category_theory.monoidal.functor_category

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

73dd4b54

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

575b4ea3

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -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.Functor.Category
 import CategoryTheory.Functor.Const

575b4ea3

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) 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.Functor.Category
-import Mathbin.CategoryTheory.Functor.Const
+import CategoryTheory.Monoidal.Braided
+import CategoryTheory.Functor.Category
+import CategoryTheory.Functor.Const
 
 #align_import category_theory.monoidal.functor_category from "leanprover-community/mathlib"@"575b4ea3738b017e30fb205cb9b4a8742e5e82b6"

575b4ea3

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) 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.functor_category
-! leanprover-community/mathlib commit 575b4ea3738b017e30fb205cb9b4a8742e5e82b6
-! 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.Functor.Category
 import Mathbin.CategoryTheory.Functor.Const
 
+#align_import category_theory.monoidal.functor_category from "leanprover-community/mathlib"@"575b4ea3738b017e30fb205cb9b4a8742e5e82b6"
+
 /-!
 # Monoidal structure on `C ⥤ D` when `D` is monoidal.

575b4ea3

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -104,85 +104,107 @@ instance functorCategoryMonoidal : MonoidalCategory (C ⥤ D)
 #align category_theory.monoidal.functor_category_monoidal CategoryTheory.Monoidal.functorCategoryMonoidal
 -/
 
+#print CategoryTheory.Monoidal.tensorUnit_obj /-
 @[simp]
 theorem tensorUnit_obj {X} : (𝟙_ (C ⥤ D)).obj X = 𝟙_ D :=
   rfl
 #align category_theory.monoidal.tensor_unit_obj CategoryTheory.Monoidal.tensorUnit_obj
+-/
 
+#print CategoryTheory.Monoidal.tensorUnit_map /-
 @[simp]
 theorem tensorUnit_map {X Y} {f : X ⟶ Y} : (𝟙_ (C ⥤ D)).map f = 𝟙 (𝟙_ D) :=
   rfl
 #align category_theory.monoidal.tensor_unit_map CategoryTheory.Monoidal.tensorUnit_map
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Monoidal.tensorObj_obj /-
 @[simp]
 theorem tensorObj_obj {F G : C ⥤ D} {X} : (F ⊗ G).obj X = F.obj X ⊗ G.obj X :=
   rfl
 #align category_theory.monoidal.tensor_obj_obj CategoryTheory.Monoidal.tensorObj_obj
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Monoidal.tensorObj_map /-
 @[simp]
 theorem tensorObj_map {F G : C ⥤ D} {X Y} {f : X ⟶ Y} : (F ⊗ G).map f = F.map f ⊗ G.map f :=
   rfl
 #align category_theory.monoidal.tensor_obj_map CategoryTheory.Monoidal.tensorObj_map
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Monoidal.tensorHom_app /-
 @[simp]
 theorem tensorHom_app {F G F' G' : C ⥤ D} {α : F ⟶ G} {β : F' ⟶ G'} {X} :
     (α ⊗ β).app X = α.app X ⊗ β.app X :=
   rfl
 #align category_theory.monoidal.tensor_hom_app CategoryTheory.Monoidal.tensorHom_app
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Monoidal.leftUnitor_hom_app /-
 @[simp]
 theorem leftUnitor_hom_app {F : C ⥤ D} {X} :
     ((λ_ F).Hom : 𝟙_ _ ⊗ F ⟶ F).app X = (λ_ (F.obj X)).Hom :=
   rfl
 #align category_theory.monoidal.left_unitor_hom_app CategoryTheory.Monoidal.leftUnitor_hom_app
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Monoidal.leftUnitor_inv_app /-
 @[simp]
 theorem leftUnitor_inv_app {F : C ⥤ D} {X} :
     ((λ_ F).inv : F ⟶ 𝟙_ _ ⊗ F).app X = (λ_ (F.obj X)).inv :=
   rfl
 #align category_theory.monoidal.left_unitor_inv_app CategoryTheory.Monoidal.leftUnitor_inv_app
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Monoidal.rightUnitor_hom_app /-
 @[simp]
 theorem rightUnitor_hom_app {F : C ⥤ D} {X} :
     ((ρ_ F).Hom : F ⊗ 𝟙_ _ ⟶ F).app X = (ρ_ (F.obj X)).Hom :=
   rfl
 #align category_theory.monoidal.right_unitor_hom_app CategoryTheory.Monoidal.rightUnitor_hom_app
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Monoidal.rightUnitor_inv_app /-
 @[simp]
 theorem rightUnitor_inv_app {F : C ⥤ D} {X} :
     ((ρ_ F).inv : F ⟶ F ⊗ 𝟙_ _).app X = (ρ_ (F.obj X)).inv :=
   rfl
 #align category_theory.monoidal.right_unitor_inv_app CategoryTheory.Monoidal.rightUnitor_inv_app
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Monoidal.associator_hom_app /-
 @[simp]
 theorem associator_hom_app {F G H : C ⥤ D} {X} :
     ((α_ F G H).Hom : (F ⊗ G) ⊗ H ⟶ F ⊗ G ⊗ H).app X = (α_ (F.obj X) (G.obj X) (H.obj X)).Hom :=
   rfl
 #align category_theory.monoidal.associator_hom_app CategoryTheory.Monoidal.associator_hom_app
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Monoidal.associator_inv_app /-
 @[simp]
 theorem associator_inv_app {F G H : C ⥤ D} {X} :
     ((α_ F G H).inv : F ⊗ G ⊗ H ⟶ (F ⊗ G) ⊗ H).app X = (α_ (F.obj X) (G.obj X) (H.obj X)).inv :=
   rfl
 #align category_theory.monoidal.associator_inv_app CategoryTheory.Monoidal.associator_inv_app
+-/
 
