category_theory.monoidal.free.coherence

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

f187f107

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

33c67ae6

bump to nightly-2023-11-29-11

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

049e2cad

Diff

@@ -76,7 +76,7 @@ local infixr:10 " ⟶ᵐ " => Hom
 /-- Auxiliary definition for `inclusion`. -/
 @[simp]
 def inclusionObj : NormalMonoidalObject C → F C
-  | normal_monoidal_object.unit => Unit
+  | normal_monoidal_object.unit => unit
   | normal_monoidal_object.tensor n a => tensor (inclusion_obj n) (of a)
 #align category_theory.free_monoidal_category.inclusion_obj CategoryTheory.FreeMonoidalCategory.inclusionObj
 -/
@@ -176,8 +176,8 @@ def normalize' : F C ⥤ N C ⥤ F C :=
 /-- The normalization functor for the free monoidal category over `C`. -/
 def fullNormalize : F C ⥤ N C
     where
-  obj X := ((normalize C).obj X).obj ⟨NormalMonoidalObject.Unit⟩
-  map X Y f := ((normalize C).map f).app ⟨NormalMonoidalObject.Unit⟩
+  obj X := ((normalize C).obj X).obj ⟨NormalMonoidalObject.unit⟩
+  map X Y f := ((normalize C).map f).app ⟨NormalMonoidalObject.unit⟩
 #align category_theory.free_monoidal_category.full_normalize CategoryTheory.FreeMonoidalCategory.fullNormalize
 -/
 
@@ -342,7 +342,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
 /-- The isomorphism between an object and its normal form is natural. -/
 def fullNormalizeIso : 𝟭 (F C) ≅ fullNormalize C ⋙ inclusion :=
   NatIso.ofComponents
-    (fun X => (λ_ X).symm ≪≫ ((normalizeIso C).app X).app ⟨NormalMonoidalObject.Unit⟩)
+    (fun X => (λ_ X).symm ≪≫ ((normalizeIso C).app X).app ⟨NormalMonoidalObject.unit⟩)
     (by
       intro X Y f
       dsimp

33c67ae6

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 Markus Himmel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Markus Himmel
 -/
-import Mathbin.CategoryTheory.Monoidal.Free.Basic
-import Mathbin.CategoryTheory.Groupoid
-import Mathbin.CategoryTheory.DiscreteCategory
+import CategoryTheory.Monoidal.Free.Basic
+import CategoryTheory.Groupoid
+import CategoryTheory.DiscreteCategory
 
 #align_import category_theory.monoidal.free.coherence from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"

33c67ae6

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 Markus Himmel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.monoidal.free.coherence
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Monoidal.Free.Basic
 import Mathbin.CategoryTheory.Groupoid
 import Mathbin.CategoryTheory.DiscreteCategory
 
+#align_import category_theory.monoidal.free.coherence from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
+
 /-!
 # The monoidal coherence theorem

33c67ae6

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -69,13 +69,10 @@ inductive NormalMonoidalObject : Type u
 
 end
 
--- mathport name: exprF
 local notation "F" => FreeMonoidalCategory
 
--- mathport name: exprN
 local notation "N" => Discrete ∘ NormalMonoidalObject
 
--- mathport name: «expr ⟶ᵐ »
 local infixr:10 " ⟶ᵐ " => Hom
 
 #print CategoryTheory.FreeMonoidalCategory.inclusionObj /-
@@ -105,17 +102,21 @@ def normalizeObj : F C → NormalMonoidalObject C → N C
 #align category_theory.free_monoidal_category.normalize_obj CategoryTheory.FreeMonoidalCategory.normalizeObj
 -/
 
+#print CategoryTheory.FreeMonoidalCategory.normalizeObj_unitor /-
 @[simp]
 theorem normalizeObj_unitor (n : NormalMonoidalObject C) : normalizeObj (𝟙_ (F C)) n = ⟨n⟩ :=
   rfl
 #align category_theory.free_monoidal_category.normalize_obj_unitor CategoryTheory.FreeMonoidalCategory.normalizeObj_unitor
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.FreeMonoidalCategory.normalizeObj_tensor /-
 @[simp]
 theorem normalizeObj_tensor (X Y : F C) (n : NormalMonoidalObject C) :
     normalizeObj (X ⊗ Y) n = normalizeObj Y (normalizeObj X n).as :=
   rfl
 #align category_theory.free_monoidal_category.normalize_obj_tensor CategoryTheory.FreeMonoidalCategory.normalizeObj_tensor
+-/
 
 section
 
@@ -197,15 +198,20 @@ def tensorFunc : F C ⥤ N C ⥤ F C
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app /-
 theorem tensorFunc_map_app {X Y : F C} (f : X ⟶ Y) (n) : ((tensorFunc C).map f).app n = 𝟙 _ ⊗ f :=
   rfl
 #align category_theory.free_monoidal_category.tensor_func_map_app CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map /-
 theorem tensorFunc_obj_map (Z : F C) {n n' : N C} (f : n ⟶ n') :
     ((tensorFunc C).obj Z).map f = inclusion.map f ⊗ 𝟙 Z := by cases n; cases n'; tidy
 #align category_theory.free_monoidal_category.tensor_func_obj_map CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map
+-/
 
+#print CategoryTheory.FreeMonoidalCategory.normalizeIsoApp /-
 /-- Auxiliary definition for `normalize_iso`. Here we construct the isomorphism between
     `n ⊗ X` and `normalize X n`. -/
 @[simp]
@@ -216,40 +222,51 @@ def normalizeIsoApp :
   | tensor X Y, n =>
     (α_ _ _ _).symm ≪≫ tensorIso (normalize_iso_app X n) (Iso.refl _) ≪≫ normalize_iso_app _ _
 #align category_theory.free_monoidal_category.normalize_iso_app CategoryTheory.FreeMonoidalCategory.normalizeIsoApp
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor /-
 @[simp]
 theorem normalizeIsoApp_tensor (X Y : F C) (n : N C) :
     normalizeIsoApp C (X ⊗ Y) n =
       (α_ _ _ _).symm ≪≫ tensorIso (normalizeIsoApp C X n) (Iso.refl _) ≪≫ normalizeIsoApp _ _ _ :=
   rfl
 #align category_theory.free_monoidal_category.normalize_iso_app_tensor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor
+-/
 
+#print CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitor /-
 @[simp]
 theorem normalizeIsoApp_unitor (n : N C) : normalizeIsoApp C (𝟙_ (F C)) n = ρ_ _ :=
   rfl
 #align category_theory.free_monoidal_category.normalize_iso_app_unitor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitor
+-/
 
+#print CategoryTheory.FreeMonoidalCategory.normalizeIsoAux /-
 /-- Auxiliary definition for `normalize_iso`. -/
 @[simp]
 def normalizeIsoAux (X : F C) : (tensorFunc C).obj X ≅ (normalize' C).obj X :=
   NatIso.ofComponents (normalizeIsoApp C X) (by rintro ⟨X⟩ ⟨Y⟩; tidy)
 #align category_theory.free_monoidal_category.normalize_iso_aux CategoryTheory.FreeMonoidalCategory.normalizeIsoAux
+-/
 
 section
 
 variable {D : Type u} [Category.{u} D] {I : Type u} (f : I → D) (X : Discrete I)
 
+#print CategoryTheory.FreeMonoidalCategory.discrete_functor_obj_eq_as /-
 -- TODO: move to discrete_category.lean, decide whether this should be a global simp lemma
 @[simp]
 theorem discrete_functor_obj_eq_as : (Discrete.functor f).obj X = f X.as :=
   rfl
 #align category_theory.free_monoidal_category.discrete_functor_obj_eq_as CategoryTheory.FreeMonoidalCategory.discrete_functor_obj_eq_as
+-/
 
+#print CategoryTheory.FreeMonoidalCategory.discrete_functor_map_eq_id /-
 -- TODO: move to discrete_category.lean, decide whether this should be a global simp lemma
 @[simp]
 theorem discrete_functor_map_eq_id (g : X ⟶ X) : (Discrete.functor f).map g = 𝟙 _ := by tidy
 #align category_theory.free_monoidal_category.discrete_functor_map_eq_id CategoryTheory.FreeMonoidalCategory.discrete_functor_map_eq_id
+-/
 
 end

33c67ae6

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -290,7 +290,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
           right_unitor_naturality]
         simp only [iso.cancel_iso_inv_left, category.assoc]
         congr 1
-        convert(category.comp_id _).symm
+        convert (category.comp_id _).symm
         convert discrete_functor_map_eq_id inclusion_obj _ _
         ext
         rfl
@@ -299,7 +299,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
           category.assoc, iso.hom_inv_id, iso.hom_inv_id_assoc, iso.inv_hom_id,
           iso.inv_hom_id_assoc]
         congr
-        convert(discrete_functor_map_eq_id inclusion_obj _ _).symm
+        convert (discrete_functor_map_eq_id inclusion_obj _ _).symm
         ext; rfl
       · dsimp at *
         rw [id_tensor_comp, category.assoc, f_ih_g ⟦f_g⟧, ← category.assoc, f_ih_f ⟦f_f⟧,
@@ -319,7 +319,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
         dsimp
         simp only [category.assoc, category.comp_id]
         congr 1
-        convert(normalize_iso_aux C f_Z).Hom.naturality ((normalize_map_aux f_f).app n)
+        convert (normalize_iso_aux C f_Z).Hom.naturality ((normalize_map_aux f_f).app n)
         exact (tensor_func_obj_map _ _ _).symm)
 #align category_theory.free_monoidal_category.normalize_iso CategoryTheory.FreeMonoidalCategory.normalizeIso
 -/

33c67ae6

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -105,23 +105,11 @@ def normalizeObj : F C → NormalMonoidalObject C → N C
 #align category_theory.free_monoidal_category.normalize_obj CategoryTheory.FreeMonoidalCategory.normalizeObj
 -/
 
-/- warning: category_theory.free_monoidal_category.normalize_obj_unitor -> CategoryTheory.FreeMonoidalCategory.normalizeObj_unitor is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_obj_unitor CategoryTheory.FreeMonoidalCategory.normalizeObj_unitorₓ'. -/
 @[simp]
 theorem normalizeObj_unitor (n : NormalMonoidalObject C) : normalizeObj (𝟙_ (F C)) n = ⟨n⟩ :=
   rfl
 #align category_theory.free_monoidal_category.normalize_obj_unitor CategoryTheory.FreeMonoidalCategory.normalizeObj_unitor
 
