category_theory.monoidal.internal.functor_category
⟷
Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory
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
@@ -3,8 +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.CommMon_
-import Mathbin.CategoryTheory.Monoidal.FunctorCategory
+import CategoryTheory.Monoidal.CommMon_
+import CategoryTheory.Monoidal.FunctorCategory
#align_import category_theory.monoidal.internal.functor_category from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
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.internal.functor_category
-! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Monoidal.CommMon_
import Mathbin.CategoryTheory.Monoidal.FunctorCategory
+#align_import category_theory.monoidal.internal.functor_category from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
+
/-!
# `Mon_ (C ⥤ D) ≌ C ⥤ Mon_ D`
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -50,6 +50,7 @@ namespace MonFunctorCategoryEquivalence
variable {C D}
+#print CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor /-
/-- Functor translating a monoid object in a functor category
to a functor into the category of monoid objects.
-/
@@ -77,7 +78,9 @@ def functor : Mon_ (C ⥤ D) ⥤ C ⥤ Mon_ D
one_hom' := congr_app f.OneHom X
mul_hom' := congr_app f.MulHom X } }
#align category_theory.monoidal.Mon_functor_category_equivalence.functor CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor
+-/
+#print CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse /-
/-- Functor translating a functor into the category of monoid objects
to a monoid object in the functor category
-/
@@ -98,7 +101,9 @@ def inverse : (C ⥤ Mon_ D) ⥤ Mon_ (C ⥤ D)
one_hom' := by ext x; dsimp; rw [(α.app x).OneHom]
mul_hom' := by ext x; dsimp; rw [(α.app x).MulHom] }
#align category_theory.monoidal.Mon_functor_category_equivalence.inverse CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse
+-/
+#print CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso /-
/-- The unit for the equivalence `Mon_ (C ⥤ D) ≌ C ⥤ Mon_ D`.
-/
@[simps]
@@ -119,7 +124,9 @@ def unitIso : 𝟭 (Mon_ (C ⥤ D)) ≅ functor ⋙ inverse :=
simp only [functor.id_map, functor.comp_map, functor_map_app_hom, Mon_.comp_hom',
category.id_comp, category.comp_id, inverse_map_hom_app, nat_trans.comp_app]
#align category_theory.monoidal.Mon_functor_category_equivalence.unit_iso CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.unitIso
+-/
+#print CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso /-
/-- The counit for the equivalence `Mon_ (C ⥤ D) ≌ C ⥤ Mon_ D`.
-/
@[simps]
@@ -133,11 +140,13 @@ def counitIso : inverse ⋙ functor ≅ 𝟭 (C ⥤ Mon_ D) :=
(by tidy))
(by tidy)
#align category_theory.monoidal.Mon_functor_category_equivalence.counit_iso CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.counitIso
+-/
end MonFunctorCategoryEquivalence
open MonFunctorCategoryEquivalence
+#print CategoryTheory.Monoidal.monFunctorCategoryEquivalence /-
/-- When `D` is a monoidal category,
monoid objects in `C ⥤ D` are the same thing
as functors from `C` into the monoid objects of `D`.
@@ -150,6 +159,7 @@ def monFunctorCategoryEquivalence : Mon_ (C ⥤ D) ≌ C ⥤ Mon_ D
unitIso := unitIso
counitIso := counitIso
#align category_theory.monoidal.Mon_functor_category_equivalence CategoryTheory.Monoidal.monFunctorCategoryEquivalence
+-/
variable [BraidedCategory.{v₂} D]
@@ -157,6 +167,7 @@ namespace CommMonFunctorCategoryEquivalence
variable {C D}
+#print CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor /-
/-- Functor translating a commutative monoid object in a functor category
to a functor into the category of commutative monoid objects.
