category_theory.monoidal.center | Mathlib porting status

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

14b69e9f

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

44e2ae8c

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -379,7 +379,7 @@ def forget : MonoidalFunctor (Center C) C
 #align category_theory.center.forget CategoryTheory.Center.forget
 -/
 
-instance : ReflectsIsomorphisms (forget C).toFunctor
+instance : CategoryTheory.Functor.ReflectsIsomorphisms (forget C).toFunctor
     where reflects A B f i := by dsimp at i; skip; change is_iso (iso_mk f).Hom; infer_instance
 
 end

44e2ae8c

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import CategoryTheory.Monoidal.Braided
-import CategoryTheory.Functor.ReflectsIsomorphisms
-import CategoryTheory.Monoidal.Coherence
+import CategoryTheory.Monoidal.Braided.Basic
+import CategoryTheory.Functor.ReflectsIso
+import Tactic.CategoryTheory.Coherence
 
 #align_import category_theory.monoidal.center from "leanprover-community/mathlib"@"44e2ae8cffc713925494e4975ee31ec1d06929b3"

44e2ae8c

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -380,7 +380,7 @@ def forget : MonoidalFunctor (Center C) C
 -/
 
 instance : ReflectsIsomorphisms (forget C).toFunctor
-    where reflects A B f i := by dsimp at i ; skip; change is_iso (iso_mk f).Hom; infer_instance
+    where reflects A B f i := by dsimp at i; skip; change is_iso (iso_mk f).Hom; infer_instance
 
 end

44e2ae8c

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) 2021 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.ReflectsIsomorphisms
-import Mathbin.CategoryTheory.Monoidal.Coherence
+import CategoryTheory.Monoidal.Braided
+import CategoryTheory.Functor.ReflectsIsomorphisms
+import CategoryTheory.Monoidal.Coherence
 
 #align_import category_theory.monoidal.center from "leanprover-community/mathlib"@"44e2ae8cffc713925494e4975ee31ec1d06929b3"

44e2ae8c

bump to nightly-2023-09-06-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

f3106448

Diff

@@ -76,13 +76,9 @@ structure HalfBraiding (X : C) where
 #align category_theory.half_braiding CategoryTheory.HalfBraiding
 -/
 
-restate_axiom half_braiding.monoidal'
-
 attribute [reassoc, simp] half_braiding.monoidal
 
 -- the reassoc lemma is redundant as a simp lemma
-restate_axiom half_braiding.naturality'
-
 attribute [simp, reassoc] half_braiding.naturality
 
 variable (C)
@@ -112,8 +108,6 @@ structure Hom (X Y : Center C) where
 #align category_theory.center.hom CategoryTheory.Center.Hom
 -/
 
-restate_axiom hom.comm'
-
 attribute [simp, reassoc] hom.comm
 
 instance : Category (Center C) where

44e2ae8c

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) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.monoidal.center
-! leanprover-community/mathlib commit 44e2ae8cffc713925494e4975ee31ec1d06929b3
-! 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.ReflectsIsomorphisms
 import Mathbin.CategoryTheory.Monoidal.Coherence
 
+#align_import category_theory.monoidal.center from "leanprover-community/mathlib"@"44e2ae8cffc713925494e4975ee31ec1d06929b3"
+
 /-!
 # Half braidings and the Drinfeld center of a monoidal category

44e2ae8c

bump to nightly-2023-06-14-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/8efcf8022aac8e01df8d302dcebdbc25d6a886c8

f4ed04bb

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.center
-! leanprover-community/mathlib commit 14b69e9f3c16630440a2cbd46f1ddad0d561dee7
+! leanprover-community/mathlib commit 44e2ae8cffc713925494e4975ee31ec1d06929b3
 ! 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.Monoidal.Coherence
 /-!
 # Half braidings and the Drinfeld center of a monoidal category
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define `center C` to be pairs `⟨X, b⟩`, where `X : C` and `b` is a half-braiding on `X`.
 
 We show that `center C` is braided monoidal,

14b69e9f

bump to nightly-2023-06-12-17

mathlib commit https://github.com/leanprover-community/mathlib/commit/ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f

ae53e046

Diff

@@ -47,6 +47,7 @@ namespace CategoryTheory
 
 variable {C : Type u₁} [Category.{v₁} C] [MonoidalCategory C]
 
+#print CategoryTheory.HalfBraiding /-
 /- ./././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 -/
@@ -73,6 +74,7 @@ structure HalfBraiding (X : C) where
   naturality' : ∀ {U U'} (f : U ⟶ U'), (𝟙 X ⊗ f) ≫ (β U').Hom = (β U).Hom ≫ (f ⊗ 𝟙 X) := by
     obviously
 #align category_theory.half_braiding CategoryTheory.HalfBraiding
+-/
 
 restate_axiom half_braiding.monoidal'
 
@@ -85,6 +87,7 @@ attribute [simp, reassoc] half_braiding.naturality
 
 variable (C)
 
+#print CategoryTheory.Center /-
 /-- The Drinfeld center of a monoidal category `C` has as objects pairs `⟨X, b⟩`, where `X : C`
 and `b` is a half-braiding on `X`.
 -/
@@ -92,11 +95,13 @@ and `b` is a half-braiding on `X`.
 def Center :=
   Σ X : C, HalfBraiding X
 #align category_theory.center CategoryTheory.Center
+-/
 
 namespace Center
 
 variable {C}
 
+#print CategoryTheory.Center.Hom /-
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- A morphism in the Drinfeld center of `C`. -/
@@ -105,6 +110,7 @@ structure Hom (X Y : Center C) where
   f : X.1 ⟶ Y.1
   comm' : ∀ U, (f ⊗ 𝟙 U) ≫ (Y.2.β U).Hom = (X.2.β U).Hom ≫ (𝟙 U ⊗ f) := by obviously
 #align category_theory.center.hom CategoryTheory.Center.Hom
+-/
 
 restate_axiom hom.comm'
 
@@ -115,22 +121,29 @@ instance : Category (Center C) where
   id X := { f := 𝟙 X.1 }
   comp X Y Z f g := { f := f.f ≫ g.f }
 
+#print CategoryTheory.Center.id_f /-
 @[simp]
 theorem id_f (X : Center C) : Hom.f (𝟙 X) = 𝟙 X.1 :=
   rfl
 #align category_theory.center.id_f CategoryTheory.Center.id_f
+-/
 
+#print CategoryTheory.Center.comp_f /-
 @[simp]
 theorem comp_f {X Y Z : Center C} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g).f = f.f ≫ g.f :=
   rfl
 #align category_theory.center.comp_f CategoryTheory.Center.comp_f
+-/
 