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-but is expected to have type
-  forall {C : Type.{u1}} (X : CategoryTheory.FreeMonoidalCategory.{u1} C) (Y : CategoryTheory.FreeMonoidalCategory.{u1} C) (n : CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C), Eq.{succ u1} (Function.comp.{succ (succ u1), succ (succ u1), succ (succ u1)} Type.{u1} Type.{u1} Type.{u1} CategoryTheory.Discrete.{u1} CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C) (CategoryTheory.FreeMonoidalCategory.normalizeObj.{u1} C (CategoryTheory.MonoidalCategory.tensorObj.{u1, u1} (CategoryTheory.FreeMonoidalCategory.{u1} C) (CategoryTheory.FreeMonoidalCategory.categoryFreeMonoidalCategory.{u1} C) (CategoryTheory.FreeMonoidalCategory.instMonoidalCategoryFreeMonoidalCategoryCategoryFreeMonoidalCategory.{u1} C) X Y) n) (CategoryTheory.FreeMonoidalCategory.normalizeObj.{u1} C Y (CategoryTheory.Discrete.as.{u1} (CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C) (CategoryTheory.FreeMonoidalCategory.normalizeObj.{u1} C X n)))
-Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_obj_tensor CategoryTheory.FreeMonoidalCategory.normalizeObj_tensorₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem normalizeObj_tensor (X Y : F C) (n : NormalMonoidalObject C) :
@@ -208,25 +196,16 @@ def tensorFunc : F C ⥤ N C ⥤ F C
 #align category_theory.free_monoidal_category.tensor_func CategoryTheory.FreeMonoidalCategory.tensorFunc
 -/
 
-/- warning: category_theory.free_monoidal_category.tensor_func_map_app -> CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.tensor_func_map_app CategoryTheory.FreeMonoidalCategory.tensorFunc_map_appₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem tensorFunc_map_app {X Y : F C} (f : X ⟶ Y) (n) : ((tensorFunc C).map f).app n = 𝟙 _ ⊗ f :=
   rfl
 #align category_theory.free_monoidal_category.tensor_func_map_app CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app
 
-/- warning: category_theory.free_monoidal_category.tensor_func_obj_map -> CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.tensor_func_obj_map CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_mapₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem tensorFunc_obj_map (Z : F C) {n n' : N C} (f : n ⟶ n') :
     ((tensorFunc C).obj Z).map f = inclusion.map f ⊗ 𝟙 Z := by cases n; cases n'; tidy
 #align category_theory.free_monoidal_category.tensor_func_obj_map CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map
 
-/- warning: category_theory.free_monoidal_category.normalize_iso_app -> CategoryTheory.FreeMonoidalCategory.normalizeIsoApp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_app CategoryTheory.FreeMonoidalCategory.normalizeIsoAppₓ'. -/
 /-- Auxiliary definition for `normalize_iso`. Here we construct the isomorphism between
     `n ⊗ X` and `normalize X n`. -/
 @[simp]
@@ -238,9 +217,6 @@ def normalizeIsoApp :
     (α_ _ _ _).symm ≪≫ tensorIso (normalize_iso_app X n) (Iso.refl _) ≪≫ normalize_iso_app _ _
 #align category_theory.free_monoidal_category.normalize_iso_app CategoryTheory.FreeMonoidalCategory.normalizeIsoApp
 
-/- warning: category_theory.free_monoidal_category.normalize_iso_app_tensor -> CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_app_tensor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensorₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem normalizeIsoApp_tensor (X Y : F C) (n : N C) :
@@ -249,17 +225,11 @@ theorem normalizeIsoApp_tensor (X Y : F C) (n : N C) :
   rfl
 #align category_theory.free_monoidal_category.normalize_iso_app_tensor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor
 
-/- warning: category_theory.free_monoidal_category.normalize_iso_app_unitor -> CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitor is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_app_unitor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitorₓ'. -/
 @[simp]
 theorem normalizeIsoApp_unitor (n : N C) : normalizeIsoApp C (𝟙_ (F C)) n = ρ_ _ :=
   rfl
 #align category_theory.free_monoidal_category.normalize_iso_app_unitor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitor
 
-/- warning: category_theory.free_monoidal_category.normalize_iso_aux -> CategoryTheory.FreeMonoidalCategory.normalizeIsoAux is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_aux CategoryTheory.FreeMonoidalCategory.normalizeIsoAuxₓ'. -/
 /-- Auxiliary definition for `normalize_iso`. -/
 @[simp]
 def normalizeIsoAux (X : F C) : (tensorFunc C).obj X ≅ (normalize' C).obj X :=
@@ -270,24 +240,12 @@ section
 
 variable {D : Type u} [Category.{u} D] {I : Type u} (f : I → D) (X : Discrete I)
 
-/- warning: category_theory.free_monoidal_category.discrete_functor_obj_eq_as -> CategoryTheory.FreeMonoidalCategory.discrete_functor_obj_eq_as is a dubious translation:
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-but is expected to have type
-  forall {D : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u1, u1} D] {I : Type.{u1}} (f : I -> D) (X : CategoryTheory.Discrete.{u1} I), Eq.{succ u1} D (Prefunctor.obj.{succ u1, succ u1, u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.discreteCategory.{u1} I))) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} D (CategoryTheory.Category.toCategoryStruct.{u1, u1} D _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.discreteCategory.{u1} I) D _inst_1 (CategoryTheory.Discrete.functor.{u1, u1, u1} D _inst_1 I f)) X) (f (CategoryTheory.Discrete.as.{u1} I X))
-Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.discrete_functor_obj_eq_as CategoryTheory.FreeMonoidalCategory.discrete_functor_obj_eq_asₓ'. -/
 -- TODO: move to discrete_category.lean, decide whether this should be a global simp lemma
 @[simp]
 theorem discrete_functor_obj_eq_as : (Discrete.functor f).obj X = f X.as :=
   rfl
 #align category_theory.free_monoidal_category.discrete_functor_obj_eq_as CategoryTheory.FreeMonoidalCategory.discrete_functor_obj_eq_as
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.discrete_functor_map_eq_id CategoryTheory.FreeMonoidalCategory.discrete_functor_map_eq_idₓ'. -/
 -- TODO: move to discrete_category.lean, decide whether this should be a global simp lemma
 @[simp]
 theorem discrete_functor_map_eq_id (g : X ⟶ X) : (Discrete.functor f).map g = 𝟙 _ := by tidy

33c67ae6

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -143,30 +143,12 @@ def normalizeMapAux :
     ∀ {X Y : F C},
       (X ⟶ᵐ Y) → ((Discrete.functor (normalizeObj X) : _ ⥤ N C) ⟶ Discrete.functor (normalizeObj Y))
   | _, _, id _ => 𝟙 _
-  | _, _, α_hom _ _ _ =>
-    ⟨fun X => 𝟙 _, by
-      rintro ⟨X⟩ ⟨Y⟩ f
-      simp⟩
-  | _, _, α_inv _ _ _ =>
-    ⟨fun X => 𝟙 _, by
-      rintro ⟨X⟩ ⟨Y⟩ f
-      simp⟩
-  | _, _, l_hom _ =>
-    ⟨fun X => 𝟙 _, by
-      rintro ⟨X⟩ ⟨Y⟩ f
-      simp⟩
-  | _, _, l_inv _ =>
-    ⟨fun X => 𝟙 _, by
-      rintro ⟨X⟩ ⟨Y⟩ f
-      simp⟩
-  | _, _, ρ_hom _ =>
-    ⟨fun ⟨X⟩ => ⟨⟨by simp⟩⟩, by
-      rintro ⟨X⟩ ⟨Y⟩ f
-      simp⟩
-  | _, _, ρ_inv _ =>
-    ⟨fun ⟨X⟩ => ⟨⟨by simp⟩⟩, by
-      rintro ⟨X⟩ ⟨Y⟩ f
-      simp⟩
+  | _, _, α_hom _ _ _ => ⟨fun X => 𝟙 _, by rintro ⟨X⟩ ⟨Y⟩ f; simp⟩
+  | _, _, α_inv _ _ _ => ⟨fun X => 𝟙 _, by rintro ⟨X⟩ ⟨Y⟩ f; simp⟩
+  | _, _, l_hom _ => ⟨fun X => 𝟙 _, by rintro ⟨X⟩ ⟨Y⟩ f; simp⟩
+  | _, _, l_inv _ => ⟨fun X => 𝟙 _, by rintro ⟨X⟩ ⟨Y⟩ f; simp⟩
+  | _, _, ρ_hom _ => ⟨fun ⟨X⟩ => ⟨⟨by simp⟩⟩, by rintro ⟨X⟩ ⟨Y⟩ f; simp⟩
+  | _, _, ρ_inv _ => ⟨fun ⟨X⟩ => ⟨⟨by simp⟩⟩, by rintro ⟨X⟩ ⟨Y⟩ f; simp⟩
   | X, Y, @comp _ U V W f g => normalize_map_aux f ≫ normalize_map_aux g
   | X, Y, @hom.tensor _ T U V W f g =>
     ⟨fun X =>
@@ -222,10 +204,7 @@ def fullNormalize : F C ⥤ N C
 def tensorFunc : F C ⥤ N C ⥤ F C
     where
   obj X := Discrete.functor fun n => inclusion.obj ⟨n⟩ ⊗ X
-  map X Y f :=
-    ⟨fun n => 𝟙 _ ⊗ f, by
-      rintro ⟨X⟩ ⟨Y⟩
-      tidy⟩
+  map X Y f := ⟨fun n => 𝟙 _ ⊗ f, by rintro ⟨X⟩ ⟨Y⟩; tidy⟩
 #align category_theory.free_monoidal_category.tensor_func CategoryTheory.FreeMonoidalCategory.tensorFunc
 -/
 
@@ -242,11 +221,7 @@ theorem tensorFunc_map_app {X Y : F C} (f : X ⟶ Y) (n) : ((tensorFunc C).map f
 Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.tensor_func_obj_map CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_mapₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem tensorFunc_obj_map (Z : F C) {n n' : N C} (f : n ⟶ n') :
-    ((tensorFunc C).obj Z).map f = inclusion.map f ⊗ 𝟙 Z :=
-  by
-  cases n
-  cases n'
-  tidy
+    ((tensorFunc C).obj Z).map f = inclusion.map f ⊗ 𝟙 Z := by cases n; cases n'; tidy
 #align category_theory.free_monoidal_category.tensor_func_obj_map CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map
 