-/
@@ -170,7 +181,9 @@ def functor : CommMon_ (C ⥤ D) ⥤ C ⥤ CommMon_ D
mul_comm' := congr_app A.mul_comm X } }
map A B f := { app := fun X => ((monFunctorCategoryEquivalence C D).Functor.map f).app X }
#align category_theory.monoidal.CommMon_functor_category_equivalence.functor CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor
+-/
+#print CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse /-
/-- Functor translating a functor into the category of commutative monoid objects
to a commutative monoid object in the functor category
-/
@@ -182,7 +195,9 @@ def inverse : (C ⥤ CommMon_ D) ⥤ CommMon_ (C ⥤ D)
mul_comm' := by ext X; exact (F.obj X).mul_comm }
map F G α := (monFunctorCategoryEquivalence C D).inverse.map (whiskerRight α _)
#align category_theory.monoidal.CommMon_functor_category_equivalence.inverse CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse
+-/
+#print CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso /-
/-- The unit for the equivalence `CommMon_ (C ⥤ D) ≌ C ⥤ CommMon_ D`.
-/
@[simps]
@@ -203,7 +218,9 @@ def unitIso : 𝟭 (CommMon_ (C ⥤ D)) ≅ functor ⋙ inverse :=
dsimp
simp only [category.id_comp, category.comp_id]
#align category_theory.monoidal.CommMon_functor_category_equivalence.unit_iso CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso
+-/
+#print CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso /-
/-- The counit for the equivalence `CommMon_ (C ⥤ D) ≌ C ⥤ CommMon_ D`.
-/
@[simps]
@@ -217,11 +234,13 @@ def counitIso : inverse ⋙ functor ≅ 𝟭 (C ⥤ CommMon_ D) :=
(by tidy))
(by tidy)
#align category_theory.monoidal.CommMon_functor_category_equivalence.counit_iso CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso
+-/
end CommMonFunctorCategoryEquivalence
open CommMonFunctorCategoryEquivalence
+#print CategoryTheory.Monoidal.commMonFunctorCategoryEquivalence /-
/-- When `D` is a braided monoidal category,
commutative monoid objects in `C ⥤ D` are the same thing
as functors from `C` into the commutative monoid objects of `D`.
@@ -234,6 +253,7 @@ def commMonFunctorCategoryEquivalence : CommMon_ (C ⥤ D) ≌ C ⥤ CommMon_ D
unitIso := unitIso
counitIso := counitIso
#align category_theory.monoidal.CommMon_functor_category_equivalence CategoryTheory.Monoidal.commMonFunctorCategoryEquivalence
+-/
end CategoryTheory.Monoidal
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -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.internal.functor_category
-! leanprover-community/mathlib commit f153a85a8dc0a96ce9133fed69e34df72f7f191f
+! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.Monoidal.FunctorCategory
/-!
# `Mon_ (C ⥤ D) ≌ C ⥤ Mon_ D`
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
When `D` is a monoidal category,
monoid objects in `C ⥤ D` are the same thing as functors from `C` into the monoid objects of `D`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -63,21 +63,10 @@ def functor : Mon_ (C ⥤ D) ⥤ C ⥤ Mon_ D
mul_assoc' := congr_app A.mul_assoc X }
map := fun X Y f =>
{ Hom := A.pt.map f
- one_hom' := by
- rw [← A.one.naturality, tensor_unit_map]
- dsimp
- rw [category.id_comp]
- mul_hom' := by
- dsimp
- rw [← A.mul.naturality, tensor_obj_map] }
- map_id' := fun X => by
- ext
- dsimp