+#print CategoryTheory.Center.ext /-
 @[ext]
 theorem ext {X Y : Center C} (f g : X ⟶ Y) (w : f.f = g.f) : f = g := by cases f; cases g; congr;
   exact w
 #align category_theory.center.ext CategoryTheory.Center.ext
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Center.isoMk /-
 /-- Construct an isomorphism in the Drinfeld center from
 a morphism whose underlying morphism is an isomorphism.
 -/
@@ -141,16 +154,20 @@ def isoMk {X Y : Center C} (f : X ⟶ Y) [IsIso f.f] : X ≅ Y
   inv :=
     ⟨inv f.f, fun U => by simp [← cancel_epi (f.f ⊗ 𝟙 U), ← comp_tensor_id_assoc, ← id_tensor_comp]⟩
 #align category_theory.center.iso_mk CategoryTheory.Center.isoMk
+-/
 
+#print CategoryTheory.Center.isIso_of_f_isIso /-
 instance isIso_of_f_isIso {X Y : Center C} (f : X ⟶ Y) [IsIso f.f] : IsIso f :=
   by
   change is_iso (iso_mk f).Hom
   infer_instance
 #align category_theory.center.is_iso_of_f_is_iso CategoryTheory.Center.isIso_of_f_isIso
+-/
 
 /- ./././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.Center.tensorObj /-
 /-- Auxiliary definition for the `monoidal_category` instance on `center C`. -/
 @[simps]
 def tensorObj (X Y : Center C) : Center C :=
@@ -184,8 +201,10 @@ def tensorObj (X Y : Center C) : Center C :=
           id_tensor_comp_assoc, associator_inv_naturality_assoc, ← comp_tensor_id_assoc,
           half_braiding.naturality, comp_tensor_id_assoc, associator_naturality, ← tensor_id] }⟩
 #align category_theory.center.tensor_obj CategoryTheory.Center.tensorObj
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Center.tensorHom /-
 /-- Auxiliary definition for the `monoidal_category` instance on `center C`. -/
 @[simps]
 def tensorHom {X₁ Y₁ X₂ Y₂ : Center C} (f : X₁ ⟶ Y₁) (g : X₂ ⟶ Y₂) :
@@ -201,7 +220,9 @@ def tensorHom {X₁ Y₁ X₂ Y₂ : Center C} (f : X₁ ⟶ Y₁) (g : X₂ ⟶
       comp_tensor_id_assoc, f.comm, comp_tensor_id_assoc, id_tensor_associator_naturality,
       associator_naturality_assoc, ← id_tensor_comp, tensor_id_comp_id_tensor]
 #align category_theory.center.tensor_hom CategoryTheory.Center.tensorHom
+-/
 
+#print CategoryTheory.Center.tensorUnit /-
 /-- Auxiliary definition for the `monoidal_category` instance on `center C`. -/
 @[simps]
 def tensorUnit : Center C :=
@@ -212,7 +233,9 @@ def tensorUnit : Center C :=
         dsimp
         rw [left_unitor_naturality_assoc, right_unitor_inv_naturality, category.assoc] }⟩
 #align category_theory.center.tensor_unit CategoryTheory.Center.tensorUnit
+-/
 
+#print CategoryTheory.Center.associator /-
 /-- Auxiliary definition for the `monoidal_category` instance on `center C`. -/
 def associator (X Y Z : Center C) : tensorObj (tensorObj X Y) Z ≅ tensorObj X (tensorObj Y Z) :=
   isoMk
@@ -221,7 +244,9 @@ def associator (X Y Z : Center C) : tensorObj (tensorObj X Y) Z ≅ tensorObj X
       simp only [comp_tensor_id, id_tensor_comp, ← tensor_id, associator_conjugation]
       coherence⟩
 #align category_theory.center.associator CategoryTheory.Center.associator
+-/
 
+#print CategoryTheory.Center.leftUnitor /-
 /-- Auxiliary definition for the `monoidal_category` instance on `center C`. -/
 def leftUnitor (X : Center C) : tensorObj tensorUnit X ≅ X :=
   isoMk
@@ -231,7 +256,9 @@ def leftUnitor (X : Center C) : tensorObj tensorUnit X ≅ X :=
         tensor_id_comp_id_tensor, triangle_assoc_comp_right_inv]
       rw [← left_unitor_tensor, left_unitor_naturality, left_unitor_tensor'_assoc]⟩
 #align category_theory.center.left_unitor CategoryTheory.Center.leftUnitor
+-/
 
+#print CategoryTheory.Center.rightUnitor /-
 /-- Auxiliary definition for the `monoidal_category` instance on `center C`. -/
 def rightUnitor (X : Center C) : tensorObj X tensorUnit ≅ X :=
   isoMk
@@ -242,6 +269,7 @@ def rightUnitor (X : Center C) : tensorObj X tensorUnit ≅ X :=
         ← right_unitor_inv_naturality_assoc]
       simp⟩
 #align category_theory.center.right_unitor CategoryTheory.Center.rightUnitor
+-/
 
 section
 
@@ -260,14 +288,17 @@ instance : MonoidalCategory (Center C)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Center.tensor_fst /-
 @[simp]
 theorem tensor_fst (X Y : Center C) : (X ⊗ Y).1 = X.1 ⊗ Y.1 :=
   rfl
 #align category_theory.center.tensor_fst CategoryTheory.Center.tensor_fst
+-/
 
 /- ./././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.Center.tensor_β /-
 @[simp]
 theorem tensor_β (X Y : Center C) (U : C) :
     (X ⊗ Y).2.β U =
@@ -275,48 +306,65 @@ theorem tensor_β (X Y : Center C) (U : C) :
         (Iso.refl X.1 ⊗ Y.2.β U) ≪≫ (α_ _ _ _).symm ≪≫ (X.2.β U ⊗ Iso.refl Y.1) ≪≫ α_ _ _ _ :=
   rfl
 #align category_theory.center.tensor_β CategoryTheory.Center.tensor_β
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Center.tensor_f /-
 @[simp]
 theorem tensor_f {X₁ Y₁ X₂ Y₂ : Center C} (f : X₁ ⟶ Y₁) (g : X₂ ⟶ Y₂) : (f ⊗ g).f = f.f ⊗ g.f :=
   rfl
 #align category_theory.center.tensor_f CategoryTheory.Center.tensor_f
+-/
 
+#print CategoryTheory.Center.tensorUnit_β /-
 @[simp]
 theorem tensorUnit_β (U : C) : (𝟙_ (Center C)).2.β U = λ_ U ≪≫ (ρ_ U).symm :=
   rfl
 #align category_theory.center.tensor_unit_β CategoryTheory.Center.tensorUnit_β
+-/
 
+#print CategoryTheory.Center.associator_hom_f /-
 @[simp]
 theorem associator_hom_f (X Y Z : Center C) : Hom.f (α_ X Y Z).Hom = (α_ X.1 Y.1 Z.1).Hom :=
   rfl
 #align category_theory.center.associator_hom_f CategoryTheory.Center.associator_hom_f
+-/
 