 /- warning: category_theory.free_monoidal_category.normalize_iso_app -> CategoryTheory.FreeMonoidalCategory.normalizeIsoApp is a dubious translation:
@@ -288,10 +263,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.free_m
 /-- Auxiliary definition for `normalize_iso`. -/
 @[simp]
 def normalizeIsoAux (X : F C) : (tensorFunc C).obj X ≅ (normalize' C).obj X :=
-  NatIso.ofComponents (normalizeIsoApp C X)
-    (by
-      rintro ⟨X⟩ ⟨Y⟩
-      tidy)
+  NatIso.ofComponents (normalizeIsoApp C X) (by rintro ⟨X⟩ ⟨Y⟩; tidy)
 #align category_theory.free_monoidal_category.normalize_iso_aux CategoryTheory.FreeMonoidalCategory.normalizeIsoAux
 
 section
@@ -340,26 +312,21 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
         simp only [id_tensor_associator_inv_naturality_assoc, ← pentagon_inv_assoc,
           tensor_hom_inv_id_assoc, tensor_id, category.id_comp, discrete.functor_map_id,
           comp_tensor_id, iso.cancel_iso_inv_left, category.assoc]
-        dsimp
-        simp only [category.comp_id]
+        dsimp; simp only [category.comp_id]
       · dsimp
         simp only [discrete.functor_map_id, comp_tensor_id, category.assoc, pentagon_inv_assoc, ←
           associator_inv_naturality_assoc, tensor_id, iso.cancel_iso_inv_left]
-        dsimp
-        simp only [category.comp_id]
+        dsimp; simp only [category.comp_id]
       · dsimp
         rw [triangle_assoc_comp_right_assoc]
         simp only [discrete.functor_map_id, category.assoc]
         cases n
-        dsimp
-        simp only [category.comp_id]
+        dsimp; simp only [category.comp_id]
       · dsimp
         simp only [triangle_assoc_comp_left_inv_assoc, inv_hom_id_tensor_assoc, tensor_id,
           category.id_comp, discrete.functor_map_id]
-        dsimp
-        simp only [category.comp_id]
-        cases n
-        simp
+        dsimp; simp only [category.comp_id]
+        cases n; simp
       · dsimp
         rw [← (iso.inv_comp_eq _).2 (right_unitor_tensor _ _), category.assoc, ←
           right_unitor_naturality]
@@ -375,8 +342,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
           iso.inv_hom_id_assoc]
         congr
         convert(discrete_functor_map_eq_id inclusion_obj _ _).symm
-        ext
-        rfl
+        ext; rfl
       · dsimp at *
         rw [id_tensor_comp, category.assoc, f_ih_g ⟦f_g⟧, ← category.assoc, f_ih_f ⟦f_f⟧,
           category.assoc, ← functor.map_comp]

33c67ae6

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -230,10 +230,7 @@ def tensorFunc : F C ⥤ N C ⥤ F C
 -/
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.tensor_func_map_app CategoryTheory.FreeMonoidalCategory.tensorFunc_map_appₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem tensorFunc_map_app {X Y : F C} (f : X ⟶ Y) (n) : ((tensorFunc C).map f).app n = 𝟙 _ ⊗ f :=
@@ -241,10 +238,7 @@ theorem tensorFunc_map_app {X Y : F C} (f : X ⟶ Y) (n) : ((tensorFunc C).map f
 #align category_theory.free_monoidal_category.tensor_func_map_app CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem tensorFunc_obj_map (Z : F C) {n n' : N C} (f : n ⟶ n') :
@@ -256,10 +250,7 @@ theorem tensorFunc_obj_map (Z : F C) {n n' : N C} (f : n ⟶ n') :
 #align category_theory.free_monoidal_category.tensor_func_obj_map CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_app CategoryTheory.FreeMonoidalCategory.normalizeIsoAppₓ'. -/
 /-- Auxiliary definition for `normalize_iso`. Here we construct the isomorphism between
     `n ⊗ X` and `normalize X n`. -/
@@ -273,10 +264,7 @@ def normalizeIsoApp :
 #align category_theory.free_monoidal_category.normalize_iso_app CategoryTheory.FreeMonoidalCategory.normalizeIsoApp
 
 /- warning: category_theory.free_monoidal_category.normalize_iso_app_tensor -> CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_app_tensor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensorₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
@@ -287,10 +275,7 @@ theorem normalizeIsoApp_tensor (X Y : F C) (n : N C) :
 #align category_theory.free_monoidal_category.normalize_iso_app_tensor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor
 
 /- warning: category_theory.free_monoidal_category.normalize_iso_app_unitor -> CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitor is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_app_unitor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitorₓ'. -/
 @[simp]
 theorem normalizeIsoApp_unitor (n : N C) : normalizeIsoApp C (𝟙_ (F C)) n = ρ_ _ :=
@@ -298,10 +283,7 @@ theorem normalizeIsoApp_unitor (n : N C) : normalizeIsoApp C (𝟙_ (F C)) n = 
 #align category_theory.free_monoidal_category.normalize_iso_app_unitor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitor
 
 /- warning: category_theory.free_monoidal_category.normalize_iso_aux -> CategoryTheory.FreeMonoidalCategory.normalizeIsoAux is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_aux CategoryTheory.FreeMonoidalCategory.normalizeIsoAuxₓ'. -/
 /-- Auxiliary definition for `normalize_iso`. -/
 @[simp]

33c67ae6

bump to nightly-2023-05-21-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

7b1466d5

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Markus Himmel
 
 ! This file was ported from Lean 3 source module category_theory.monoidal.free.coherence
-! leanprover-community/mathlib commit f187f1074fa1857c94589cc653c786cadc4c35ff
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
 ! 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.DiscreteCategory
 /-!
 # The monoidal coherence theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we prove the monoidal coherence theorem, stated in the following form: the free
 monoidal category over any type `C` is thin.

f187f107

bump to nightly-2023-05-19-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

58288f62

Diff

@@ -54,6 +54,7 @@ section
 
 variable (C)
 
+#print CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject /-
 /-- We say an object in the free monoidal category is in normal form if it is of the form
     `(((𝟙_ C) ⊗ X₁) ⊗ X₂) ⊗ ⋯`. -/
 @[nolint has_nonempty_instance]
@@ -61,6 +62,7 @@ inductive NormalMonoidalObject : Type u
   | Unit : normal_monoidal_object
   | tensor : normal_monoidal_object → C → normal_monoidal_object
 #align category_theory.free_monoidal_category.normal_monoidal_object CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject
+-/
 
 end
 
@@ -73,19 +75,24 @@ local notation "N" => Discrete ∘ NormalMonoidalObject
 -- mathport name: «expr ⟶ᵐ »
 local infixr:10 " ⟶ᵐ " => Hom
 
+#print CategoryTheory.FreeMonoidalCategory.inclusionObj /-
 /-- Auxiliary definition for `inclusion`. -/
 @[simp]
 def inclusionObj : NormalMonoidalObject C → F C
   | normal_monoidal_object.unit => Unit
   | normal_monoidal_object.tensor n a => tensor (inclusion_obj n) (of a)
 #align category_theory.free_monoidal_category.inclusion_obj CategoryTheory.FreeMonoidalCategory.inclusionObj
+-/
 
+#print CategoryTheory.FreeMonoidalCategory.inclusion /-
 /-- The discrete subcategory of objects in normal form includes into the free monoidal category. -/
 @[simp]
 def inclusion : N C ⥤ F C :=
   Discrete.functor inclusionObj
 #align category_theory.free_monoidal_category.inclusion CategoryTheory.FreeMonoidalCategory.inclusion
+-/
 
+#print CategoryTheory.FreeMonoidalCategory.normalizeObj /-
 /-- Auxiliary definition for `normalize`. -/
 @[simp]
 def normalizeObj : F C → NormalMonoidalObject C → N C
@@ -93,12 +100,25 @@ def normalizeObj : F C → NormalMonoidalObject C → N C
   | of X, n => ⟨NormalMonoidalObject.tensor n X⟩
   | tensor X Y, n => normalize_obj Y (normalize_obj X n).as
 #align category_theory.free_monoidal_category.normalize_obj CategoryTheory.FreeMonoidalCategory.normalizeObj
+-/
 
+/- warning: category_theory.free_monoidal_category.normalize_obj_unitor -> CategoryTheory.FreeMonoidalCategory.normalizeObj_unitor is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} (n : CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C), Eq.{succ u1} (Function.comp.{succ (succ u1), succ (succ u1), succ (succ u1)} Type.{u1} Type.{u1} Type.{u1} CategoryTheory.Discrete.{u1} CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C) (CategoryTheory.FreeMonoidalCategory.normalizeObj.{u1} C (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u1} (CategoryTheory.FreeMonoidalCategory.{u1} C) (CategoryTheory.FreeMonoidalCategory.categoryFreeMonoidalCategory.{u1} C) (CategoryTheory.FreeMonoidalCategory.CategoryTheory.monoidalCategory.{u1} C)) n) (CategoryTheory.Discrete.mk.{u1} (CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C) n)
+but is expected to have type
+  forall {C : Type.{u1}} (n : CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C), Eq.{succ u1} (Function.comp.{succ (succ u1), succ (succ u1), succ (succ u1)} Type.{u1} Type.{u1} Type.{u1} CategoryTheory.Discrete.{u1} CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C) (CategoryTheory.FreeMonoidalCategory.normalizeObj.{u1} C (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u1} (CategoryTheory.FreeMonoidalCategory.{u1} C) (CategoryTheory.FreeMonoidalCategory.categoryFreeMonoidalCategory.{u1} C) (CategoryTheory.FreeMonoidalCategory.instMonoidalCategoryFreeMonoidalCategoryCategoryFreeMonoidalCategory.{u1} C)) n) (CategoryTheory.Discrete.mk.{u1} (CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C) n)
+Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_obj_unitor CategoryTheory.FreeMonoidalCategory.normalizeObj_unitorₓ'. -/
 @[simp]
 theorem normalizeObj_unitor (n : NormalMonoidalObject C) : normalizeObj (𝟙_ (F C)) n = ⟨n⟩ :=
   rfl
 #align category_theory.free_monoidal_category.normalize_obj_unitor CategoryTheory.FreeMonoidalCategory.normalizeObj_unitor
 