- rw [CategoryTheory.Functor.map_id]
- map_comp' := fun X Y Z f g => by
- ext
- dsimp
- rw [functor.map_comp] }
+ one_hom' := by rw [← A.one.naturality, tensor_unit_map]; dsimp; rw [category.id_comp]
+ mul_hom' := by dsimp; rw [← A.mul.naturality, tensor_obj_map] }
+ map_id' := fun X => by ext; dsimp; rw [CategoryTheory.Functor.map_id]
+ map_comp' := fun X Y Z f g => by ext; dsimp; rw [functor.map_comp] }
map A B f :=
{
app := fun X =>
@@ -96,27 +85,15 @@ def inverse : (C ⥤ Mon_ D) ⥤ Mon_ (C ⥤ D)
{ pt := F ⋙ Mon_.forget D
one := { app := fun X => (F.obj X).one }
mul := { app := fun X => (F.obj X).mul }
- one_mul' := by
- ext X
- exact (F.obj X).one_mul
- mul_one' := by
- ext X
- exact (F.obj X).mul_one
- mul_assoc' := by
- ext X
- exact (F.obj X).mul_assoc }
+ one_mul' := by ext X; exact (F.obj X).one_mul
+ mul_one' := by ext X; exact (F.obj X).mul_one
+ mul_assoc' := by ext X; exact (F.obj X).mul_assoc }
map F G α :=
{ Hom :=
{ app := fun X => (α.app X).Hom
naturality' := fun X Y f => congr_arg Mon_.Hom.hom (α.naturality f) }
- one_hom' := by
- ext x
- dsimp
- rw [(α.app x).OneHom]
- mul_hom' := by
- ext x
- dsimp
- rw [(α.app x).MulHom] }
+ one_hom' := by ext x; dsimp; rw [(α.app x).OneHom]
+ mul_hom' := by ext x; dsimp; rw [(α.app x).MulHom] }
#align category_theory.monoidal.Mon_functor_category_equivalence.inverse CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse
/-- The unit for the equivalence `Mon_ (C ⥤ D) ≌ C ⥤ Mon_ D`.
@@ -127,23 +104,12 @@ def unitIso : 𝟭 (Mon_ (C ⥤ D)) ≅ functor ⋙ inverse :=
(fun A =>
{ Hom :=
{ Hom := { app := fun _ => 𝟙 _ }
- one_hom' := by
- ext X
- dsimp
- simp only [category.comp_id]
- mul_hom' := by
- ext X
- dsimp
- simp only [tensor_id, category.id_comp, category.comp_id] }
+ one_hom' := by ext X; dsimp; simp only [category.comp_id]
+ mul_hom' := by ext X; dsimp; simp only [tensor_id, category.id_comp, category.comp_id] }
inv :=
{ Hom := { app := fun _ => 𝟙 _ }
- one_hom' := by
- ext X
- dsimp
- simp only [category.comp_id]
- mul_hom' := by
- ext X
- dsimp
+ one_hom' := by ext X; dsimp; simp only [category.comp_id]
+ mul_hom' := by ext X; dsimp;
simp only [tensor_id, category.id_comp, category.comp_id] } })
fun A B f => by
ext X
@@ -210,9 +176,7 @@ def inverse : (C ⥤ CommMon_ D) ⥤ CommMon_ (C ⥤ D)
where
obj F :=
{ (monFunctorCategoryEquivalence C D).inverse.obj (F ⋙ CommMon_.forget₂Mon_ D) with
- mul_comm' := by
- ext X
- exact (F.obj X).mul_comm }
+ mul_comm' := by ext X; exact (F.obj X).mul_comm }
map F G α := (monFunctorCategoryEquivalence C D).inverse.map (whiskerRight α _)
#align category_theory.monoidal.CommMon_functor_category_equivalence.inverse CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse
@@ -224,23 +188,12 @@ def unitIso : 𝟭 (CommMon_ (C ⥤ D)) ≅ functor ⋙ inverse :=
(fun A =>
{ Hom :=
{ Hom := { app := fun _ => 𝟙 _ }
- one_hom' := by
- ext X
- dsimp
- simp only [category.comp_id]
- mul_hom' := by
- ext X
- dsimp
- simp only [tensor_id, category.id_comp, category.comp_id] }
+ one_hom' := by ext X; dsimp; simp only [category.comp_id]
+ mul_hom' := by ext X; dsimp; simp only [tensor_id, category.id_comp, category.comp_id] }
inv :=
{ Hom := { app := fun _ => 𝟙 _ }
- one_hom' := by
- ext X
- dsimp
- simp only [category.comp_id]