 section BraidedCategory

575b4ea3

bump to nightly-2023-06-06-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

90f9e14f

Diff

@@ -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.functor_category
-! leanprover-community/mathlib commit 73dd4b5411ec8fafb18a9d77c9c826907730af80
+! leanprover-community/mathlib commit 575b4ea3738b017e30fb205cb9b4a8742e5e82b6
 ! 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.Functor.Const
 /-!
 # Monoidal structure on `C ⥤ D` when `D` is monoidal.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 When `C` is any category, and `D` is a monoidal category,
 there is a natural "pointwise" monoidal structure on `C ⥤ D`.

73dd4b54

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -40,6 +40,7 @@ variable (F G F' G' : C ⥤ D)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Monoidal.FunctorCategory.tensorObj /-
 /-- (An auxiliary definition for `functor_category_monoidal`.)
 Tensor product of functors `C ⥤ D`, when `D` is monoidal.
  -/
@@ -50,12 +51,14 @@ def tensorObj : C ⥤ D where
   map_id' X := by rw [F.map_id, G.map_id, tensor_id]
   map_comp' X Y Z f g := by rw [F.map_comp, G.map_comp, tensor_comp]
 #align category_theory.monoidal.functor_category.tensor_obj CategoryTheory.Monoidal.FunctorCategory.tensorObj
+-/
 
 variable {F G F' G'}
 
 variable (α : F ⟶ G) (β : F' ⟶ G')
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Monoidal.FunctorCategory.tensorHom /-
 /-- (An auxiliary definition for `functor_category_monoidal`.)
 Tensor product of natural transformations into `D`, when `D` is monoidal.
 -/
@@ -65,11 +68,13 @@ def tensorHom : tensorObj F F' ⟶ tensorObj G G'
   app X := α.app X ⊗ β.app X
   naturality' X Y f := by dsimp; rw [← tensor_comp, α.naturality, β.naturality, tensor_comp]
 #align category_theory.monoidal.functor_category.tensor_hom CategoryTheory.Monoidal.FunctorCategory.tensorHom
+-/
 
 end FunctorCategory
 
 open CategoryTheory.Monoidal.FunctorCategory
 
+#print CategoryTheory.Monoidal.functorCategoryMonoidal /-
 /-- When `C` is any category, and `D` is a monoidal category,
 the functor category `C ⥤ D` has a natural pointwise monoidal structure,
 where `(F ⊗ G).obj X = F.obj X ⊗ G.obj X`.
@@ -94,6 +99,7 @@ instance functorCategoryMonoidal : MonoidalCategory (C ⥤ D)
   triangle' F G := by ext X; dsimp; rw [triangle]
   pentagon' F G H K := by ext X; dsimp; rw [pentagon]
 #align category_theory.monoidal.functor_category_monoidal CategoryTheory.Monoidal.functorCategoryMonoidal
+-/
 