+/- warning: category_theory.free_monoidal_category.normalize_obj_tensor -> CategoryTheory.FreeMonoidalCategory.normalizeObj_tensor is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} (X : CategoryTheory.FreeMonoidalCategory.{u1} C) (Y : CategoryTheory.FreeMonoidalCategory.{u1} C) (n : CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C), Eq.{succ u1} (Function.comp.{succ (succ u1), succ (succ u1), succ (succ u1)} Type.{u1} Type.{u1} Type.{u1} CategoryTheory.Discrete.{u1} CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C) (CategoryTheory.FreeMonoidalCategory.normalizeObj.{u1} C (CategoryTheory.MonoidalCategory.tensorObj.{u1, u1} (CategoryTheory.FreeMonoidalCategory.{u1} C) (CategoryTheory.FreeMonoidalCategory.categoryFreeMonoidalCategory.{u1} C) (CategoryTheory.FreeMonoidalCategory.CategoryTheory.monoidalCategory.{u1} C) X Y) n) (CategoryTheory.FreeMonoidalCategory.normalizeObj.{u1} C Y (CategoryTheory.Discrete.as.{u1} (CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C) (CategoryTheory.FreeMonoidalCategory.normalizeObj.{u1} C X n)))
+but is expected to have type
+  forall {C : Type.{u1}} (X : CategoryTheory.FreeMonoidalCategory.{u1} C) (Y : CategoryTheory.FreeMonoidalCategory.{u1} C) (n : CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C), Eq.{succ u1} (Function.comp.{succ (succ u1), succ (succ u1), succ (succ u1)} Type.{u1} Type.{u1} Type.{u1} CategoryTheory.Discrete.{u1} CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C) (CategoryTheory.FreeMonoidalCategory.normalizeObj.{u1} C (CategoryTheory.MonoidalCategory.tensorObj.{u1, u1} (CategoryTheory.FreeMonoidalCategory.{u1} C) (CategoryTheory.FreeMonoidalCategory.categoryFreeMonoidalCategory.{u1} C) (CategoryTheory.FreeMonoidalCategory.instMonoidalCategoryFreeMonoidalCategoryCategoryFreeMonoidalCategory.{u1} C) X Y) n) (CategoryTheory.FreeMonoidalCategory.normalizeObj.{u1} C Y (CategoryTheory.Discrete.as.{u1} (CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u1} C) (CategoryTheory.FreeMonoidalCategory.normalizeObj.{u1} C X n)))
+Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_obj_tensor CategoryTheory.FreeMonoidalCategory.normalizeObj_tensorₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem normalizeObj_tensor (X Y : F C) (n : NormalMonoidalObject C) :
@@ -112,6 +132,7 @@ open Hom
 
 attribute [local tidy] tactic.discrete_cases
 
+#print CategoryTheory.FreeMonoidalCategory.normalizeMapAux /-
 /-- Auxiliary definition for `normalize`. Here we prove that objects that are related by
     associators and unitors map to the same normal form. -/
 @[simp]
@@ -150,6 +171,7 @@ def normalizeMapAux :
         (Discrete.functor (normalizeObj W) : _ ⥤ N C).map ((normalize_map_aux f).app X),
       by tidy⟩
 #align category_theory.free_monoidal_category.normalize_map_aux CategoryTheory.FreeMonoidalCategory.normalizeMapAux
+-/
 
 end
 
@@ -157,6 +179,7 @@ section
 
 variable (C)
 
+#print CategoryTheory.FreeMonoidalCategory.normalize /-
 /-- Our normalization procedure works by first defining a functor `F C ⥤ (N C ⥤ N C)` (which turns
     out to be very easy), and then obtain a functor `F C ⥤ N C` by plugging in the normal object
     `𝟙_ C`. -/
@@ -166,7 +189,9 @@ def normalize : F C ⥤ N C ⥤ N C
   obj X := Discrete.functor (normalizeObj X)
   map X Y := Quotient.lift normalizeMapAux (by tidy)
 #align category_theory.free_monoidal_category.normalize CategoryTheory.FreeMonoidalCategory.normalize
+-/
 
+#print CategoryTheory.FreeMonoidalCategory.normalize' /-
 /-- A variant of the normalization functor where we consider the result as an object in the free
     monoidal category (rather than an object of the discrete subcategory of objects in normal
     form). -/
@@ -174,16 +199,20 @@ def normalize : F C ⥤ N C ⥤ N C
 def normalize' : F C ⥤ N C ⥤ F C :=
   normalize C ⋙ (whiskeringRight _ _ _).obj inclusion
 #align category_theory.free_monoidal_category.normalize' CategoryTheory.FreeMonoidalCategory.normalize'
+-/
 
+#print CategoryTheory.FreeMonoidalCategory.fullNormalize /-
 /-- The normalization functor for the free monoidal category over `C`. -/
 def fullNormalize : F C ⥤ N C
     where
-  obj X := ((normalize C).obj X).obj ⟨NormalMonoidalObject.unit⟩
-  map X Y f := ((normalize C).map f).app ⟨NormalMonoidalObject.unit⟩
+  obj X := ((normalize C).obj X).obj ⟨NormalMonoidalObject.Unit⟩
+  map X Y f := ((normalize C).map f).app ⟨NormalMonoidalObject.Unit⟩
 #align category_theory.free_monoidal_category.full_normalize CategoryTheory.FreeMonoidalCategory.fullNormalize
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.FreeMonoidalCategory.tensorFunc /-
 /-- Given an object `X` of the free monoidal category and an object `n` in normal form, taking
     the tensor product `n ⊗ X` in the free monoidal category is functorial in both `X` and `n`. -/
 @[simp]
@@ -195,12 +224,25 @@ def tensorFunc : F C ⥤ N C ⥤ F C
       rintro ⟨X⟩ ⟨Y⟩
       tidy⟩
 #align category_theory.free_monoidal_category.tensor_func CategoryTheory.FreeMonoidalCategory.tensorFunc
+-/
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem tensorFunc_map_app {X Y : F C} (f : X ⟶ Y) (n) : ((tensorFunc C).map f).app n = 𝟙 _ ⊗ f :=
   rfl
 #align category_theory.free_monoidal_category.tensor_func_map_app CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.tensor_func_obj_map CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_mapₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem tensorFunc_obj_map (Z : F C) {n n' : N C} (f : n ⟶ n') :
     ((tensorFunc C).obj Z).map f = inclusion.map f ⊗ 𝟙 Z :=
@@ -210,6 +252,12 @@ theorem tensorFunc_obj_map (Z : F C) {n n' : N C} (f : n ⟶ n') :
   tidy
 #align category_theory.free_monoidal_category.tensor_func_obj_map CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_app CategoryTheory.FreeMonoidalCategory.normalizeIsoAppₓ'. -/
 /-- Auxiliary definition for `normalize_iso`. Here we construct the isomorphism between
     `n ⊗ X` and `normalize X n`. -/
 @[simp]
@@ -221,6 +269,12 @@ def normalizeIsoApp :
     (α_ _ _ _).symm ≪≫ tensorIso (normalize_iso_app X n) (Iso.refl _) ≪≫ normalize_iso_app _ _
 #align category_theory.free_monoidal_category.normalize_iso_app CategoryTheory.FreeMonoidalCategory.normalizeIsoApp
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_app_tensor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensorₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem normalizeIsoApp_tensor (X Y : F C) (n : N C) :
@@ -229,11 +283,23 @@ theorem normalizeIsoApp_tensor (X Y : F C) (n : N C) :
   rfl
 #align category_theory.free_monoidal_category.normalize_iso_app_tensor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_app_unitor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitorₓ'. -/
 @[simp]
 theorem normalizeIsoApp_unitor (n : N C) : normalizeIsoApp C (𝟙_ (F C)) n = ρ_ _ :=
   rfl
 #align category_theory.free_monoidal_category.normalize_iso_app_unitor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_unitor
 
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(CategoryTheory.FreeMonoidalCategory.categoryFreeMonoidalCategory.{u1} C)) (CategoryTheory.FreeMonoidalCategory.normalize'.{u1} C)) X)
+Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.normalize_iso_aux CategoryTheory.FreeMonoidalCategory.normalizeIsoAuxₓ'. -/
 /-- Auxiliary definition for `normalize_iso`. -/
 @[simp]
 def normalizeIsoAux (X : F C) : (tensorFunc C).obj X ≅ (normalize' C).obj X :=
@@ -247,12 +313,24 @@ section
 
 variable {D : Type u} [Category.{u} D] {I : Type u} (f : I → D) (X : Discrete I)
 
+/- warning: category_theory.free_monoidal_category.discrete_functor_obj_eq_as -> CategoryTheory.FreeMonoidalCategory.discrete_functor_obj_eq_as is a dubious translation:
+lean 3 declaration is
+  forall {D : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u1, u1} D] {I : Type.{u1}} (f : I -> D) (X : CategoryTheory.Discrete.{u1} I), Eq.{succ u1} D (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.discreteCategory.{u1} I) D _inst_1 (CategoryTheory.Discrete.functor.{u1, u1, u1} D _inst_1 I f) X) (f (CategoryTheory.Discrete.as.{u1} I X))
+but is expected to have type
+  forall {D : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u1, u1} D] {I : Type.{u1}} (f : I -> D) (X : CategoryTheory.Discrete.{u1} I), Eq.{succ u1} D (Prefunctor.obj.{succ u1, succ u1, u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.discreteCategory.{u1} I))) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} D (CategoryTheory.Category.toCategoryStruct.{u1, u1} D _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.discreteCategory.{u1} I) D _inst_1 (CategoryTheory.Discrete.functor.{u1, u1, u1} D _inst_1 I f)) X) (f (CategoryTheory.Discrete.as.{u1} I X))
+Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.discrete_functor_obj_eq_as CategoryTheory.FreeMonoidalCategory.discrete_functor_obj_eq_asₓ'. -/
 -- TODO: move to discrete_category.lean, decide whether this should be a global simp lemma
 @[simp]
 theorem discrete_functor_obj_eq_as : (Discrete.functor f).obj X = f X.as :=
   rfl
 #align category_theory.free_monoidal_category.discrete_functor_obj_eq_as CategoryTheory.FreeMonoidalCategory.discrete_functor_obj_eq_as
 
+/- warning: category_theory.free_monoidal_category.discrete_functor_map_eq_id -> CategoryTheory.FreeMonoidalCategory.discrete_functor_map_eq_id is a dubious translation:
+lean 3 declaration is
+  forall {D : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u1, u1} D] {I : Type.{u1}} (f : I -> D) (X : CategoryTheory.Discrete.{u1} I) (g : Quiver.Hom.{succ u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.discreteCategory.{u1} I))) X X), Eq.{succ u1} (Quiver.Hom.{succ u1, u1} D (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} D (CategoryTheory.Category.toCategoryStruct.{u1, u1} D _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.discreteCategory.{u1} I) D _inst_1 (CategoryTheory.Discrete.functor.{u1, u1, u1} D _inst_1 I f) X) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.discreteCategory.{u1} I) D _inst_1 (CategoryTheory.Discrete.functor.{u1, u1, u1} D _inst_1 I f) X)) (CategoryTheory.Functor.map.{u1, u1, u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.discreteCategory.{u1} I) D _inst_1 (CategoryTheory.Discrete.functor.{u1, u1, u1} D _inst_1 I f) X X g) (CategoryTheory.CategoryStruct.id.{u1, u1} D (CategoryTheory.Category.toCategoryStruct.{u1, u1} D _inst_1) (CategoryTheory.Functor.obj.{u1, u1, u1, u1} (CategoryTheory.Discrete.{u1} I) (CategoryTheory.discreteCategory.{u1} I) D _inst_1 (CategoryTheory.Discrete.functor.{u1, u1, u1} D _inst_1 I f) X))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.free_monoidal_category.discrete_functor_map_eq_id CategoryTheory.FreeMonoidalCategory.discrete_functor_map_eq_idₓ'. -/
 -- TODO: move to discrete_category.lean, decide whether this should be a global simp lemma
 @[simp]
 theorem discrete_functor_map_eq_id (g : X ⟶ X) : (Discrete.functor f).map g = 𝟙 _ := by tidy
@@ -260,6 +338,7 @@ theorem discrete_functor_map_eq_id (g : X ⟶ X) : (Discrete.functor f).map g =
 
 end
 
+#print CategoryTheory.FreeMonoidalCategory.normalizeIso /-
 /-- The isomorphism between `n ⊗ X` and `normalize X n` is natural (in both `X` and `n`, but
     naturality in `n` is trivial and was "proved" in `normalize_iso_aux`). This is the real heart
     of our proof of the coherence theorem. -/
@@ -334,11 +413,13 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
         convert(normalize_iso_aux C f_Z).Hom.naturality ((normalize_map_aux f_f).app n)
         exact (tensor_func_obj_map _ _ _).symm)
 #align category_theory.free_monoidal_category.normalize_iso CategoryTheory.FreeMonoidalCategory.normalizeIso
+-/
 