+#print CategoryTheory.Center.associator_inv_f /-
 @[simp]
 theorem associator_inv_f (X Y Z : Center C) : Hom.f (α_ X Y Z).inv = (α_ X.1 Y.1 Z.1).inv := by ext;
   rw [← associator_hom_f, ← comp_f, iso.hom_inv_id]; rfl
 #align category_theory.center.associator_inv_f CategoryTheory.Center.associator_inv_f
+-/
 
+#print CategoryTheory.Center.leftUnitor_hom_f /-
 @[simp]
 theorem leftUnitor_hom_f (X : Center C) : Hom.f (λ_ X).Hom = (λ_ X.1).Hom :=
   rfl
 #align category_theory.center.left_unitor_hom_f CategoryTheory.Center.leftUnitor_hom_f
+-/
 
+#print CategoryTheory.Center.leftUnitor_inv_f /-
 @[simp]
 theorem leftUnitor_inv_f (X : Center C) : Hom.f (λ_ X).inv = (λ_ X.1).inv := by ext;
   rw [← left_unitor_hom_f, ← comp_f, iso.hom_inv_id]; rfl
 #align category_theory.center.left_unitor_inv_f CategoryTheory.Center.leftUnitor_inv_f
+-/
 
+#print CategoryTheory.Center.rightUnitor_hom_f /-
 @[simp]
 theorem rightUnitor_hom_f (X : Center C) : Hom.f (ρ_ X).Hom = (ρ_ X.1).Hom :=
   rfl
 #align category_theory.center.right_unitor_hom_f CategoryTheory.Center.rightUnitor_hom_f
+-/
 
+#print CategoryTheory.Center.rightUnitor_inv_f /-
 @[simp]
 theorem rightUnitor_inv_f (X : Center C) : Hom.f (ρ_ X).inv = (ρ_ X.1).inv := by ext;
   rw [← right_unitor_hom_f, ← comp_f, iso.hom_inv_id]; rfl
 #align category_theory.center.right_unitor_inv_f CategoryTheory.Center.rightUnitor_inv_f
+-/
 
 end
 
@@ -325,6 +373,7 @@ section
 variable (C)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Center.forget /-
 /-- The forgetful monoidal functor from the Drinfeld center to the original category. -/
 @[simps]
 def forget : MonoidalFunctor (Center C) C
@@ -334,6 +383,7 @@ def forget : MonoidalFunctor (Center C) C
   ε := 𝟙 (𝟙_ C)
   μ X Y := 𝟙 (X.1 ⊗ Y.1)
 #align category_theory.center.forget CategoryTheory.Center.forget
+-/
 
 instance : ReflectsIsomorphisms (forget C).toFunctor
     where reflects A B f i := by dsimp at i ; skip; change is_iso (iso_mk f).Hom; infer_instance
@@ -342,6 +392,7 @@ end
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.Center.braiding /-
 /-- Auxiliary definition for the `braided_category` instance on `center C`. -/
 @[simps]
 def braiding (X Y : Center C) : X ⊗ Y ≅ Y ⊗ X :=
@@ -353,7 +404,9 @@ def braiding (X Y : Center C) : X ⊗ Y ≅ Y ⊗ X :=
         half_braiding.naturality_assoc, half_braiding.monoidal]
       simp⟩
 #align category_theory.center.braiding CategoryTheory.Center.braiding
+-/
 
+#print CategoryTheory.Center.braidedCategoryCenter /-
 instance braidedCategoryCenter : BraidedCategory (Center C)
     where
   braiding := braiding
@@ -363,6 +416,7 @@ instance braidedCategoryCenter : BraidedCategory (Center C)
     rw [← tensor_id_comp_id_tensor, category.assoc, half_braiding.naturality, f.comm_assoc,
       id_tensor_comp_tensor_id]
 #align category_theory.center.braided_category_center CategoryTheory.Center.braidedCategoryCenter
+-/
 
 -- `obviously` handles the hexagon axioms
 section
@@ -371,6 +425,7 @@ variable [BraidedCategory C]
 
 open BraidedCategory
 
+#print CategoryTheory.Center.ofBraidedObj /-
 /-- Auxiliary construction for `of_braided`. -/
 @[simps]
 def ofBraidedObj (X : C) : Center C :=
@@ -382,9 +437,11 @@ def ofBraidedObj (X : C) : Center C :=
           category.assoc]
         exact hexagon_forward X U U' }⟩
 #align category_theory.center.of_braided_obj CategoryTheory.Center.ofBraidedObj
+-/
 
 variable (C)
 
+#print CategoryTheory.Center.ofBraided /-
 /-- The functor lifting a braided category to its center, using the braiding as the half-braiding.
 -/
 @[simps]
@@ -408,6 +465,7 @@ def ofBraided : MonoidalFunctor C (Center C)
           category.assoc, ← category.assoc, ← iso.comp_inv_eq, category.assoc, hexagon_reverse,
           category.assoc] }
 #align category_theory.center.of_braided CategoryTheory.Center.ofBraided
+-/
 
 end

14b69e9f

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -90,7 +90,7 @@ and `b` is a half-braiding on `X`.
 -/
 @[nolint has_nonempty_instance]
 def Center :=
-  ΣX : C, HalfBraiding X
+  Σ X : C, HalfBraiding X
 #align category_theory.center CategoryTheory.Center
 
 namespace Center
@@ -126,7 +126,7 @@ theorem comp_f {X Y Z : Center C} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g).f = f.
 #align category_theory.center.comp_f CategoryTheory.Center.comp_f
 
 @[ext]
-theorem ext {X Y : Center C} (f g : X ⟶ Y) (w : f.f = g.f) : f = g := by cases f; cases g; congr ;
+theorem ext {X Y : Center C} (f g : X ⟶ Y) (w : f.f = g.f) : f = g := by cases f; cases g; congr;
   exact w
 #align category_theory.center.ext CategoryTheory.Center.ext
 
@@ -336,7 +336,7 @@ def forget : MonoidalFunctor (Center C) C
 #align category_theory.center.forget CategoryTheory.Center.forget
 
 instance : ReflectsIsomorphisms (forget C).toFunctor
-    where reflects A B f i := by dsimp at i; skip; change is_iso (iso_mk f).Hom; infer_instance
+    where reflects A B f i := by dsimp at i ; skip; change is_iso (iso_mk f).Hom; infer_instance
 
 end

14b69e9f

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -126,11 +126,7 @@ theorem comp_f {X Y Z : Center C} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g).f = f.
 #align category_theory.center.comp_f CategoryTheory.Center.comp_f
 
 @[ext]
-theorem ext {X Y : Center C} (f g : X ⟶ Y) (w : f.f = g.f) : f = g :=
-  by
-  cases f
-  cases g
-  congr
+theorem ext {X Y : Center C} (f g : X ⟶ Y) (w : f.f = g.f) : f = g := by cases f; cases g; congr ;
   exact w
 #align category_theory.center.ext CategoryTheory.Center.ext
 