 @[simp]
 theorem tensorUnit_obj {X} : (𝟙_ (C ⥤ D)).obj X = 𝟙_ D :=
@@ -181,6 +187,7 @@ open CategoryTheory.BraidedCategory
 
 variable [BraidedCategory.{v₂} D]
 
+#print CategoryTheory.Monoidal.functorCategoryBraided /-
 /-- When `C` is any category, and `D` is a braided monoidal category,
 the natural pointwise monoidal structure on the functor category `C ⥤ D`
 is also braided.
@@ -191,6 +198,7 @@ instance functorCategoryBraided : BraidedCategory (C ⥤ D)
   hexagon_forward' F G H := by ext X; apply hexagon_forward
   hexagon_reverse' F G H := by ext X; apply hexagon_reverse
 #align category_theory.monoidal.functor_category_braided CategoryTheory.Monoidal.functorCategoryBraided
+-/
 
 example : BraidedCategory (C ⥤ D) :=
   CategoryTheory.Monoidal.functorCategoryBraided
@@ -203,6 +211,7 @@ open CategoryTheory.SymmetricCategory
 
 variable [SymmetricCategory.{v₂} D]
 
+#print CategoryTheory.Monoidal.functorCategorySymmetric /-
 /-- When `C` is any category, and `D` is a symmetric monoidal category,
 the natural pointwise monoidal structure on the functor category `C ⥤ D`
 is also symmetric.
@@ -210,6 +219,7 @@ is also symmetric.
 instance functorCategorySymmetric : SymmetricCategory (C ⥤ D)
     where symmetry' F G := by ext X; apply symmetry
 #align category_theory.monoidal.functor_category_symmetric CategoryTheory.Monoidal.functorCategorySymmetric
+-/
 
 end SymmetricCategory

73dd4b54

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -63,9 +63,7 @@ Tensor product of natural transformations into `D`, when `D` is monoidal.
 def tensorHom : tensorObj F F' ⟶ tensorObj G G'
     where
   app X := α.app X ⊗ β.app X
-  naturality' X Y f := by
-    dsimp
-    rw [← tensor_comp, α.naturality, β.naturality, tensor_comp]
+  naturality' X Y f := by dsimp; rw [← tensor_comp, α.naturality, β.naturality, tensor_comp]
 #align category_theory.monoidal.functor_category.tensor_hom CategoryTheory.Monoidal.FunctorCategory.tensorHom
 
