_
mathlib commit https://github.com/leanprover-community/mathlib/commit/bf9bbbcf0c1c1ead18280b0d010e417b10abb1b6
@@ -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.monoidal.CommMon_
-! leanprover-community/mathlib commit a836c6dba9bd1ee2a0cdc9af0006a596f243031c
+! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
! 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.Monoidal.Mon_
/-!
# The category of commutative monoids in a braided monoidal category.
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -68,7 +68,8 @@ variable (C)
/-- The forgetful functor from commutative monoid objects to monoid objects. -/
def forget₂Mon_ : CommMon_ C ⥤ Mon_ C :=
- inducedFunctor CommMon_.toMon_ deriving Full, Faithful
+ inducedFunctor CommMon_.toMon_
+deriving Full, Faithful
#align CommMon_.forget₂_Mon_ CommMon_.forget₂Mon_
@[simp]
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -158,9 +158,7 @@ def commMonToLaxBraided : CommMon_ C ⥤ LaxBraidedFunctor (Discrete PUnit.{u +
map_comp' := fun _ _ _ _ _ => (Category.id_comp (𝟙 A.pt)).symm }
map A B f :=
{ app := fun _ => f.Hom
- naturality' := fun _ _ _ => by
- dsimp
- rw [category.id_comp, category.comp_id]
+ naturality' := fun _ _ _ => by dsimp; rw [category.id_comp, category.comp_id]
unit' := f.OneHom
tensor' := fun _ _ => f.MulHom }
#align CommMon_.equiv_lax_braided_functor_punit.CommMon_to_lax_braided CommMon_.EquivLaxBraidedFunctorPunit.commMonToLaxBraided
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -32,7 +32,7 @@ structure CommMon_ extends Mon_ C where
restate_axiom CommMon_.mul_comm'
-attribute [simp, reassoc.1] CommMon_.mul_comm
+attribute [simp, reassoc] CommMon_.mul_comm
namespace CommMon_
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -52,7 +52,7 @@ instance : Category (CommMon_ C) :=
InducedCategory.category CommMon_.toMon_
@[simp]
-theorem id_hom (A : CommMon_ C) : Mon_.Hom.hom (𝟙 A) = 𝟙 A.x :=
+theorem id_hom (A : CommMon_ C) : Mon_.Hom.hom (𝟙 A) = 𝟙 A.pt :=
rfl
#align CommMon_.id_hom CommMon_.id_hom
@@ -126,7 +126,7 @@ variable (C) (D)
def mapCommMonFunctor : LaxBraidedFunctor C D ⥤ CommMon_ C ⥤ CommMon_ D
where
obj := mapCommMon
- map F G α := { app := fun A => { Hom := α.app A.x } }
+ map F G α := { app := fun A => { Hom := α.app A.pt } }
#align category_theory.lax_braided_functor.map_CommMon_functor CategoryTheory.LaxBraidedFunctor.mapCommMonFunctor
end CategoryTheory.LaxBraidedFunctor
@@ -150,12 +150,12 @@ def laxBraidedToCommMon : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ⥤ CommM
def commMonToLaxBraided : CommMon_ C ⥤ LaxBraidedFunctor (Discrete PUnit.{u + 1}) C
where
obj A :=
- { obj := fun _ => A.x
+ { obj := fun _ => A.pt
map := fun _ _ _ => 𝟙 _
ε := A.one
μ := fun _ _ => A.mul
map_id' := fun _ => rfl
- map_comp' := fun _ _ _ _ _ => (Category.id_comp (𝟙 A.x)).symm }
+ map_comp' := fun _ _ _ _ _ => (Category.id_comp (𝟙 A.pt)).symm }
map A B f :=
{ app := fun _ => f.Hom
naturality' := fun _ _ _ => by
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
These notions on functors are now Functor.Full
, Functor.Faithful
, Functor.EssSurj
, Functor.IsEquivalence
, Functor.ReflectsIsomorphisms
. Deprecated aliases are introduced for the previous names.