@@ -298,11 +294,8 @@ theorem associator_hom_f (X Y Z : Center C) : Hom.f (α_ X Y Z).Hom = (α_ X.1 Y
 #align category_theory.center.associator_hom_f CategoryTheory.Center.associator_hom_f
 
 @[simp]
-theorem associator_inv_f (X Y Z : Center C) : Hom.f (α_ X Y Z).inv = (α_ X.1 Y.1 Z.1).inv :=
-  by
-  ext
-  rw [← associator_hom_f, ← comp_f, iso.hom_inv_id]
-  rfl
+theorem associator_inv_f (X Y Z : Center C) : Hom.f (α_ X Y Z).inv = (α_ X.1 Y.1 Z.1).inv := by ext;
+  rw [← associator_hom_f, ← comp_f, iso.hom_inv_id]; rfl
 #align category_theory.center.associator_inv_f CategoryTheory.Center.associator_inv_f
 
 @[simp]
@@ -311,11 +304,8 @@ theorem leftUnitor_hom_f (X : Center C) : Hom.f (λ_ X).Hom = (λ_ X.1).Hom :=
 #align category_theory.center.left_unitor_hom_f CategoryTheory.Center.leftUnitor_hom_f
 
 @[simp]
-theorem leftUnitor_inv_f (X : Center C) : Hom.f (λ_ X).inv = (λ_ X.1).inv :=
-  by
-  ext
-  rw [← left_unitor_hom_f, ← comp_f, iso.hom_inv_id]
-  rfl
+theorem leftUnitor_inv_f (X : Center C) : Hom.f (λ_ X).inv = (λ_ X.1).inv := by ext;
+  rw [← left_unitor_hom_f, ← comp_f, iso.hom_inv_id]; rfl
 #align category_theory.center.left_unitor_inv_f CategoryTheory.Center.leftUnitor_inv_f
 
 @[simp]
@@ -324,11 +314,8 @@ theorem rightUnitor_hom_f (X : Center C) : Hom.f (ρ_ X).Hom = (ρ_ X.1).Hom :=
 #align category_theory.center.right_unitor_hom_f CategoryTheory.Center.rightUnitor_hom_f
 
 @[simp]
-theorem rightUnitor_inv_f (X : Center C) : Hom.f (ρ_ X).inv = (ρ_ X.1).inv :=
-  by
-  ext
-  rw [← right_unitor_hom_f, ← comp_f, iso.hom_inv_id]
-  rfl
+theorem rightUnitor_inv_f (X : Center C) : Hom.f (ρ_ X).inv = (ρ_ X.1).inv := by ext;
+  rw [← right_unitor_hom_f, ← comp_f, iso.hom_inv_id]; rfl
 #align category_theory.center.right_unitor_inv_f CategoryTheory.Center.rightUnitor_inv_f
 
 end
@@ -349,11 +336,7 @@ def forget : MonoidalFunctor (Center C) C
 #align category_theory.center.forget CategoryTheory.Center.forget
 
 instance : ReflectsIsomorphisms (forget C).toFunctor
-    where reflects A B f i := by
-    dsimp at i
-    skip
-    change is_iso (iso_mk f).Hom
-    infer_instance
+    where reflects A B f i := by dsimp at i; skip; change is_iso (iso_mk f).Hom; infer_instance
 
 end

14b69e9f

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -76,12 +76,12 @@ structure HalfBraiding (X : C) where
 
 restate_axiom half_braiding.monoidal'
 
-attribute [reassoc.1, simp] half_braiding.monoidal
+attribute [reassoc, simp] half_braiding.monoidal
 
 -- the reassoc lemma is redundant as a simp lemma
 restate_axiom half_braiding.naturality'
 
-attribute [simp, reassoc.1] half_braiding.naturality
+attribute [simp, reassoc] half_braiding.naturality
 
 variable (C)
 
@@ -108,7 +108,7 @@ structure Hom (X Y : Center C) where
 
 restate_axiom hom.comm'
 
-attribute [simp, reassoc.1] hom.comm
+attribute [simp, reassoc] hom.comm
 
 instance : Category (Center C) where
   Hom := Hom

14b69e9f

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

14b69e9f

chore: classify porting notes referring to missing linters (#12098)

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

c5b5490c

Diff

@@ -51,7 +51,7 @@ Thinking of `C` as a 2-category with a single `0`-morphism, these are the same a
 transformations (in the pseudo- sense) of the identity 2-functor on `C`, which send the unique
 `0`-morphism to `X`.
 -/
--- @[nolint has_nonempty_instance] -- Porting note: This linter does not exist yet.
+-- @[nolint has_nonempty_instance] -- Porting note(#5171): This linter does not exist yet.
 structure HalfBraiding (X : C) where
   β : ∀ U, X ⊗ U ≅ U ⊗ X
   monoidal : ∀ U U', (β (U ⊗ U')).hom =
@@ -71,7 +71,7 @@ variable (C)
 /-- The Drinfeld center of a monoidal category `C` has as objects pairs `⟨X, b⟩`, where `X : C`
 and `b` is a half-braiding on `X`.
 -/
--- @[nolint has_nonempty_instance] -- Porting note: This linter does not exist yet.
+-- @[nolint has_nonempty_instance] -- Porting note(#5171): This linter does not exist yet.
 def Center :=
   Σ X : C, HalfBraiding X
 #align category_theory.center CategoryTheory.Center
@@ -81,7 +81,8 @@ namespace Center
 variable {C}
 
 /-- A morphism in the Drinfeld center of `C`. -/
-@[ext] -- @[nolint has_nonempty_instance] -- Porting note: This linter does not exist yet.
+-- Porting note(#5171): linter not ported yet
+@[ext] -- @[nolint has_nonempty_instance]
 structure Hom (X Y : Center C) where
   f : X.1 ⟶ Y.1
   comm : ∀ U, (f ▷ U) ≫ (Y.2.β U).hom = (X.2.β U).hom ≫ (U ◁ f) := by aesop_cat

14b69e9f

chore(CategoryTheory): move Full, Faithful, EssSurj, IsEquivalence and ReflectsIsomorphisms to the Functor namespace (#11985)

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

65b7affc

Diff

@@ -339,7 +339,7 @@ def forget : MonoidalFunctor (Center C) C where
   μ X Y := 𝟙 (X.1 ⊗ Y.1)
 #align category_theory.center.forget CategoryTheory.Center.forget
 
-instance : ReflectsIsomorphisms (forget C).toFunctor where
+instance : (forget C).ReflectsIsomorphisms where
   reflects f i := by dsimp at i; change IsIso (isoMk f).hom; infer_instance
 
 end

14b69e9f

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) 2021 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.ReflectsIso
 