 end FunctorCategory
@@ -80,43 +78,19 @@ instance functorCategoryMonoidal : MonoidalCategory (C ⥤ D)
     where
   tensorObj F G := tensorObj F G
   tensorHom F G F' G' α β := tensorHom α β
-  tensor_id' F G := by
-    ext
-    dsimp
-    rw [tensor_id]
-  tensor_comp' F G H F' G' H' α β γ δ := by
-    ext
-    dsimp
-    rw [tensor_comp]
+  tensor_id' F G := by ext; dsimp; rw [tensor_id]
+  tensor_comp' F G H F' G' H' α β γ δ := by ext; dsimp; rw [tensor_comp]
   tensorUnit := (CategoryTheory.Functor.const C).obj (𝟙_ D)
   leftUnitor F :=
-    NatIso.ofComponents (fun X => λ_ (F.obj X)) fun X Y f =>
-      by
-      dsimp
-      rw [left_unitor_naturality]
+    NatIso.ofComponents (fun X => λ_ (F.obj X)) fun X Y f => by dsimp; rw [left_unitor_naturality]
   rightUnitor F :=
-    NatIso.ofComponents (fun X => ρ_ (F.obj X)) fun X Y f =>
-      by
-      dsimp
-      rw [right_unitor_naturality]
+    NatIso.ofComponents (fun X => ρ_ (F.obj X)) fun X Y f => by dsimp; rw [right_unitor_naturality]
   associator F G H :=
-    NatIso.ofComponents (fun X => α_ (F.obj X) (G.obj X) (H.obj X)) fun X Y f =>
-      by
-      dsimp
+    NatIso.ofComponents (fun X => α_ (F.obj X) (G.obj X) (H.obj X)) fun X Y f => by dsimp;
       rw [associator_naturality]
-  leftUnitor_naturality' F G α := by
-    ext X
-    dsimp
-    rw [left_unitor_naturality]
-  rightUnitor_naturality' F G α := by
-    ext X
-    dsimp
-    rw [right_unitor_naturality]
-  associator_naturality' F G H F' G' H' α β γ :=
-    by
-    ext X
-    dsimp
-    rw [associator_naturality]
+  leftUnitor_naturality' F G α := by ext X; dsimp; rw [left_unitor_naturality]
+  rightUnitor_naturality' F G α := by ext X; dsimp; rw [right_unitor_naturality]
+  associator_naturality' F G H F' G' H' α β γ := by ext X; dsimp; rw [associator_naturality]
   triangle' F G := by ext X; dsimp; rw [triangle]
   pentagon' F G H K := by ext X; dsimp; rw [pentagon]
 #align category_theory.monoidal.functor_category_monoidal CategoryTheory.Monoidal.functorCategoryMonoidal
@@ -214,12 +188,8 @@ is also braided.
 instance functorCategoryBraided : BraidedCategory (C ⥤ D)
     where
   braiding F G := NatIso.ofComponents (fun X => β_ _ _) (by tidy)
-  hexagon_forward' F G H := by
-    ext X
-    apply hexagon_forward
-  hexagon_reverse' F G H := by
-    ext X
-    apply hexagon_reverse
+  hexagon_forward' F G H := by ext X; apply hexagon_forward
+  hexagon_reverse' F G H := by ext X; apply hexagon_reverse
 #align category_theory.monoidal.functor_category_braided CategoryTheory.Monoidal.functorCategoryBraided
 
 example : BraidedCategory (C ⥤ D) :=
@@ -238,9 +208,7 @@ the natural pointwise monoidal structure on the functor category `C ⥤ D`
 is also symmetric.
 -/
 instance functorCategorySymmetric : SymmetricCategory (C ⥤ D)
-    where symmetry' F G := by
-    ext X
-    apply symmetry
+    where symmetry' F G := by ext X; apply symmetry
 #align category_theory.monoidal.functor_category_symmetric CategoryTheory.Monoidal.functorCategorySymmetric
 
 end SymmetricCategory

73dd4b54

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

73dd4b54

chore(*): remove empty lines between variable statements (#11418)

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)

75c86f04

Diff

@@ -28,7 +28,6 @@ open CategoryTheory.MonoidalCategory
 namespace CategoryTheory.Monoidal
 
 variable {C : Type u₁} [Category.{v₁} C]
-
 variable {D : Type u₂} [Category.{v₂} D] [MonoidalCategory.{v₂} D]
 
 namespace FunctorCategory
@@ -45,7 +44,6 @@ def tensorObj : C ⥤ D where
 #align category_theory.monoidal.functor_category.tensor_obj CategoryTheory.Monoidal.FunctorCategory.tensorObj
 
 variable {F G F' G'}
-
 variable (α : F ⟶ G) (β : F' ⟶ G')
 
 /-- (An auxiliary definition for `functorCategoryMonoidal`.)

73dd4b54

feat: the opposite of a braided category is braided (#10095)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

6dc895db

Diff

@@ -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.Functor.Category
 import Mathlib.CategoryTheory.Functor.Const

73dd4b54

feat(CategoryTheory/Monoidal): replace 𝟙 X ⊗ f with X ◁ f (#10912)

We set id_tensorHom and tensorHom_id as simp lemmas. Partially extracted from #6307.