+#print CategoryTheory.FreeMonoidalCategory.fullNormalizeIso /-
 /-- The isomorphism between an object and its normal form is natural. -/
 def fullNormalizeIso : 𝟭 (F C) ≅ fullNormalize C ⋙ inclusion :=
   NatIso.ofComponents
-    (fun X => (λ_ X).symm ≪≫ ((normalizeIso C).app X).app ⟨NormalMonoidalObject.unit⟩)
+    (fun X => (λ_ X).symm ≪≫ ((normalizeIso C).app X).app ⟨NormalMonoidalObject.Unit⟩)
     (by
       intro X Y f
       dsimp
@@ -347,9 +428,11 @@ def fullNormalizeIso : 𝟭 (F C) ≅ fullNormalize C ⋙ inclusion :=
         congr_arg (fun f => nat_trans.app f (discrete.mk normal_monoidal_object.unit))
           ((normalizeIso.{u} C).Hom.naturality f))
 #align category_theory.free_monoidal_category.full_normalize_iso CategoryTheory.FreeMonoidalCategory.fullNormalizeIso
+-/
 
 end
 
+#print CategoryTheory.FreeMonoidalCategory.subsingleton_hom /-
 /-- The monoidal coherence theorem. -/
 instance subsingleton_hom : Quiver.IsThin (F C) := fun _ _ =>
   ⟨fun f g =>
@@ -358,6 +441,7 @@ instance subsingleton_hom : Quiver.IsThin (F C) := fun _ _ =>
     rw [← functor.id_map f, ← functor.id_map g]
     simp [← nat_iso.naturality_2 (fullNormalizeIso.{u} C), this]⟩
 #align category_theory.free_monoidal_category.subsingleton_hom CategoryTheory.FreeMonoidalCategory.subsingleton_hom
+-/
 
 section Groupoid
 
@@ -365,6 +449,7 @@ section
 
 open Hom
 
+#print CategoryTheory.FreeMonoidalCategory.inverseAux /-
 /-- Auxiliary construction for showing that the free monoidal category is a groupoid. Do not use
     this, use `is_iso.inv` instead. -/
 def inverseAux : ∀ {X Y : F C}, (X ⟶ᵐ Y) → (Y ⟶ᵐ X)
@@ -378,6 +463,7 @@ def inverseAux : ∀ {X Y : F C}, (X ⟶ᵐ Y) → (Y ⟶ᵐ X)
   | _, _, comp f g => (inverse_aux g).comp (inverse_aux f)
   | _, _, hom.tensor f g => (inverse_aux f).tensor (inverse_aux g)
 #align category_theory.free_monoidal_category.inverse_aux CategoryTheory.FreeMonoidalCategory.inverseAux
+-/
 
 end

f187f107

bump to nightly-2023-05-03-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

02121ccc

Diff

@@ -76,7 +76,7 @@ local infixr:10 " ⟶ᵐ " => Hom
 /-- Auxiliary definition for `inclusion`. -/
 @[simp]
 def inclusionObj : NormalMonoidalObject C → F C
-  | normal_monoidal_object.unit => unit
+  | normal_monoidal_object.unit => Unit
   | normal_monoidal_object.tensor n a => tensor (inclusion_obj n) (of a)
 #align category_theory.free_monoidal_category.inclusion_obj CategoryTheory.FreeMonoidalCategory.inclusionObj

f187f107

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -301,7 +301,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
           right_unitor_naturality]
         simp only [iso.cancel_iso_inv_left, category.assoc]
         congr 1
-        convert (category.comp_id _).symm
+        convert(category.comp_id _).symm
         convert discrete_functor_map_eq_id inclusion_obj _ _
         ext
         rfl
@@ -310,7 +310,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
           category.assoc, iso.hom_inv_id, iso.hom_inv_id_assoc, iso.inv_hom_id,
           iso.inv_hom_id_assoc]
         congr
-        convert (discrete_functor_map_eq_id inclusion_obj _ _).symm
+        convert(discrete_functor_map_eq_id inclusion_obj _ _).symm
         ext
         rfl
       · dsimp at *
@@ -331,7 +331,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
         dsimp
         simp only [category.assoc, category.comp_id]
         congr 1
-        convert (normalize_iso_aux C f_Z).Hom.naturality ((normalize_map_aux f_f).app n)
+        convert(normalize_iso_aux C f_Z).Hom.naturality ((normalize_map_aux f_f).app n)
         exact (tensor_func_obj_map _ _ _).symm)
 #align category_theory.free_monoidal_category.normalize_iso CategoryTheory.FreeMonoidalCategory.normalizeIso

f187f107

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f187f107

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

@@ -53,7 +53,7 @@ variable (C)
 
 /-- We say an object in the free monoidal category is in normal form if it is of the form
     `(((𝟙_ C) ⊗ X₁) ⊗ X₂) ⊗ ⋯`. -/
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 inductive NormalMonoidalObject : Type u
   | unit : NormalMonoidalObject
   | tensor : NormalMonoidalObject → C → NormalMonoidalObject

f187f107

feat(CategoryTheory/Monoidal): add whiskerings to free monoidal categories (#11172)

Since the coherence tactic assume that a certain defeq property holds for structural morphisms in a monoidal category and their corresponding morphisms in the free monoidal category, we want free monoidal categories to have the whiskering operators as primitives.

This PR also simplified the proof of the coherence theorem, and removed some porting notes.

1029b4ff

Diff

@@ -78,43 +78,51 @@ def inclusionObj : NormalMonoidalObject C → F C
 #align category_theory.free_monoidal_category.inclusion_obj CategoryTheory.FreeMonoidalCategory.inclusionObj
 
 /-- The discrete subcategory of objects in normal form includes into the free monoidal category. -/
-@[simp]
 def inclusion : N C ⥤ F C :=
   Discrete.functor inclusionObj
 #align category_theory.free_monoidal_category.inclusion CategoryTheory.FreeMonoidalCategory.inclusion
 
-/-- Auxiliary definition for `normalize`. -/
 @[simp]
-def normalizeObj : F C → NormalMonoidalObject C → N C
-  | unit, n => ⟨n⟩
-  | of X, n => ⟨NormalMonoidalObject.tensor n X⟩
-  | tensor X Y, n => normalizeObj Y (normalizeObj X n).as
+theorem inclusion_obj (X : N C) :
+    inclusion.obj X = inclusionObj X.as :=
+  rfl
+
+@[simp]
+theorem inclusion_map {X Y : N C} (f : X ⟶ Y) :
+    inclusion.map f = eqToHom (congr_arg _ (Discrete.ext _ _ (Discrete.eq_of_hom f))) := by
+  rcases f with ⟨⟨⟩⟩
+  cases Discrete.ext _ _ (by assumption)
+  apply inclusion.map_id
+
+/-- Auxiliary definition for `normalize`. -/
+def normalizeObj : F C → NormalMonoidalObject C → NormalMonoidalObject C
+  | unit, n => n
+  | of X, n => NormalMonoidalObject.tensor n X
+  | tensor X Y, n => normalizeObj Y (normalizeObj X n)
 #align category_theory.free_monoidal_category.normalize_obj CategoryTheory.FreeMonoidalCategory.normalizeObj
 
 @[simp]
-theorem normalizeObj_unitor (n : NormalMonoidalObject C) : normalizeObj (𝟙_ (F C)) n = ⟨n⟩ :=
+theorem normalizeObj_unitor (n : NormalMonoidalObject C) : normalizeObj (𝟙_ (F C)) n = n :=
   rfl
 #align category_theory.free_monoidal_category.normalize_obj_unitor CategoryTheory.FreeMonoidalCategory.normalizeObj_unitor
 
 @[simp]
 theorem normalizeObj_tensor (X Y : F C) (n : NormalMonoidalObject C) :
-    normalizeObj (X ⊗ Y) n = normalizeObj Y (normalizeObj X n).as :=
+    normalizeObj (X ⊗ Y) n = normalizeObj Y (normalizeObj X n) :=
   rfl
 #align category_theory.free_monoidal_category.normalize_obj_tensor CategoryTheory.FreeMonoidalCategory.normalizeObj_tensor
 