- mul_hom' := by
- ext X
- dsimp
+ one_hom' := by ext X; dsimp; simp only [category.comp_id]
+ mul_hom' := by ext X; dsimp;
simp only [tensor_id, category.id_comp, category.comp_id] } })
fun A B f => by
ext X
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -55,14 +55,14 @@ def functor : Mon_ (C ⥤ D) ⥤ C ⥤ Mon_ D
where
obj A :=
{ obj := fun X =>
- { x := A.x.obj X
+ { pt := A.pt.obj X
one := A.one.app X
mul := A.mul.app X
one_mul' := congr_app A.one_mul X
mul_one' := congr_app A.mul_one X
mul_assoc' := congr_app A.mul_assoc X }
map := fun X Y f =>
- { Hom := A.x.map f
+ { Hom := A.pt.map f
one_hom' := by
rw [← A.one.naturality, tensor_unit_map]
dsimp
@@ -93,7 +93,7 @@ to a monoid object in the functor category
def inverse : (C ⥤ Mon_ D) ⥤ Mon_ (C ⥤ D)
where
obj F :=
- { x := F ⋙ Mon_.forget D
+ { pt := F ⋙ Mon_.forget D
one := { app := fun X => (F.obj X).one }
mul := { app := fun X => (F.obj X).mul }
one_mul' := by
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -35,7 +35,6 @@ open CategoryTheory MonoidalCategory
namespace CategoryTheory.Monoidal
variable (C : Type u₁) [Category.{v₁} C]
-
variable (D : Type u₂) [Category.{v₂} D] [MonoidalCategory.{v₂} D]
namespace MonFunctorCategoryEquivalence
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -42,7 +42,7 @@ namespace MonFunctorCategoryEquivalence
variable {C D}
--- porting note: the `obj` field of `functor : Mon_ (C ⥤ D) ⥤ C ⥤ Mon_ D` defined below
+-- Porting note: the `obj` field of `functor : Mon_ (C ⥤ D) ⥤ C ⥤ Mon_ D` defined below
-- had to be defined separately as `Functor.obj` in order to speed up the compilation
/-- A monoid object in a functor category induces a functor to the category of monoid objects. -/
@[simps]
@@ -75,7 +75,7 @@ def functor : Mon_ (C ⥤ D) ⥤ C ⥤ Mon_ D where
set_option linter.uppercaseLean3 false in
#align category_theory.monoidal.Mon_functor_category_equivalence.functor CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functor
--- porting note: the `obj` field of `inverse : (C ⥤ Mon_ D) ⥤ Mon_ (C ⥤ D)` defined below
+-- Porting note: the `obj` field of `inverse : (C ⥤ Mon_ D) ⥤ Mon_ (C ⥤ D)` defined below
-- had to be defined separately as `Inverse.obj` in order to speed up the compilation
/-- A functor to the category of monoid objects can be translated as a monoid object
in the functor category. -/
@@ -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.internal.functor_category
-! leanprover-community/mathlib commit f153a85a8dc0a96ce9133fed69e34df72f7f191f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Monoidal.CommMon_
import Mathlib.CategoryTheory.Monoidal.FunctorCategory
+#align_import category_theory.monoidal.internal.functor_category from "leanprover-community/mathlib"@"f153a85a8dc0a96ce9133fed69e34df72f7f191f"
+
/-!
# `Mon_ (C ⥤ D) ≌ C ⥤ Mon_ D`
@@ -49,7 +49,7 @@ variable {C D}
-- had to be defined separately as `Functor.obj` in order to speed up the compilation
/-- A monoid object in a functor category induces a functor to the category of monoid objects. -/
@[simps]
-def Functor.obj (A : Mon_ (C ⥤ D)) : C ⥤ Mon_ D where
+def Functor.obj (A : Mon_ (C ⥤ D)) : C ⥤ Mon_ D where
obj X :=
{ X := A.X.obj X
one := A.one.app X
The unported dependencies are