8a40b522

Diff

@@ -77,8 +77,6 @@ end FunctorCategory
 
 open CategoryTheory.Monoidal.FunctorCategory
 
-attribute [local simp] id_tensorHom tensorHom_id in
-
 /-- When `C` is any category, and `D` is a monoidal category,
 the functor category `C ⥤ D` has a natural pointwise monoidal structure,
 where `(F ⊗ G).obj X = F.obj X ⊗ G.obj X`.
@@ -165,8 +163,6 @@ theorem associator_inv_app {F G H : C ⥤ D} {X} :
   rfl
 #align category_theory.monoidal.associator_inv_app CategoryTheory.Monoidal.associator_inv_app
 
-attribute [local simp] id_tensorHom tensorHom_id in
-
 /-- When `C` is any category, and `D` is a monoidal category,
 the functor category `C ⥤ D` has a natural pointwise monoidal structure,
 where `(F ⊗ G).obj X = F.obj X ⊗ G.obj X`.

73dd4b54

feat(CategoryTheory/Monoidal): partially setting simp lemmas (#10061)

Extracted from #6307. The main reason why #6307 is so large is that many tensoring of identity morphisms that appear in mathlib should be replaced with whiskerings. This PR will leave this issue and deal with other parts. That is, we do not set id_tensorHom and tensorHom_id as simple lemmas at this moment, We can set them as simp lemmas locally to enable simple normal forms.

ec497096

Diff

@@ -77,6 +77,8 @@ end FunctorCategory
 
 open CategoryTheory.Monoidal.FunctorCategory
 
+attribute [local simp] id_tensorHom tensorHom_id in
+
 /-- When `C` is any category, and `D` is a monoidal category,
 the functor category `C ⥤ D` has a natural pointwise monoidal structure,
 where `(F ⊗ G).obj X = F.obj X ⊗ G.obj X`.
@@ -163,6 +165,8 @@ theorem associator_inv_app {F G H : C ⥤ D} {X} :
   rfl
 #align category_theory.monoidal.associator_inv_app CategoryTheory.Monoidal.associator_inv_app
 
+attribute [local simp] id_tensorHom tensorHom_id in
+
 /-- When `C` is any category, and `D` is a monoidal category,
 the functor category `C ⥤ D` has a natural pointwise monoidal structure,
 where `(F ⊗ G).obj X = F.obj X ⊗ G.obj X`.

73dd4b54

refactor: Move the data fields of MonoidalCategory into a Struct class (#7279)

This matches the approach for CategoryStruct, and allows us to use the notation within MonoidalCategory.

It also makes it easier to induce the lawful structure along a faithful functor, as again it means by the time we are providing the proof fields, the notation is already available.

This also eliminates tensorUnit vs tensorUnit', adding a custom pretty-printer to provide the unprimed version with appropriate notation.

f81eaba3

Diff

@@ -81,18 +81,15 @@ open CategoryTheory.Monoidal.FunctorCategory
 the functor category `C ⥤ D` has a natural pointwise monoidal structure,
 where `(F ⊗ G).obj X = F.obj X ⊗ G.obj X`.
 -/
-instance functorCategoryMonoidal : MonoidalCategory (C ⥤ D) where
+instance functorCategoryMonoidalStruct : MonoidalCategoryStruct (C ⥤ D) where
   tensorObj F G := tensorObj F G
   tensorHom α β := tensorHom α β
   whiskerLeft F _ _ α := FunctorCategory.whiskerLeft F α
   whiskerRight α F := FunctorCategory.whiskerRight α F
-  tensorHom_def := by intros; ext; simp [tensorHom_def]
-  tensorUnit' := (CategoryTheory.Functor.const C).obj (𝟙_ D)
+  tensorUnit := (CategoryTheory.Functor.const C).obj (𝟙_ D)
   leftUnitor F := NatIso.ofComponents fun X => λ_ (F.obj X)
   rightUnitor F := NatIso.ofComponents fun X => ρ_ (F.obj X)
   associator F G H := NatIso.ofComponents fun X => α_ (F.obj X) (G.obj X) (H.obj X)
-  pentagon F G H K := by ext X; dsimp; rw [pentagon]
-#align category_theory.monoidal.functor_category_monoidal CategoryTheory.Monoidal.functorCategoryMonoidal
 
 @[simp]
 theorem tensorUnit_obj {X} : (𝟙_ (C ⥤ D)).obj X = 𝟙_ D :=
@@ -120,6 +117,16 @@ theorem tensorHom_app {F G F' G' : C ⥤ D} {α : F ⟶ G} {β : F' ⟶ G'} {X}
   rfl
 #align category_theory.monoidal.tensor_hom_app CategoryTheory.Monoidal.tensorHom_app
 