+/-- Auxiliary definition for `normalize`. -/
+def normalizeObj' (X : F C) : N C ⥤ N C := Discrete.functor fun n ↦ ⟨normalizeObj X n⟩
+
 section
 
 open Hom
 
--- Porting note: triggers a PANIC "invalid LCNF substitution of free variable
--- with expression CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u}"
--- prevented with an initial call to dsimp...why?
 /-- Auxiliary definition for `normalize`. Here we prove that objects that are related by
     associators and unitors map to the same normal form. -/
 @[simp]
-def normalizeMapAux :
-    ∀ {X Y : F C}, (X ⟶ᵐ Y) →
-      ((Discrete.functor (normalizeObj X) : _ ⥤ N C) ⟶ Discrete.functor (normalizeObj Y))
+def normalizeMapAux : ∀ {X Y : F C}, (X ⟶ᵐ Y) → (normalizeObj' X ⟶ normalizeObj' Y)
   | _, _, Hom.id _ => 𝟙 _
   | _, _, α_hom X Y Z => by dsimp; exact Discrete.natTrans (fun _ => 𝟙 _)
   | _, _, α_inv _ _ _ => by dsimp; exact Discrete.natTrans (fun _ => 𝟙 _)
@@ -123,10 +131,13 @@ def normalizeMapAux :
   | _, _, ρ_hom _ => by dsimp; exact Discrete.natTrans (fun _ => 𝟙 _)
   | _, _, ρ_inv _ => by dsimp; exact Discrete.natTrans (fun _ => 𝟙 _)
   | _, _, (@comp _ _ _ _ f g) => normalizeMapAux f ≫ normalizeMapAux g
-  | _, _, (@Hom.tensor _ T _ _ W f g) => by
-    dsimp
-    exact Discrete.natTrans (fun ⟨X⟩ => (normalizeMapAux g).app (normalizeObj T X) ≫
-      (Discrete.functor (normalizeObj W) : _ ⥤ N C).map ((normalizeMapAux f).app ⟨X⟩))
+  | _, _, (@Hom.tensor _ T _ _ W f g) =>
+    Discrete.natTrans <| fun ⟨X⟩ => (normalizeMapAux g).app ⟨normalizeObj T X⟩ ≫
+      (normalizeObj' W).map ((normalizeMapAux f).app ⟨X⟩)
+  | _, _, (@Hom.whiskerLeft _ T _ W f) =>
+    Discrete.natTrans <| fun ⟨X⟩ => (normalizeMapAux f).app ⟨normalizeObj T X⟩
+  | _, _, (@Hom.whiskerRight _ T _ f W) =>
+    Discrete.natTrans <| fun X => (normalizeObj' W).map <| (normalizeMapAux f).app X
 #align category_theory.free_monoidal_category.normalize_map_aux CategoryTheory.FreeMonoidalCategory.normalizeMapAux
 
 end
@@ -140,7 +151,7 @@ variable (C)
     `𝟙_ C`. -/
 @[simp]
 def normalize : F C ⥤ N C ⥤ N C where
-  obj X := Discrete.functor (normalizeObj X)
+  obj X := normalizeObj' X
   map {X Y} := Quotient.lift normalizeMapAux (by aesop_cat)
 #align category_theory.free_monoidal_category.normalize CategoryTheory.FreeMonoidalCategory.normalize
 
@@ -166,7 +177,7 @@ def tensorFunc : F C ⥤ N C ⥤ F C where
   map f := Discrete.natTrans (fun n => _ ◁ f)
 #align category_theory.free_monoidal_category.tensor_func CategoryTheory.FreeMonoidalCategory.tensorFunc
 
-theorem tensorFunc_map_app {X Y : F C} (f : X ⟶ Y) (n) : ((tensorFunc C).map f).app n = 𝟙 _ ⊗ f :=
+theorem tensorFunc_map_app {X Y : F C} (f : X ⟶ Y) (n) : ((tensorFunc C).map f).app n = _ ◁ f :=
   rfl
 #align category_theory.free_monoidal_category.tensor_func_map_app CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app
 
@@ -188,14 +199,34 @@ def normalizeIsoApp :
     ∀ (X : F C) (n : N C), ((tensorFunc C).obj X).obj n ≅ ((normalize' C).obj X).obj n
   | of _, _ => Iso.refl _
   | unit, _ => ρ_ _
-  | tensor X _, n =>
-    (α_ _ _ _).symm ≪≫ tensorIso (normalizeIsoApp X n) (Iso.refl _) ≪≫ normalizeIsoApp _ _
+  | tensor X a, n =>
+    (α_ _ _ _).symm ≪≫ whiskerRightIso (normalizeIsoApp X n) a ≪≫ normalizeIsoApp _ _
 #align category_theory.free_monoidal_category.normalize_iso_app CategoryTheory.FreeMonoidalCategory.normalizeIsoApp
 
+/-- Almost non-definitionally equall to `normalizeIsoApp`, but has a better definitional property
+in the proof of `normalize_naturality`. -/
+@[simp]
+def normalizeIsoApp' :
+    ∀ (X : F C) (n : NormalMonoidalObject C), inclusionObj n ⊗ X ≅ inclusionObj (normalizeObj X n)
+  | of _, _ => Iso.refl _
+  | unit, _ => ρ_ _
+  | tensor X Y, n =>
+    (α_ _ _ _).symm ≪≫ whiskerRightIso (normalizeIsoApp' X n) Y ≪≫ normalizeIsoApp' _ _
+
+theorem normalizeIsoApp_eq :
+    ∀ (X : F C) (n : N C), normalizeIsoApp C X n = normalizeIsoApp' C X n.as
+  | of X, _ => rfl
+  | unit, _ => rfl
+  | tensor X Y, n => by
+      rw [normalizeIsoApp, normalizeIsoApp']
+      rw [normalizeIsoApp_eq X n]
+      rw [normalizeIsoApp_eq Y ⟨normalizeObj X n.as⟩]
+      rfl
+
 @[simp]
 theorem normalizeIsoApp_tensor (X Y : F C) (n : N C) :
     normalizeIsoApp C (X ⊗ Y) n =
-      (α_ _ _ _).symm ≪≫ tensorIso (normalizeIsoApp C X n) (Iso.refl _) ≪≫ normalizeIsoApp _ _ _ :=
+      (α_ _ _ _).symm ≪≫ whiskerRightIso (normalizeIsoApp C X n) Y ≪≫ normalizeIsoApp _ _ _ :=
   rfl
 #align category_theory.free_monoidal_category.normalize_iso_app_tensor CategoryTheory.FreeMonoidalCategory.normalizeIsoApp_tensor
 
@@ -233,84 +264,58 @@ theorem discrete_functor_map_eq_id (g : X ⟶ X) : (Discrete.functor f).map g =
 
 end
 
+section
+
+variable {C}
+
+theorem normalizeObj_congr (n : NormalMonoidalObject C) {X Y : F C} (f : X ⟶ Y) :
+    normalizeObj X n = normalizeObj Y n := by
+  rcases f with ⟨f'⟩
+  apply @congr_fun _ _ fun n => normalizeObj X n
+  clear n f
+  induction f' with
+  | comp _ _ _ _ => apply Eq.trans <;> assumption
+  | whiskerLeft  _ _ ih => funext; apply congr_fun ih
+  | whiskerRight _ _ ih => funext; apply congr_arg₂ _ rfl (congr_fun ih _)
+  | @tensor W X Y Z _ _ ih₁ ih₂ =>
+      funext n
+      simp [congr_fun ih₁ n, congr_fun ih₂ (normalizeObj Y n)]
+  | _ => funext; rfl
+
+theorem normalize_naturality (n : NormalMonoidalObject C) {X Y : F C} (f : X ⟶ Y) :
+    inclusionObj n ◁ f ≫ (normalizeIsoApp' C Y n).hom =
+      (normalizeIsoApp' C X n).hom ≫
+        inclusion.map (eqToHom (Discrete.ext _ _ (normalizeObj_congr n f))) := by
+  revert n
+  induction f using Hom.inductionOn
+  case comp f g ihf ihg => simp [ihg, reassoc_of% (ihf _)]
+  case whiskerLeft X' X Y f ih =>
+    intro n
+    dsimp only [normalizeObj_tensor, normalizeIsoApp', tensor_eq_tensor, Iso.trans_hom,
+      Iso.symm_hom, whiskerRightIso_hom, Function.comp_apply, inclusion_obj]
+    rw [associator_inv_naturality_right_assoc, whisker_exchange_assoc, ih]
+    simp
+  case whiskerRight X Y h η' ih =>
+    intro n
+    dsimp only [normalizeObj_tensor, normalizeIsoApp', tensor_eq_tensor, Iso.trans_hom,
+      Iso.symm_hom, whiskerRightIso_hom, Function.comp_apply, inclusion_obj]
+    rw [associator_inv_naturality_middle_assoc, ← comp_whiskerRight_assoc, ih]
+    have := dcongr_arg (fun x => (normalizeIsoApp' C η' x).hom) (normalizeObj_congr n h)
+    simp [this]
+  all_goals simp
+
+end
+
 set_option tactic.skipAssignedInstances false in
 /-- The isomorphism between `n ⊗ X` and `normalize X n` is natural (in both `X` and `n`, but
     naturality in `n` is trivial and was "proved" in `normalizeIsoAux`). This is the real heart
     of our proof of the coherence theorem. -/
 def normalizeIso : tensorFunc C ≅ normalize' C :=
-  NatIso.ofComponents (normalizeIsoAux C)
-    (by -- Porting note: the proof has been mostly rewritten
-      rintro X Y f
-      induction' f using Quotient.recOn with f; swap; rfl
-      induction' f with _ X₁ X₂ X₃ _ _ _ _ _ _ _ _ _ _ _ _ h₁ h₂ X₁ X₂ Y₁ Y₂ f g h₁ h₂
-      · simp only [mk_id, Functor.map_id, Category.comp_id, Category.id_comp]
-      · ext n
-        dsimp
-        rw [mk_α_hom, NatTrans.comp_app, NatTrans.comp_app]
-        dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp only [comp_tensor_id, associator_conjugation, tensor_id,
-          Category.comp_id]
-        simp only [← Category.assoc]
-        congr 4
-        rw [← cancel_epi ((inclusionObj n.as) ◁ (α_ X₁ X₂ X₃).inv)]
-        simp
-      · ext n
-        dsimp
-        rw [mk_α_inv, NatTrans.comp_app, NatTrans.comp_app]
-        dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp [tensorHom_id, comp_whiskerRight, Category.assoc, pentagon_inv_assoc,
-          whiskerRight_tensor, Category.comp_id, Iso.cancel_iso_inv_left]
-        erw [Iso.hom_inv_id_assoc]
-      · ext n
-        dsimp [Functor.comp]
-        rw [mk_l_hom, NatTrans.comp_app, NatTrans.comp_app]
-        dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp only [tensorHom_id, triangle_assoc_comp_right_assoc, Category.comp_id]
-        rfl
-      · ext n
-        dsimp [Functor.comp]
-        rw [mk_l_inv, NatTrans.comp_app, NatTrans.comp_app]
-        dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp only [tensorHom_id, triangle_assoc_comp_right_assoc, whiskerLeft_inv_hom_assoc,
-          Category.comp_id]
-        rfl
-      · ext n
-        dsimp
-        rw [mk_ρ_hom, NatTrans.comp_app, NatTrans.comp_app]
-        dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp only [whiskerLeft_rightUnitor, Category.assoc, tensorHom_id,
-          MonoidalCategory.whiskerRight_id, Category.comp_id, Iso.cancel_iso_inv_left,
-          Iso.cancel_iso_hom_left]
-        erw [Iso.inv_hom_id, Category.comp_id]
-      · ext n
-        dsimp
-        rw [mk_ρ_inv, NatTrans.comp_app, NatTrans.comp_app]
-        dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp only [whiskerLeft_rightUnitor_inv, tensorHom_id, MonoidalCategory.whiskerRight_id,
-          Category.assoc, Iso.hom_inv_id_assoc, Iso.inv_hom_id_assoc, Category.comp_id]
-        erw [Iso.inv_hom_id, Category.comp_id]
-      · rw [mk_comp, Functor.map_comp, Functor.map_comp, Category.assoc, h₂, reassoc_of% h₁]
-      · ext ⟨n⟩
-        replace h₁ := NatTrans.congr_app h₁ ⟨n⟩
-        replace h₂ := NatTrans.congr_app h₂ ((Discrete.functor (normalizeObj X₁)).obj ⟨n⟩)
-        have h₃ := (normalizeIsoAux _ Y₂).hom.naturality ((normalizeMapAux f).app ⟨n⟩)
-        have h₄ : ∀ (X₃ Y₃ : N C) (φ : X₃ ⟶ Y₃), (Discrete.functor inclusionObj).map φ ⊗ 𝟙 Y₂ =
-            (Discrete.functor fun n ↦ inclusionObj n ⊗ Y₂).map φ := by
-          rintro ⟨X₃⟩ ⟨Y₃⟩ φ
-          obtain rfl : X₃ = Y₃ := φ.1.1
-          simp only [discrete_functor_map_eq_id, tensor_id]
-          rfl
-        rw [NatTrans.comp_app, NatTrans.comp_app] at h₁ h₂ ⊢
-        dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight,
-          Functor.comp, Discrete.natTrans] at h₁ h₂ h₃ ⊢
-        simp only [← id_tensorHom, ← tensorHom_id] at h₁ ⊢
-        rw [mk_tensor, associator_inv_naturality_assoc, ← tensor_comp_assoc, h₁,
-          Category.assoc, Category.comp_id, ← @Category.id_comp (F C) _ _ _ (@Quotient.mk _ _ g),
-          tensor_comp, Category.assoc, Category.assoc, Functor.map_comp]
-        congr 2
-        erw [← reassoc_of% h₂]
-        rw [← h₃, ← Category.assoc, ← id_tensor_comp_tensor_id, h₄]
-        rfl)
+  NatIso.ofComponents (normalizeIsoAux C) <| by
+    intro X Y f
+    ext ⟨n⟩
+    convert normalize_naturality n f using 1
+    any_goals dsimp [NatIso.ofComponents]; congr; apply normalizeIsoApp_eq
 #align category_theory.free_monoidal_category.normalize_iso CategoryTheory.FreeMonoidalCategory.normalizeIso
 