 #align_import category_theory.monoidal.center from "leanprover-community/mathlib"@"14b69e9f3c16630440a2cbd46f1ddad0d561dee7"

14b69e9f

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

@@ -217,8 +217,6 @@ def tensorHom {X₁ Y₁ X₂ Y₂ : Center C} (f : X₁ ⟶ Y₁) (g : X₂ ⟶
 
 section
 
-attribute [local simp] id_tensorHom tensorHom_id
-
 /-- Auxiliary definition for the `MonoidalCategory` instance on `Center C`. -/
 @[simps]
 def tensorUnit : Center C :=

14b69e9f

feat: add lake exe shake to CI (#9751)

depends on: #9830
depends on: #9772
depends on: #9996

This checks files for unused imports. The output here is piped through gh-problem-matcher-wrap so that it will show up as annotations.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

056cc4b2

Diff

@@ -5,7 +5,6 @@ Authors: Scott Morrison
 -/
 import Mathlib.CategoryTheory.Monoidal.Braided
 import Mathlib.CategoryTheory.Functor.ReflectsIso
-import Mathlib.CategoryTheory.Monoidal.CoherenceLemmas
 
 #align_import category_theory.monoidal.center from "leanprover-community/mathlib"@"14b69e9f3c16630440a2cbd46f1ddad0d561dee7"

14b69e9f

refactor(CategoryTheory/Monoidal/Braided): use monoidalComp in the proofs (#10078)

depends on: #10061

007ad742

Diff

@@ -17,18 +17,19 @@ We define `Center C` to be pairs `⟨X, b⟩`, where `X : C` and `b` is a half-b
 We show that `Center C` is braided monoidal,
 and provide the monoidal functor `Center.forget` from `Center C` back to `C`.
 
-## Future work
+## Implementation notes
 
-Verifying the various axioms here is done by tedious rewriting.
+Verifying the various axioms directly requires tedious rewriting.
 Using the `slice` tactic may make the proofs marginally more readable.
 
 More exciting, however, would be to make possible one of the following options:
 1. Integration with homotopy.io / globular to give "picture proofs".
 2. The monoidal coherence theorem, so we can ignore associators
-   (after which most of these proofs are trivial;
-   I'm unsure if the monoidal coherence theorem is even usable in dependent type theory).
+   (after which most of these proofs are trivial).
 3. Automating these proofs using `rewrite_search` or some relative.
 
+In this file, we take the second approach using the monoidal composition `⊗≫` and the
+`coherence` tactic.
 -/
 
 
@@ -56,9 +57,9 @@ structure HalfBraiding (X : C) where
   β : ∀ U, X ⊗ U ≅ U ⊗ X
   monoidal : ∀ U U', (β (U ⊗ U')).hom =
       (α_ _ _ _).inv ≫
-        ((β U).hom ⊗ 𝟙 U') ≫ (α_ _ _ _).hom ≫ (𝟙 U ⊗ (β U').hom) ≫ (α_ _ _ _).inv := by
+        ((β U).hom ▷ U') ≫ (α_ _ _ _).hom ≫ (U ◁ (β U').hom) ≫ (α_ _ _ _).inv := by
     aesop_cat
-  naturality : ∀ {U U'} (f : U ⟶ U'), (𝟙 X ⊗ f) ≫ (β U').hom = (β U).hom ≫ (f ⊗ 𝟙 X) := by
+  naturality : ∀ {U U'} (f : U ⟶ U'), (X ◁ f) ≫ (β U').hom = (β U).hom ≫ (f ▷ X) := by
     aesop_cat
 #align category_theory.half_braiding CategoryTheory.HalfBraiding
 
@@ -84,7 +85,7 @@ variable {C}
 @[ext] -- @[nolint has_nonempty_instance] -- Porting note: This linter does not exist yet.
 structure Hom (X Y : Center C) where
   f : X.1 ⟶ Y.1
-  comm : ∀ U, (f ⊗ 𝟙 U) ≫ (Y.2.β U).hom = (X.2.β U).hom ≫ (𝟙 U ⊗ f) := by aesop_cat
+  comm : ∀ U, (f ▷ U) ≫ (Y.2.β U).hom = (X.2.β U).hom ≫ (U ◁ f) := by aesop_cat
 #align category_theory.center.hom CategoryTheory.Center.Hom
 
 attribute [reassoc (attr := simp)] Hom.comm
@@ -118,7 +119,8 @@ a morphism whose underlying morphism is an isomorphism.
 def isoMk {X Y : Center C} (f : X ⟶ Y) [IsIso f.f] : X ≅ Y where
   hom := f
   inv := ⟨inv f.f,
-    fun U => by simp [← cancel_epi (f.f ⊗ 𝟙 U), ← comp_tensor_id_assoc, ← id_tensor_comp]⟩
+    fun U => by simp [← cancel_epi (f.f ▷ U), ← comp_whiskerRight_assoc,
+      ← MonoidalCategory.whiskerLeft_comp] ⟩
 #align category_theory.center.iso_mk CategoryTheory.Center.isoMk
 