+@[simp]
+theorem whiskerLeft_app {F F' G' : C ⥤ D} {β : F' ⟶ G'} {X} :
+    (F ◁ β).app X = F.obj X ◁ β.app X :=
+  rfl
+
+@[simp]
+theorem whiskerRight_app {F G F' : C ⥤ D} {α : F ⟶ G} {X} :
+    (α ▷ F').app X = α.app X ▷ F'.obj X :=
+  rfl
+
 @[simp]
 theorem leftUnitor_hom_app {F : C ⥤ D} {X} :
     ((λ_ F).hom : 𝟙_ _ ⊗ F ⟶ F).app X = (λ_ (F.obj X)).hom :=
@@ -156,6 +163,15 @@ theorem associator_inv_app {F G H : C ⥤ D} {X} :
   rfl
 #align category_theory.monoidal.associator_inv_app CategoryTheory.Monoidal.associator_inv_app
 
+/-- When `C` is any category, and `D` is a monoidal category,
+the functor category `C ⥤ D` has a natural pointwise monoidal structure,
+where `(F ⊗ G).obj X = F.obj X ⊗ G.obj X`.
+-/
+instance functorCategoryMonoidal : MonoidalCategory (C ⥤ D) where
+  tensorHom_def := by intros; ext; simp [tensorHom_def]
+  pentagon F G H K := by ext X; dsimp; rw [pentagon]
+#align category_theory.monoidal.functor_category_monoidal CategoryTheory.Monoidal.functorCategoryMonoidal
+
 section BraidedCategory
 
 open CategoryTheory.BraidedCategory

73dd4b54

style: fix wrapping of where (#7149)

084cfb35

Diff

@@ -187,8 +187,8 @@ variable [SymmetricCategory.{v₂} D]
 the natural pointwise monoidal structure on the functor category `C ⥤ D`
 is also symmetric.
 -/
-instance functorCategorySymmetric : SymmetricCategory (C ⥤ D)
-    where symmetry F G := by ext X; apply symmetry
+instance functorCategorySymmetric : SymmetricCategory (C ⥤ D) where
+  symmetry F G := by ext X; apply symmetry
 #align category_theory.monoidal.functor_category_symmetric CategoryTheory.Monoidal.functorCategorySymmetric
 
 end SymmetricCategory

73dd4b54

feat(CategoryTheory/Monoidal): define whiskering operators (#6420)

Extracted from #6307. Just put the whiskerings into the constructor.

763106d3

Diff

@@ -57,6 +57,22 @@ def tensorHom : tensorObj F F' ⟶ tensorObj G G' where
   naturality X Y f := by dsimp; rw [← tensor_comp, α.naturality, β.naturality, tensor_comp]
 #align category_theory.monoidal.functor_category.tensor_hom CategoryTheory.Monoidal.FunctorCategory.tensorHom
 
+/-- (An auxiliary definition for `functorCategoryMonoidal`.) -/
+@[simps]
+def whiskerLeft (F) (β : F' ⟶ G') : tensorObj F F' ⟶ tensorObj F G' where
+  app X := F.obj X ◁ β.app X
+  naturality X Y f := by
+    simp only [← id_tensorHom]
+    apply (tensorHom (𝟙 F) β).naturality
+
+/-- (An auxiliary definition for `functorCategoryMonoidal`.) -/
+@[simps]
+def whiskerRight (F') : tensorObj F F' ⟶ tensorObj G F' where
+  app X := α.app X ▷ F'.obj X
+  naturality X Y f := by
+    simp only [← tensorHom_id]
+    apply (tensorHom α (𝟙 F')).naturality
+
 end FunctorCategory
 
 open CategoryTheory.Monoidal.FunctorCategory
@@ -68,6 +84,9 @@ where `(F ⊗ G).obj X = F.obj X ⊗ G.obj X`.
 instance functorCategoryMonoidal : MonoidalCategory (C ⥤ D) where
   tensorObj F G := tensorObj F G
   tensorHom α β := tensorHom α β
+  whiskerLeft F _ _ α := FunctorCategory.whiskerLeft F α
+  whiskerRight α F := FunctorCategory.whiskerRight α F
+  tensorHom_def := by intros; ext; simp [tensorHom_def]
   tensorUnit' := (CategoryTheory.Functor.const C).obj (𝟙_ D)
   leftUnitor F := NatIso.ofComponents fun X => λ_ (F.obj X)
   rightUnitor F := NatIso.ofComponents fun X => ρ_ (F.obj X)