@@ -87,8 +87,8 @@ set_option linter.uppercaseLean3 false in
#align CommMon_.forget₂_Mon_ CommMon_.forget₂Mon_
-- Porting note: no delta derive handler, see https://github.com/leanprover-community/mathlib4/issues/5020
-instance : Full (forget₂Mon_ C) := InducedCategory.full _
-instance : Faithful (forget₂Mon_ C) := InducedCategory.faithful _
+instance : (forget₂Mon_ C).Full := InducedCategory.full _
+instance : (forget₂Mon_ C).Faithful := InducedCategory.faithful _
@[simp]
theorem forget₂_Mon_obj_one (A : CommMon_ C) : ((forget₂Mon_ C).obj A).one = A.one :=
@@ -3,7 +3,7 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathlib.CategoryTheory.Monoidal.Braided
+import Mathlib.CategoryTheory.Monoidal.Braided.Basic
import Mathlib.CategoryTheory.Monoidal.Mon_
#align_import category_theory.monoidal.CommMon_ from "leanprover-community/mathlib"@"a836c6dba9bd1ee2a0cdc9af0006a596f243031c"
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -60,7 +60,7 @@ theorem comp_hom {R S T : CommMon_ C} (f : R ⟶ S) (g : S ⟶ T) :
set_option linter.uppercaseLean3 false in
#align CommMon_.comp_hom CommMon_.comp_hom
--- porting note: added because `Mon_.Hom.ext` is not triggered automatically
+-- Porting note: added because `Mon_.Hom.ext` is not triggered automatically
-- for morphisms in `CommMon_ C`
-- See https://github.com/leanprover-community/mathlib4/issues/5229
@[ext]
@@ -172,8 +172,6 @@ def laxBraidedToCommMon : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ⥤ CommM
set_option linter.uppercaseLean3 false in
#align CommMon_.equiv_lax_braided_functor_punit.lax_braided_to_CommMon CommMon_.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon
-attribute [local simp] id_tensorHom tensorHom_id
-
/-- Implementation of `CommMon_.equivLaxBraidedFunctorPunit`. -/
@[simps]
def commMonToLaxBraided : CommMon_ C ⥤ LaxBraidedFunctor (Discrete PUnit.{u + 1}) C where
@@ -67,7 +67,8 @@ set_option linter.uppercaseLean3 false in
lemma hom_ext {A B : CommMon_ C} (f g : A ⟶ B) (h : f.hom = g.hom) : f = g :=
Mon_.Hom.ext _ _ h
--- porting note: the following two lemmas `id'` and `comp'` have been added to ease automation;
+-- Porting note (#10688): the following two lemmas `id'` and `comp'`
+-- have been added to ease automation;
@[simp]
lemma id' (A : CommMon_ C) : (𝟙 A : A.toMon_ ⟶ A.toMon_) = 𝟙 (A.toMon_) := rfl
@@ -144,7 +145,7 @@ set_option linter.uppercaseLean3 false in
variable (C) (D)
--- porting note: added @[simps] to ease automation
+-- Porting note (#10688): added @[simps] to ease automation
/-- `mapCommMon` is functorial in the lax braided functor. -/
@[simps]
def mapCommMonFunctor : LaxBraidedFunctor C D ⥤ CommMon_ C ⥤ CommMon_ D where
@@ -171,7 +171,9 @@ def laxBraidedToCommMon : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ⥤ CommM
set_option linter.uppercaseLean3 false in
#align CommMon_.equiv_lax_braided_functor_punit.lax_braided_to_CommMon CommMon_.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon
-/-- Implementation of `CommMon_.equivLaxBraidedFunctorPUnit`. -/
+attribute [local simp] id_tensorHom tensorHom_id
+
+/-- Implementation of `CommMon_.equivLaxBraidedFunctorPunit`. -/
@[simps]