 instance isIso_of_f_isIso {X Y : Center C} (f : X ⟶ Y) [IsIso f.f] : IsIso f := by
@@ -132,48 +134,86 @@ def tensorObj (X Y : Center C) : Center C :=
   ⟨X.1 ⊗ Y.1,
     { β := fun U =>
         α_ _ _ _ ≪≫
-          (Iso.refl X.1 ⊗ Y.2.β U) ≪≫ (α_ _ _ _).symm ≪≫ (X.2.β U ⊗ Iso.refl Y.1) ≪≫ α_ _ _ _
+          (whiskerLeftIso X.1 (Y.2.β U)) ≪≫ (α_ _ _ _).symm ≪≫
+            (whiskerRightIso (X.2.β U) Y.1) ≪≫ α_ _ _ _
       monoidal := fun U U' => by
-        dsimp
-        simp only [comp_tensor_id, id_tensor_comp, Category.assoc, HalfBraiding.monoidal]
-        -- On the RHS, we'd like to commute `((X.snd.β U).hom ⊗ 𝟙 Y.fst) ⊗ 𝟙 U'`
-        -- and `𝟙 U ⊗ 𝟙 X.fst ⊗ (Y.snd.β U').hom` past each other,
-        -- but there are some associators we need to get out of the way first.
-        slice_rhs 6 8 => rw [pentagon]
-        slice_rhs 5 6 => rw [associator_naturality]
-        slice_rhs 7 8 => rw [← associator_naturality]
-        slice_rhs 6 7 =>
-          rw [tensor_id, tensor_id, tensor_id_comp_id_tensor, ← id_tensor_comp_tensor_id,
-            ← tensor_id, ← tensor_id]
-        -- Now insert associators as needed to make the four half-braidings look identical
-        slice_rhs 10 10 => rw [associator_inv_conjugation]
-        slice_rhs 7 7 => rw [associator_inv_conjugation]
-        slice_rhs 6 6 => rw [associator_conjugation]
-        slice_rhs 3 3 => rw [associator_conjugation]
-        -- Finish with an application of the coherence theorem.
-        coherence
-      naturality := fun f => by
-        dsimp
-        rw [Category.assoc, Category.assoc, Category.assoc, Category.assoc,
-          id_tensor_associator_naturality_assoc, ← id_tensor_comp_assoc, HalfBraiding.naturality,
-          id_tensor_comp_assoc, associator_inv_naturality_assoc, ← comp_tensor_id_assoc,
-          HalfBraiding.naturality, comp_tensor_id_assoc, associator_naturality, ← tensor_id] }⟩
+        dsimp only [Iso.trans_hom, whiskerLeftIso_hom, Iso.symm_hom, whiskerRightIso_hom]
+        simp only [HalfBraiding.monoidal]
+        -- We'd like to commute `X.1 ◁ U ◁ (HalfBraiding.β Y.2 U').hom`
+        -- and `((HalfBraiding.β X.2 U).hom ▷ U' ▷ Y.1)` past each other.
+        -- We do this with the help of the monoidal composition `⊗≫` and the `coherence` tactic.
+        calc
+          _ = 𝟙 _ ⊗≫
+            X.1 ◁ (HalfBraiding.β Y.2 U).hom ▷ U' ⊗≫
+              (_ ◁ (HalfBraiding.β Y.2 U').hom ≫
+                (HalfBraiding.β X.2 U).hom ▷ _) ⊗≫
+                  U ◁ (HalfBraiding.β X.2 U').hom ▷ Y.1 ⊗≫ 𝟙 _ := by coherence
+          _ = _ := by rw [whisker_exchange]; coherence
+      naturality := fun {U U'} f => by
+        dsimp only [Iso.trans_hom, whiskerLeftIso_hom, Iso.symm_hom, whiskerRightIso_hom]
+        calc
+          _ = 𝟙 _ ⊗≫
+            (X.1 ◁ (Y.1 ◁ f ≫ (HalfBraiding.β Y.2 U').hom)) ⊗≫
+              (HalfBraiding.β X.2 U').hom ▷ Y.1 ⊗≫ 𝟙 _ := by coherence
+          _ = 𝟙 _ ⊗≫
+            X.1 ◁ (HalfBraiding.β Y.2 U).hom ⊗≫
+              (X.1 ◁ f ≫ (HalfBraiding.β X.2 U').hom) ▷ Y.1 ⊗≫ 𝟙 _ := by
+            rw [HalfBraiding.naturality]; coherence
+          _ = _ := by rw [HalfBraiding.naturality]; coherence }⟩
 #align category_theory.center.tensor_obj CategoryTheory.Center.tensorObj
 
+@[reassoc]
+theorem whiskerLeft_comm (X : Center C) {Y₁ Y₂ : Center C} (f : Y₁ ⟶ Y₂) (U : C) :
+    (X.1 ◁ f.f) ▷ U ≫ ((tensorObj X Y₂).2.β U).hom =
+      ((tensorObj X Y₁).2.β U).hom ≫ U ◁ X.1 ◁ f.f := by
+  dsimp only [tensorObj_fst, tensorObj_snd_β, Iso.trans_hom, whiskerLeftIso_hom,
+    Iso.symm_hom, whiskerRightIso_hom]
+  calc
+    _ = 𝟙 _ ⊗≫
+      X.fst ◁ (f.f ▷ U ≫ (HalfBraiding.β Y₂.snd U).hom) ⊗≫
+        (HalfBraiding.β X.snd U).hom ▷ Y₂.fst ⊗≫ 𝟙 _ := by coherence
+    _ = 𝟙 _ ⊗≫
+      X.fst ◁ (HalfBraiding.β Y₁.snd U).hom ⊗≫
+        ((X.fst ⊗ U) ◁ f.f ≫ (HalfBraiding.β X.snd U).hom ▷ Y₂.fst) ⊗≫ 𝟙 _ := by
+      rw [f.comm]; coherence
+    _ = _ := by rw [whisker_exchange]; coherence
+
+/-- Auxiliary definition for the `MonoidalCategory` instance on `Center C`. -/
+def whiskerLeft (X : Center C) {Y₁ Y₂ : Center C} (f : Y₁ ⟶ Y₂) :
+    tensorObj X Y₁ ⟶ tensorObj X Y₂ where
+  f := X.1 ◁ f.f
+  comm U := whiskerLeft_comm X f U
+
+@[reassoc]
+theorem whiskerRight_comm {X₁ X₂: Center C} (f : X₁ ⟶ X₂) (Y : Center C) (U : C) :
+    f.f ▷ Y.1 ▷ U ≫ ((tensorObj X₂ Y).2.β U).hom =
+      ((tensorObj X₁ Y).2.β U).hom ≫ U ◁ f.f ▷ Y.1 := by
+  dsimp only [tensorObj_fst, tensorObj_snd_β, Iso.trans_hom, whiskerLeftIso_hom,
+    Iso.symm_hom, whiskerRightIso_hom]
+  calc
+    _ = 𝟙 _ ⊗≫
+      (f.f ▷ (Y.fst ⊗ U) ≫ X₂.fst ◁ (HalfBraiding.β Y.snd U).hom) ⊗≫
+        (HalfBraiding.β X₂.snd U).hom ▷ Y.fst ⊗≫ 𝟙 _ := by coherence
+    _ = 𝟙 _ ⊗≫
+      X₁.fst ◁ (HalfBraiding.β Y.snd U).hom ⊗≫
+        (f.f ▷ U ≫ (HalfBraiding.β X₂.snd U).hom) ▷ Y.fst ⊗≫ 𝟙 _ := by
+      rw [← whisker_exchange]; coherence
+    _ = _ := by rw [f.comm]; coherence
+
+/-- Auxiliary definition for the `MonoidalCategory` instance on `Center C`. -/
+def whiskerRight {X₁ X₂ : Center C} (f : X₁ ⟶ X₂) (Y : Center C) :
+    tensorObj X₁ Y ⟶ tensorObj X₂ Y where
+  f := f.f ▷ Y.1
+  comm U := whiskerRight_comm f Y U
+
 /-- Auxiliary definition for the `MonoidalCategory` instance on `Center C`. -/
 @[simps]
 def tensorHom {X₁ Y₁ X₂ Y₂ : Center C} (f : X₁ ⟶ Y₁) (g : X₂ ⟶ Y₂) :
     tensorObj X₁ X₂ ⟶ tensorObj Y₁ Y₂ where
   f := f.f ⊗ g.f
   comm U := by
-    dsimp
-    rw [Category.assoc, Category.assoc, Category.assoc, Category.assoc, associator_naturality_assoc,
-      ← tensor_id_comp_id_tensor, Category.assoc, ← id_tensor_comp_assoc, g.comm,
-      id_tensor_comp_assoc, tensor_id_comp_id_tensor_assoc, ← id_tensor_comp_tensor_id,
-      Category.assoc, associator_inv_naturality_assoc, id_tensor_associator_inv_naturality_assoc,
-      tensor_id, id_tensor_comp_tensor_id_assoc, ← tensor_id_comp_id_tensor g.f, Category.assoc,
-      ← comp_tensor_id_assoc, f.comm, comp_tensor_id_assoc, id_tensor_associator_naturality,
-      associator_naturality_assoc, ← id_tensor_comp, tensor_id_comp_id_tensor]
+    rw [tensorHom_def, comp_whiskerRight_assoc, whiskerLeft_comm, whiskerRight_comm_assoc,
+      MonoidalCategory.whiskerLeft_comp]
 #align category_theory.center.tensor_hom CategoryTheory.Center.tensorHom
 