73dd4b54

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) 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.functor_category
-! leanprover-community/mathlib commit 73dd4b5411ec8fafb18a9d77c9c826907730af80
-! 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.Functor.Category
 import Mathlib.CategoryTheory.Functor.Const
 
+#align_import category_theory.monoidal.functor_category from "leanprover-community/mathlib"@"73dd4b5411ec8fafb18a9d77c9c826907730af80"
+
 /-!
 # Monoidal structure on `C ⥤ D` when `D` is monoidal.

73dd4b54

chore: review of automation in category theory (#4793)

Clean up of automation in the category theory library. Leaving out unnecessary proof steps, or fields done by aesop_cat, and making more use of available autoparameters.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

5b958613

Diff

@@ -71,19 +71,10 @@ where `(F ⊗ G).obj X = F.obj X ⊗ G.obj X`.
 instance functorCategoryMonoidal : MonoidalCategory (C ⥤ D) where
   tensorObj F G := tensorObj F G
   tensorHom α β := tensorHom α β
-  tensor_id F G := by ext; dsimp; rw [tensor_id]
-  tensor_comp α β γ δ := by ext; dsimp; rw [tensor_comp]
   tensorUnit' := (CategoryTheory.Functor.const C).obj (𝟙_ D)
-  leftUnitor F := NatIso.ofComponents (fun X => λ_ (F.obj X))
-    (fun f => by dsimp; rw [leftUnitor_naturality])
-  rightUnitor F := NatIso.ofComponents (fun X => ρ_ (F.obj X))
-    (fun f => by dsimp; rw [rightUnitor_naturality])
-  associator F G H := NatIso.ofComponents (fun X => α_ (F.obj X) (G.obj X) (H.obj X))
-    (fun f => by dsimp;rw [associator_naturality])
-  leftUnitor_naturality α := by ext X; dsimp; rw [leftUnitor_naturality]
-  rightUnitor_naturality α := by ext X; dsimp; rw [rightUnitor_naturality]
-  associator_naturality α β γ := by ext X; dsimp; rw [associator_naturality]
-  triangle F G := by ext X; dsimp; rw [triangle]
+  leftUnitor F := NatIso.ofComponents fun X => λ_ (F.obj X)
+  rightUnitor F := NatIso.ofComponents fun X => ρ_ (F.obj X)
+  associator F G H := NatIso.ofComponents fun X => α_ (F.obj X) (G.obj X) (H.obj X)
   pentagon F G H K := by ext X; dsimp; rw [pentagon]
 #align category_theory.monoidal.functor_category_monoidal CategoryTheory.Monoidal.functorCategoryMonoidal
 
@@ -160,7 +151,7 @@ the natural pointwise monoidal structure on the functor category `C ⥤ D`
 is also braided.
 -/
 instance functorCategoryBraided : BraidedCategory (C ⥤ D) where
-  braiding F G := NatIso.ofComponents (fun X => β_ _ _) (by aesop_cat)
+  braiding F G := NatIso.ofComponents fun X => β_ _ _
   hexagon_forward F G H := by ext X; apply hexagon_forward
   hexagon_reverse F G H := by ext X; apply hexagon_reverse
 #align category_theory.monoidal.functor_category_braided CategoryTheory.Monoidal.functorCategoryBraided

73dd4b54

feat: port CategoryTheory.Monoidal.FunctorCategory (#4646)

9e1c6b39

`category_theory.monoidal.functor_category` ⟷ `Mathlib.CategoryTheory.Monoidal.FunctorCategory`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 77

category_theory.monoidal.functor_category ⟷ Mathlib.CategoryTheory.Monoidal.FunctorCategory

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 77

`category_theory.monoidal.functor_category` ⟷ `Mathlib.CategoryTheory.Monoidal.FunctorCategory`