def commMonToLaxBraided : CommMon_ C ⥤ LaxBraidedFunctor (Discrete PUnit.{u + 1}) C where
obj A :=
@@ -161,17 +161,17 @@ namespace CommMon_
open CategoryTheory.LaxBraidedFunctor
-namespace EquivLaxBraidedFunctorPunit
+namespace EquivLaxBraidedFunctorPUnit
-/-- Implementation of `CommMon_.equivLaxBraidedFunctorPunit`. -/
+/-- Implementation of `CommMon_.equivLaxBraidedFunctorPUnit`. -/
@[simps]
def laxBraidedToCommMon : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ⥤ CommMon_ C where
obj F := (F.mapCommMon : CommMon_ _ ⥤ CommMon_ C).obj (trivial (Discrete PUnit.{u+1}))
map α := ((mapCommMonFunctor (Discrete PUnit.{u+1}) C).map α).app _
set_option linter.uppercaseLean3 false in
-#align CommMon_.equiv_lax_braided_functor_punit.lax_braided_to_CommMon CommMon_.EquivLaxBraidedFunctorPunit.laxBraidedToCommMon
+#align CommMon_.equiv_lax_braided_functor_punit.lax_braided_to_CommMon CommMon_.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon
-/-- Implementation of `CommMon_.equivLaxBraidedFunctorPunit`. -/
+/-- Implementation of `CommMon_.equivLaxBraidedFunctorPUnit`. -/
@[simps]
def commMonToLaxBraided : CommMon_ C ⥤ LaxBraidedFunctor (Discrete PUnit.{u + 1}) C where
obj A :=
@@ -187,9 +187,9 @@ def commMonToLaxBraided : CommMon_ C ⥤ LaxBraidedFunctor (Discrete PUnit.{u +
unit := Mon_.Hom.one_hom f
tensor := fun _ _ => Mon_.Hom.mul_hom f }
set_option linter.uppercaseLean3 false in
-#align CommMon_.equiv_lax_braided_functor_punit.CommMon_to_lax_braided CommMon_.EquivLaxBraidedFunctorPunit.commMonToLaxBraided
+#align CommMon_.equiv_lax_braided_functor_punit.CommMon_to_lax_braided CommMon_.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided
-/-- Implementation of `CommMon_.equivLaxBraidedFunctorPunit`. -/
+/-- Implementation of `CommMon_.equivLaxBraidedFunctorPUnit`. -/
@[simps!]
def unitIso :
𝟭 (LaxBraidedFunctor (Discrete PUnit.{u + 1}) C) ≅
@@ -201,9 +201,9 @@ def unitIso :
(fun _ => F.toLaxMonoidalFunctor.toFunctor.mapIso (eqToIso (by ext)))
(by rintro ⟨⟩ ⟨⟩ f; aesop_cat) (by aesop_cat) (by aesop_cat)))
set_option linter.uppercaseLean3 false in
-#align CommMon_.equiv_lax_braided_functor_punit.unit_iso CommMon_.EquivLaxBraidedFunctorPunit.unitIso
+#align CommMon_.equiv_lax_braided_functor_punit.unit_iso CommMon_.EquivLaxBraidedFunctorPUnit.unitIso
-/-- Implementation of `CommMon_.equivLaxBraidedFunctorPunit`. -/
+/-- Implementation of `CommMon_.equivLaxBraidedFunctorPUnit`. -/
@[simps!]
def counitIso : commMonToLaxBraided C ⋙ laxBraidedToCommMon C ≅ 𝟭 (CommMon_ C) :=
NatIso.ofComponents
@@ -211,22 +211,22 @@ def counitIso : commMonToLaxBraided C ⋙ laxBraidedToCommMon C ≅ 𝟭 (CommMo
{ hom := { hom := 𝟙 _ }
inv := { hom := 𝟙 _ } })
set_option linter.uppercaseLean3 false in
-#align CommMon_.equiv_lax_braided_functor_punit.counit_iso CommMon_.EquivLaxBraidedFunctorPunit.counitIso
+#align CommMon_.equiv_lax_braided_functor_punit.counit_iso CommMon_.EquivLaxBraidedFunctorPUnit.counitIso
-end EquivLaxBraidedFunctorPunit
+end EquivLaxBraidedFunctorPUnit
-open EquivLaxBraidedFunctorPunit
+open EquivLaxBraidedFunctorPUnit
/-- Commutative monoid objects in `C` are "just" braided lax monoidal functors from the trivial
braided monoidal category to `C`.