 section
@@ -209,14 +249,14 @@ attribute [local simp] associator_naturality leftUnitor_naturality rightUnitor_n
 
 attribute [local simp] Center.associator Center.leftUnitor Center.rightUnitor
 
+attribute [local simp] Center.whiskerLeft Center.whiskerRight Center.tensorHom
+
 instance : MonoidalCategory (Center C) where
   tensorObj X Y := tensorObj X Y
   tensorHom f g := tensorHom f g
   tensorHom_def := by intros; ext; simp [tensorHom_def]
-  -- Todo: replace it by `X.1 ◁ f.f`
-  whiskerLeft X _ _ f := tensorHom (𝟙 X) f
-  -- Todo: replace it by `f.f ▷ Y.1`
-  whiskerRight f Y := tensorHom f (𝟙 Y)
+  whiskerLeft X _ _ f := whiskerLeft X f
+  whiskerRight f Y := whiskerRight f Y
   tensorUnit := tensorUnit
   associator := associator
   leftUnitor := leftUnitor
@@ -231,17 +271,18 @@ theorem tensor_fst (X Y : Center C) : (X ⊗ Y).1 = X.1 ⊗ Y.1 :=
 theorem tensor_β (X Y : Center C) (U : C) :
     (X ⊗ Y).2.β U =
       α_ _ _ _ ≪≫
-        (Iso.refl X.1 ⊗ Y.2.β U) ≪≫ (α_ _ _ _).symm ≪≫ (X.2.β U ⊗ Iso.refl Y.1) ≪≫ α_ _ _ _ :=
+        (whiskerLeftIso X.1 (Y.2.β U)) ≪≫ (α_ _ _ _).symm ≪≫
+          (whiskerRightIso (X.2.β U) Y.1) ≪≫ α_ _ _ _ :=
   rfl
 #align category_theory.center.tensor_β CategoryTheory.Center.tensor_β
 
 @[simp]
 theorem whiskerLeft_f (X : Center C) {Y₁ Y₂ : Center C} (f : Y₁ ⟶ Y₂) : (X ◁ f).f = X.1 ◁ f.f :=
-  id_tensorHom X.1 f.f
+  rfl
 
 @[simp]
 theorem whiskerRight_f {X₁ X₂ : Center C} (f : X₁ ⟶ X₂) (Y : Center C) : (f ▷ Y).f = f.f ▷ Y.1 :=
-  tensorHom_id f.f Y.1
+  rfl
 
 @[simp]
 theorem tensor_f {X₁ Y₁ X₂ Y₂ : Center C} (f : X₁ ⟶ Y₁) (g : X₂ ⟶ Y₂) : (f ⊗ g).f = f.f ⊗ g.f :=
@@ -344,20 +385,9 @@ def ofBraided : MonoidalFunctor C (Center C) where
   obj := ofBraidedObj
   map f :=
     { f
-      comm := fun U => braiding_naturality _ _ }
-  ε :=
-    { f := 𝟙 _
-      comm := fun U => by
-        dsimp
-        rw [tensor_id, Category.id_comp, tensor_id, Category.comp_id, ← braiding_rightUnitor,
-          Category.assoc, Iso.hom_inv_id, Category.comp_id] }
-  μ X Y :=
-    { f := 𝟙 _
-      comm := fun U => by
-        dsimp
-        rw [tensor_id, tensor_id, Category.id_comp, Category.comp_id, ← Iso.inv_comp_eq,
-          ← Category.assoc, ← Category.assoc, ← Iso.comp_inv_eq, Category.assoc, hexagon_reverse,
-          Category.assoc] }
+      comm := fun U => braiding_naturality_left f U }
+  ε := { f := 𝟙 _ }
+  μ X Y := { f := 𝟙 _ }
 #align category_theory.center.of_braided CategoryTheory.Center.ofBraided
 
 end

14b69e9f

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

@@ -176,47 +176,33 @@ def tensorHom {X₁ Y₁ X₂ Y₂ : Center C} (f : X₁ ⟶ Y₁) (g : X₂ ⟶
       associator_naturality_assoc, ← id_tensor_comp, tensor_id_comp_id_tensor]
 #align category_theory.center.tensor_hom CategoryTheory.Center.tensorHom
 
+section
+
+attribute [local simp] id_tensorHom tensorHom_id
+
 /-- Auxiliary definition for the `MonoidalCategory` instance on `Center C`. -/
 @[simps]
 def tensorUnit : Center C :=
-  ⟨𝟙_ C,
-    { β := fun U => λ_ U ≪≫ (ρ_ U).symm
-      monoidal := fun U U' => by simp
-      naturality := fun f => by
-        dsimp
-        rw [leftUnitor_naturality_assoc, rightUnitor_inv_naturality, Category.assoc] }⟩
+  ⟨𝟙_ C, { β := fun U => λ_ U ≪≫ (ρ_ U).symm }⟩
 #align category_theory.center.tensor_unit CategoryTheory.Center.tensorUnit
 
 /-- Auxiliary definition for the `MonoidalCategory` instance on `Center C`. -/
 def associator (X Y Z : Center C) : tensorObj (tensorObj X Y) Z ≅ tensorObj X (tensorObj Y Z) :=
-  isoMk
-    ⟨(α_ X.1 Y.1 Z.1).hom, fun U => by
-      dsimp
-      simp only [comp_tensor_id, id_tensor_comp, ← tensor_id, associator_conjugation]
-      coherence⟩
+  isoMk ⟨(α_ X.1 Y.1 Z.1).hom, fun U => by simp⟩
 #align category_theory.center.associator CategoryTheory.Center.associator
 