 /-- The isomorphism between an object and its normal form is natural. -/
@@ -354,6 +359,8 @@ def inverseAux : ∀ {X Y : F C}, (X ⟶ᵐ Y) → (Y ⟶ᵐ X)
   | _, _, l_hom _ => l_inv _
   | _, _, l_inv _ => l_hom _
   | _, _, comp f g => (inverseAux g).comp (inverseAux f)
+  | _, _, Hom.whiskerLeft X f => (inverseAux f).whiskerLeft X
+  | _, _, Hom.whiskerRight f X => (inverseAux f).whiskerRight X
   | _, _, Hom.tensor f g => (inverseAux f).tensor (inverseAux g)
 #align category_theory.free_monoidal_category.inverse_aux CategoryTheory.FreeMonoidalCategory.inverseAux

f187f107

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -233,6 +233,7 @@ theorem discrete_functor_map_eq_id (g : X ⟶ X) : (Discrete.functor f).map g =
 
 end
 
+set_option tactic.skipAssignedInstances false in
 /-- The isomorphism between `n ⊗ X` and `normalize X n` is natural (in both `X` and `n`, but
     naturality in `n` is trivial and was "proved" in `normalizeIsoAux`). This is the real heart
     of our proof of the coherence theorem. -/

f187f107

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -67,7 +67,7 @@ local notation "N" => Discrete ∘ NormalMonoidalObject
 
 local infixr:10 " ⟶ᵐ " => Hom
 
--- porting note: this was automatic in mathlib 3
+-- Porting note: this was automatic in mathlib 3
 instance (x y : N C) : Subsingleton (x ⟶ y) := Discrete.instSubsingletonDiscreteHom _ _
 
 /-- Auxiliary definition for `inclusion`. -/
@@ -106,7 +106,7 @@ section
 
 open Hom
 
--- porting note: triggers a PANIC "invalid LCNF substitution of free variable
+-- Porting note: triggers a PANIC "invalid LCNF substitution of free variable
 -- with expression CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u}"
 -- prevented with an initial call to dsimp...why?
 /-- Auxiliary definition for `normalize`. Here we prove that objects that are related by
@@ -238,7 +238,7 @@ end
     of our proof of the coherence theorem. -/
 def normalizeIso : tensorFunc C ≅ normalize' C :=
   NatIso.ofComponents (normalizeIsoAux C)
-    (by -- porting note: the proof has been mostly rewritten
+    (by -- Porting note: the proof has been mostly rewritten
       rintro X Y f
       induction' f using Quotient.recOn with f; swap; rfl
       induction' f with _ X₁ X₂ X₃ _ _ _ _ _ _ _ _ _ _ _ _ h₁ h₂ X₁ X₂ Y₁ Y₂ f g h₁ h₂

f187f107

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

@@ -163,7 +163,7 @@ def fullNormalize : F C ⥤ N C where
 @[simp]
 def tensorFunc : F C ⥤ N C ⥤ F C where
   obj X := Discrete.functor fun n => inclusion.obj ⟨n⟩ ⊗ X
-  map f := Discrete.natTrans (fun n => 𝟙 _ ⊗ f)
+  map f := Discrete.natTrans (fun n => _ ◁ f)
 #align category_theory.free_monoidal_category.tensor_func CategoryTheory.FreeMonoidalCategory.tensorFunc
 
 theorem tensorFunc_map_app {X Y : F C} (f : X ⟶ Y) (n) : ((tensorFunc C).map f).app n = 𝟙 _ ⊗ f :=
@@ -171,7 +171,7 @@ theorem tensorFunc_map_app {X Y : F C} (f : X ⟶ Y) (n) : ((tensorFunc C).map f
 #align category_theory.free_monoidal_category.tensor_func_map_app CategoryTheory.FreeMonoidalCategory.tensorFunc_map_app
 
 theorem tensorFunc_obj_map (Z : F C) {n n' : N C} (f : n ⟶ n') :
-    ((tensorFunc C).obj Z).map f = inclusion.map f ⊗ 𝟙 Z := by
+    ((tensorFunc C).obj Z).map f = inclusion.map f ▷ Z := by
   cases n
   cases n'
   rcases f with ⟨⟨h⟩⟩
@@ -251,42 +251,43 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
           Category.comp_id]
         simp only [← Category.assoc]
         congr 4
-        simp only [Category.assoc, ← cancel_epi (𝟙 (inclusionObj n.as) ⊗ (α_ X₁ X₂ X₃).inv),
-          tensor_inv_hom_id_assoc, tensor_id, Category.id_comp,
-          pentagon_inv_assoc (inclusionObj n.as) X₁ X₂ X₃, Iso.inv_hom_id, Category.comp_id]
+        rw [← cancel_epi ((inclusionObj n.as) ◁ (α_ X₁ X₂ X₃).inv)]
+        simp
       · ext n
         dsimp
         rw [mk_α_inv, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp only [Category.assoc, comp_tensor_id, tensor_id, Category.comp_id,
-          pentagon_inv_assoc, ← associator_inv_naturality_assoc]
-        rfl
+        simp [tensorHom_id, comp_whiskerRight, Category.assoc, pentagon_inv_assoc,
+          whiskerRight_tensor, Category.comp_id, Iso.cancel_iso_inv_left]
+        erw [Iso.hom_inv_id_assoc]
       · ext n
         dsimp [Functor.comp]
         rw [mk_l_hom, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp only [triangle_assoc_comp_right_assoc, Category.assoc, Category.comp_id]
+        simp only [tensorHom_id, triangle_assoc_comp_right_assoc, Category.comp_id]
         rfl
       · ext n
         dsimp [Functor.comp]
         rw [mk_l_inv, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp only [triangle_assoc_comp_right_assoc, tensor_inv_hom_id_assoc, tensor_id,
-          Category.id_comp, Category.comp_id]
+        simp only [tensorHom_id, triangle_assoc_comp_right_assoc, whiskerLeft_inv_hom_assoc,
+          Category.comp_id]
         rfl
       · ext n
         dsimp
         rw [mk_ρ_hom, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp only [← (Iso.inv_comp_eq _).2 (rightUnitor_tensor _ _), Category.assoc,
-          ← rightUnitor_naturality, Category.comp_id]; rfl
+        simp only [whiskerLeft_rightUnitor, Category.assoc, tensorHom_id,
+          MonoidalCategory.whiskerRight_id, Category.comp_id, Iso.cancel_iso_inv_left,
+          Iso.cancel_iso_hom_left]
+        erw [Iso.inv_hom_id, Category.comp_id]
       · ext n
         dsimp
         rw [mk_ρ_inv, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp only [← (Iso.eq_comp_inv _).1 (rightUnitor_tensor_inv _ _), rightUnitor_conjugation,
-          Category.assoc, Iso.hom_inv_id_assoc, Iso.inv_hom_id_assoc, Iso.inv_hom_id,
-          Discrete.functor, Category.comp_id, Function.comp]
+        simp only [whiskerLeft_rightUnitor_inv, tensorHom_id, MonoidalCategory.whiskerRight_id,
+          Category.assoc, Iso.hom_inv_id_assoc, Iso.inv_hom_id_assoc, Category.comp_id]
+        erw [Iso.inv_hom_id, Category.comp_id]
       · rw [mk_comp, Functor.map_comp, Functor.map_comp, Category.assoc, h₂, reassoc_of% h₁]
       · ext ⟨n⟩
         replace h₁ := NatTrans.congr_app h₁ ⟨n⟩
@@ -301,6 +302,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
         rw [NatTrans.comp_app, NatTrans.comp_app] at h₁ h₂ ⊢
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight,
           Functor.comp, Discrete.natTrans] at h₁ h₂ h₃ ⊢
+        simp only [← id_tensorHom, ← tensorHom_id] at h₁ ⊢
         rw [mk_tensor, associator_inv_naturality_assoc, ← tensor_comp_assoc, h₁,
           Category.assoc, Category.comp_id, ← @Category.id_comp (F C) _ _ _ (@Quotient.mk _ _ g),
           tensor_comp, Category.assoc, Category.assoc, Functor.map_comp]

f187f107

chore: classify removed @[nolint has_nonempty_instance] porting notes (#10929)

Classifies by adding issue number (#10927) to porting notes claiming removed @[nolint has_nonempty_instance].