-/
@[simps]
-def equivLaxBraidedFunctorPunit : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ≌ CommMon_ C where
+def equivLaxBraidedFunctorPUnit : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ≌ CommMon_ C where
functor := laxBraidedToCommMon C
inverse := commMonToLaxBraided C
unitIso := unitIso C
counitIso := counitIso C
set_option linter.uppercaseLean3 false in
-#align CommMon_.equiv_lax_braided_functor_punit CommMon_.equivLaxBraidedFunctorPunit
+#align CommMon_.equiv_lax_braided_functor_punit CommMon_.equivLaxBraidedFunctorPUnit
end CommMon_
@@ -73,7 +73,7 @@ lemma id' (A : CommMon_ C) : (𝟙 A : A.toMon_ ⟶ A.toMon_) = 𝟙 (A.toMon_)
@[simp]
lemma comp' {A₁ A₂ A₃ : CommMon_ C} (f : A₁ ⟶ A₂) (g : A₂ ⟶ A₃) :
- ((f ≫ g : A₁ ⟶ A₃) : A₁.toMon_ ⟶ A₃.toMon_) = @CategoryStruct.comp (Mon_ C) _ _ _ _ f g := rfl
+ ((f ≫ g : A₁ ⟶ A₃) : A₁.toMon_ ⟶ A₃.toMon_) = @CategoryStruct.comp (Mon_ C) _ _ _ _ f g := rfl
section
These declarations broke when I tweaked instances a little bit (in a separate branch that is not ready yet), and I think these declarations can use some extra robustness (usually by providing some extra information explicitly).
@@ -166,8 +166,8 @@ namespace EquivLaxBraidedFunctorPunit
/-- Implementation of `CommMon_.equivLaxBraidedFunctorPunit`. -/
@[simps]
def laxBraidedToCommMon : LaxBraidedFunctor (Discrete PUnit.{u + 1}) C ⥤ CommMon_ C where
- obj F := (F.mapCommMon : CommMon_ _ ⥤ CommMon_ C).obj (trivial (Discrete PUnit))
- map α := ((mapCommMonFunctor (Discrete PUnit) C).map α).app _
+ obj F := (F.mapCommMon : CommMon_ _ ⥤ CommMon_ C).obj (trivial (Discrete PUnit.{u+1}))
+ map α := ((mapCommMonFunctor (Discrete PUnit.{u+1}) C).map α).app _
set_option linter.uppercaseLean3 false in
#align CommMon_.equiv_lax_braided_functor_punit.lax_braided_to_CommMon CommMon_.EquivLaxBraidedFunctorPunit.laxBraidedToCommMon
@@ -2,15 +2,12 @@
Copyright (c) 2020 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.monoidal.CommMon_
-! leanprover-community/mathlib commit a836c6dba9bd1ee2a0cdc9af0006a596f243031c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Monoidal.Braided
import Mathlib.CategoryTheory.Monoidal.Mon_
+#align_import category_theory.monoidal.CommMon_ from "leanprover-community/mathlib"@"a836c6dba9bd1ee2a0cdc9af0006a596f243031c"
+
/-!
# The category of commutative monoids in a braided monoidal category.
-/
This is the second half of the changes originally in #5699, removing all occurrences of ;
after a space and implementing a linter rule to enforce it.
In most cases this 2-character substring has a space after it, so the following command was run first:
find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;
The remaining cases were few enough in number that they were done manually.
@@ -154,7 +154,7 @@ def mapCommMonFunctor : LaxBraidedFunctor C D ⥤ CommMon_ C ⥤ CommMon_ D wher
obj := mapCommMon
map α :=
{ app := fun A => { hom := α.app A.X }
- naturality := by intros ; ext ; simp }
+ naturality := by intros; ext; simp }
set_option linter.uppercaseLean3 false in
#align category_theory.lax_braided_functor.map_CommMon_functor CategoryTheory.LaxBraidedFunctor.mapCommMonFunctor
@@ -202,7 +202,7 @@ def unitIso :
LaxBraidedFunctor.mkIso
(MonoidalNatIso.ofComponents
(fun _ => F.toLaxMonoidalFunctor.toFunctor.mapIso (eqToIso (by ext)))
- (by rintro ⟨⟩ ⟨⟩ f ; aesop_cat) (by aesop_cat) (by aesop_cat)))
+ (by rintro ⟨⟩ ⟨⟩ f; aesop_cat) (by aesop_cat) (by aesop_cat)))
set_option linter.uppercaseLean3 false in
#align CommMon_.equiv_lax_braided_functor_punit.unit_iso CommMon_.EquivLaxBraidedFunctorPunit.unitIso
@@ -65,6 +65,7 @@ set_option linter.uppercaseLean3 false in
-- porting note: added because `Mon_.Hom.ext` is not triggered automatically
-- for morphisms in `CommMon_ C`
+-- See https://github.com/leanprover-community/mathlib4/issues/5229
@[ext]
lemma hom_ext {A B : CommMon_ C} (f g : A ⟶ B) (h : f.hom = g.hom) : f = g :=
Mon_.Hom.ext _ _ h
The unported dependencies are