 /-- Auxiliary definition for the `MonoidalCategory` instance on `Center C`. -/
 def leftUnitor (X : Center C) : tensorObj tensorUnit X ≅ X :=
-  isoMk
-    ⟨(λ_ X.1).hom, fun U => by
-      dsimp
-      simp only [Category.comp_id, Category.assoc, tensor_inv_hom_id, comp_tensor_id,
-        tensor_id_comp_id_tensor, triangle_assoc_comp_right_inv]
-      rw [← leftUnitor_tensor, leftUnitor_naturality, leftUnitor_tensor'_assoc]⟩
+  isoMk ⟨(λ_ X.1).hom, fun U => by simp⟩
 #align category_theory.center.left_unitor CategoryTheory.Center.leftUnitor
 
 /-- Auxiliary definition for the `MonoidalCategory` instance on `Center C`. -/
 def rightUnitor (X : Center C) : tensorObj X tensorUnit ≅ X :=
-  isoMk
-    ⟨(ρ_ X.1).hom, fun U => by
-      dsimp
-      simp only [tensor_id_comp_id_tensor_assoc, triangle_assoc, id_tensor_comp, Category.assoc]
-      rw [← tensor_id_comp_id_tensor_assoc (ρ_ U).inv, cancel_epi, ← rightUnitor_tensor_inv_assoc,
-        ← rightUnitor_inv_naturality_assoc]
-      simp⟩
+  isoMk ⟨(ρ_ X.1).hom, fun U => by simp⟩
 #align category_theory.center.right_unitor CategoryTheory.Center.rightUnitor
 
+end
+
 section
 
 attribute [local simp] associator_naturality leftUnitor_naturality rightUnitor_naturality pentagon
@@ -226,6 +212,7 @@ attribute [local simp] Center.associator Center.leftUnitor Center.rightUnitor
 instance : MonoidalCategory (Center C) where
   tensorObj X Y := tensorObj X Y
   tensorHom f g := tensorHom f g
+  tensorHom_def := by intros; ext; simp [tensorHom_def]
   -- Todo: replace it by `X.1 ◁ f.f`
   whiskerLeft X _ _ f := tensorHom (𝟙 X) f
   -- Todo: replace it by `f.f ▷ Y.1`

14b69e9f

feat(CategoryTheory/Monoidal): add lemmas for the whiskerings (#9995)

Extracted from #6307.

f1919fd4

Diff

@@ -248,6 +248,14 @@ theorem tensor_β (X Y : Center C) (U : C) :
   rfl
 #align category_theory.center.tensor_β CategoryTheory.Center.tensor_β
 
+@[simp]
+theorem whiskerLeft_f (X : Center C) {Y₁ Y₂ : Center C} (f : Y₁ ⟶ Y₂) : (X ◁ f).f = X.1 ◁ f.f :=
+  id_tensorHom X.1 f.f
+
+@[simp]
+theorem whiskerRight_f {X₁ X₂ : Center C} (f : X₁ ⟶ X₂) (Y : Center C) : (f ▷ Y).f = f.f ▷ Y.1 :=
+  tensorHom_id f.f Y.1
+
 @[simp]
 theorem tensor_f {X₁ Y₁ X₂ Y₂ : Center C} (f : X₁ ⟶ Y₁) (g : X₂ ⟶ Y₂) : (f ⊗ g).f = f.f ⊗ g.f :=
   rfl
@@ -337,12 +345,7 @@ open BraidedCategory
 /-- Auxiliary construction for `ofBraided`. -/
 @[simps]
 def ofBraidedObj (X : C) : Center C :=
-  ⟨X, {
-      β := fun Y => β_ X Y
-      monoidal := fun U U' => by
-        rw [Iso.eq_inv_comp, ← Category.assoc, ← Category.assoc, Iso.eq_comp_inv, Category.assoc,
-          Category.assoc]
-        exact hexagon_forward X U U' }⟩
+  ⟨X, { β := fun Y => β_ X Y}⟩
 #align category_theory.center.of_braided_obj CategoryTheory.Center.ofBraidedObj
 
 variable (C)

14b69e9f

refactor(CategoryTheory/Monoidal): replace axioms with those more suitable for the whiskerings (#9991)

Extracted from #6307. We replace some axioms by those more preferable when using the whiskerings instead of the tensor of morphisms.

d3da7bbc

Diff

@@ -325,11 +325,6 @@ def braiding (X Y : Center C) : X ⊗ Y ≅ Y ⊗ X :=
 
 instance braidedCategoryCenter : BraidedCategory (Center C) where
   braiding := braiding
-  braiding_naturality f g := by
-    ext
-    dsimp
-    rw [← tensor_id_comp_id_tensor, Category.assoc, HalfBraiding.naturality, f.comm_assoc,
-      id_tensor_comp_tensor_id]
 #align category_theory.center.braided_category_center CategoryTheory.Center.braidedCategoryCenter
 
 -- `aesop_cat` handles the hexagon axioms

14b69e9f

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

@@ -230,7 +230,7 @@ instance : MonoidalCategory (Center C) where
   whiskerLeft X _ _ f := tensorHom (𝟙 X) f
   -- Todo: replace it by `f.f ▷ Y.1`
   whiskerRight f Y := tensorHom f (𝟙 Y)
-  tensorUnit' := tensorUnit
+  tensorUnit := tensorUnit
   associator := associator
   leftUnitor := leftUnitor
   rightUnitor := rightUnitor

14b69e9f

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

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

763106d3

Diff

@@ -226,6 +226,10 @@ attribute [local simp] Center.associator Center.leftUnitor Center.rightUnitor
 instance : MonoidalCategory (Center C) where
   tensorObj X Y := tensorObj X Y
   tensorHom f g := tensorHom f g
+  -- Todo: replace it by `X.1 ◁ f.f`
+  whiskerLeft X _ _ f := tensorHom (𝟙 X) f
+  -- Todo: replace it by `f.f ▷ Y.1`
+  whiskerRight f Y := tensorHom f (𝟙 Y)
   tensorUnit' := tensorUnit
   associator := associator
   leftUnitor := leftUnitor

14b69e9f

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) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.monoidal.center
-! leanprover-community/mathlib commit 14b69e9f3c16630440a2cbd46f1ddad0d561dee7
-! 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.ReflectsIso
 import Mathlib.CategoryTheory.Monoidal.CoherenceLemmas
 
+#align_import category_theory.monoidal.center from "leanprover-community/mathlib"@"14b69e9f3c16630440a2cbd46f1ddad0d561dee7"
+
 /-!
 # Half braidings and the Drinfeld center of a monoidal category

14b69e9f

feat: port CategoryTheory.Monoidal.Center (#4941)

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

1ab969a0

`category_theory.monoidal.center` ⟷ `Mathlib.CategoryTheory.Monoidal.Center`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 87

category_theory.monoidal.center ⟷ Mathlib.CategoryTheory.Monoidal.Center

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 87

`category_theory.monoidal.center` ⟷ `Mathlib.CategoryTheory.Monoidal.Center`