2599c3bb

Diff

@@ -53,7 +53,7 @@ variable (C)
 
 /-- We say an object in the free monoidal category is in normal form if it is of the form
     `(((𝟙_ C) ⊗ X₁) ⊗ X₂) ⊗ ⋯`. -/
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 inductive NormalMonoidalObject : Type u
   | unit : NormalMonoidalObject
   | tensor : NormalMonoidalObject → C → NormalMonoidalObject

f187f107

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

@@ -252,9 +252,8 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
         simp only [← Category.assoc]
         congr 4
         simp only [Category.assoc, ← cancel_epi (𝟙 (inclusionObj n.as) ⊗ (α_ X₁ X₂ X₃).inv),
-          pentagon_inv_assoc (inclusionObj n.as) X₁ X₂ X₃,
-          tensor_inv_hom_id_assoc, tensor_id, Category.id_comp, Iso.inv_hom_id,
-          Category.comp_id]
+          tensor_inv_hom_id_assoc, tensor_id, Category.id_comp,
+          pentagon_inv_assoc (inclusionObj n.as) X₁ X₂ X₃, Iso.inv_hom_id, Category.comp_id]
       · ext n
         dsimp
         rw [mk_α_inv, NatTrans.comp_app, NatTrans.comp_app]
@@ -272,7 +271,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
         dsimp [Functor.comp]
         rw [mk_l_inv, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
-        simp only [triangle_assoc_comp_left_inv_assoc, inv_hom_id_tensor_assoc, tensor_id,
+        simp only [triangle_assoc_comp_right_assoc, tensor_inv_hom_id_assoc, tensor_id,
           Category.id_comp, Category.comp_id]
         rfl
       · ext n

f187f107

fix: lean4-ify names of inductive constructors (#8652)

These inductive types carry data, so these should be functionCase not theorem_case.

It seems that mathport didn't do this.

79254c97

Diff

@@ -55,7 +55,7 @@ variable (C)
     `(((𝟙_ C) ⊗ X₁) ⊗ X₂) ⊗ ⋯`. -/
 -- porting note: removed @[nolint has_nonempty_instance]
 inductive NormalMonoidalObject : Type u
-  | Unit : NormalMonoidalObject
+  | unit : NormalMonoidalObject
   | tensor : NormalMonoidalObject → C → NormalMonoidalObject
 #align category_theory.free_monoidal_category.normal_monoidal_object CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject
 
@@ -73,7 +73,7 @@ instance (x y : N C) : Subsingleton (x ⟶ y) := Discrete.instSubsingletonDiscre
 /-- Auxiliary definition for `inclusion`. -/
 @[simp]
 def inclusionObj : NormalMonoidalObject C → F C
-  | NormalMonoidalObject.Unit => Unit
+  | NormalMonoidalObject.unit => unit
   | NormalMonoidalObject.tensor n a => tensor (inclusionObj n) (of a)
 #align category_theory.free_monoidal_category.inclusion_obj CategoryTheory.FreeMonoidalCategory.inclusionObj
 
@@ -86,7 +86,7 @@ def inclusion : N C ⥤ F C :=
 /-- Auxiliary definition for `normalize`. -/
 @[simp]
 def normalizeObj : F C → NormalMonoidalObject C → N C
-  | Unit, n => ⟨n⟩
+  | unit, n => ⟨n⟩
   | of X, n => ⟨NormalMonoidalObject.tensor n X⟩
   | tensor X Y, n => normalizeObj Y (normalizeObj X n).as
 #align category_theory.free_monoidal_category.normalize_obj CategoryTheory.FreeMonoidalCategory.normalizeObj
@@ -154,8 +154,8 @@ def normalize' : F C ⥤ N C ⥤ F C :=
 
 /-- The normalization functor for the free monoidal category over `C`. -/
 def fullNormalize : F C ⥤ N C where
-  obj X := ((normalize C).obj X).obj ⟨NormalMonoidalObject.Unit⟩
-  map f := ((normalize C).map f).app ⟨NormalMonoidalObject.Unit⟩
+  obj X := ((normalize C).obj X).obj ⟨NormalMonoidalObject.unit⟩
+  map f := ((normalize C).map f).app ⟨NormalMonoidalObject.unit⟩
 #align category_theory.free_monoidal_category.full_normalize CategoryTheory.FreeMonoidalCategory.fullNormalize
 
 /-- Given an object `X` of the free monoidal category and an object `n` in normal form, taking
@@ -187,7 +187,7 @@ theorem tensorFunc_obj_map (Z : F C) {n n' : N C} (f : n ⟶ n') :
 def normalizeIsoApp :
     ∀ (X : F C) (n : N C), ((tensorFunc C).obj X).obj n ≅ ((normalize' C).obj X).obj n
   | of _, _ => Iso.refl _
-  | Unit, _ => ρ_ _
+  | unit, _ => ρ_ _
   | tensor X _, n =>
     (α_ _ _ _).symm ≪≫ tensorIso (normalizeIsoApp X n) (Iso.refl _) ≪≫ normalizeIsoApp _ _
 #align category_theory.free_monoidal_category.normalize_iso_app CategoryTheory.FreeMonoidalCategory.normalizeIsoApp
@@ -314,13 +314,13 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
 /-- The isomorphism between an object and its normal form is natural. -/
 def fullNormalizeIso : 𝟭 (F C) ≅ fullNormalize C ⋙ inclusion :=
   NatIso.ofComponents
-  (fun X => (λ_ X).symm ≪≫ ((normalizeIso C).app X).app ⟨NormalMonoidalObject.Unit⟩)
+  (fun X => (λ_ X).symm ≪≫ ((normalizeIso C).app X).app ⟨NormalMonoidalObject.unit⟩)
     (by
       intro X Y f
       dsimp
       rw [leftUnitor_inv_naturality_assoc, Category.assoc, Iso.cancel_iso_inv_left]
       exact
-        congr_arg (fun f => NatTrans.app f (Discrete.mk NormalMonoidalObject.Unit))
+        congr_arg (fun f => NatTrans.app f (Discrete.mk NormalMonoidalObject.unit))
           ((normalizeIso.{u} C).hom.naturality f))
 #align category_theory.free_monoidal_category.full_normalize_iso CategoryTheory.FreeMonoidalCategory.fullNormalizeIso

f187f107

chore: cleanup some spaces (#7484)

Purely cosmetic PR.

c93575a3

Diff

@@ -308,7 +308,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
         congr 2
         erw [← reassoc_of% h₂]
         rw [← h₃, ← Category.assoc, ← id_tensor_comp_tensor_id, h₄]
-        rfl )
+        rfl)
 #align category_theory.free_monoidal_category.normalize_iso CategoryTheory.FreeMonoidalCategory.normalizeIso
 
 /-- The isomorphism between an object and its normal form is natural. -/

f187f107

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 Markus Himmel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.monoidal.free.coherence
-! leanprover-community/mathlib commit f187f1074fa1857c94589cc653c786cadc4c35ff
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Monoidal.Free.Basic
 import Mathlib.CategoryTheory.Groupoid
 import Mathlib.CategoryTheory.DiscreteCategory
 
+#align_import category_theory.monoidal.free.coherence from "leanprover-community/mathlib"@"f187f1074fa1857c94589cc653c786cadc4c35ff"
+
 /-!
 # The monoidal coherence theorem

f187f107

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

12343aa5

Diff

@@ -117,7 +117,7 @@ open Hom
 @[simp]
 def normalizeMapAux :
     ∀ {X Y : F C}, (X ⟶ᵐ Y) →
-      ((Discrete.functor (normalizeObj X) : _ ⥤  N C) ⟶ Discrete.functor (normalizeObj Y))
+      ((Discrete.functor (normalizeObj X) : _ ⥤ N C) ⟶ Discrete.functor (normalizeObj Y))
   | _, _, Hom.id _ => 𝟙 _
   | _, _, α_hom X Y Z => by dsimp; exact Discrete.natTrans (fun _ => 𝟙 _)
   | _, _, α_inv _ _ _ => by dsimp; exact Discrete.natTrans (fun _ => 𝟙 _)
@@ -128,7 +128,7 @@ def normalizeMapAux :
   | _, _, (@comp _ _ _ _ f g) => normalizeMapAux f ≫ normalizeMapAux g
   | _, _, (@Hom.tensor _ T _ _ W f g) => by
     dsimp
-    exact Discrete.natTrans (fun ⟨X⟩  => (normalizeMapAux g).app (normalizeObj T X) ≫
+    exact Discrete.natTrans (fun ⟨X⟩ => (normalizeMapAux g).app (normalizeObj T X) ≫
       (Discrete.functor (normalizeObj W) : _ ⥤ N C).map ((normalizeMapAux f).app ⟨X⟩))
 #align category_theory.free_monoidal_category.normalize_map_aux CategoryTheory.FreeMonoidalCategory.normalizeMapAux

f187f107

chore: remove occurrences of semicolon after space (#5713)

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

c795bd35

Diff

@@ -243,7 +243,7 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
   NatIso.ofComponents (normalizeIsoAux C)
     (by -- porting note: the proof has been mostly rewritten
       rintro X Y f
-      induction' f using Quotient.recOn with f ; swap ; rfl
+      induction' f using Quotient.recOn with f; swap; rfl
       induction' f with _ X₁ X₂ X₃ _ _ _ _ _ _ _ _ _ _ _ _ h₁ h₂ X₁ X₂ Y₁ Y₂ f g h₁ h₂
       · simp only [mk_id, Functor.map_id, Category.comp_id, Category.id_comp]
       · ext n

f187f107

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -245,8 +245,8 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
       rintro X Y f
       induction' f using Quotient.recOn with f ; swap ; rfl
       induction' f with _ X₁ X₂ X₃ _ _ _ _ _ _ _ _ _ _ _ _ h₁ h₂ X₁ X₂ Y₁ Y₂ f g h₁ h₂
-      . simp only [mk_id, Functor.map_id, Category.comp_id, Category.id_comp]
-      . ext n
+      · simp only [mk_id, Functor.map_id, Category.comp_id, Category.id_comp]
+      · ext n
         dsimp
         rw [mk_α_hom, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
@@ -258,41 +258,41 @@ def normalizeIso : tensorFunc C ≅ normalize' C :=
           pentagon_inv_assoc (inclusionObj n.as) X₁ X₂ X₃,
           tensor_inv_hom_id_assoc, tensor_id, Category.id_comp, Iso.inv_hom_id,
           Category.comp_id]
-      . ext n
+      · ext n
         dsimp
         rw [mk_α_inv, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
         simp only [Category.assoc, comp_tensor_id, tensor_id, Category.comp_id,
           pentagon_inv_assoc, ← associator_inv_naturality_assoc]
         rfl
-      . ext n
+      · ext n
         dsimp [Functor.comp]
         rw [mk_l_hom, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
         simp only [triangle_assoc_comp_right_assoc, Category.assoc, Category.comp_id]
         rfl
-      . ext n
+      · ext n
         dsimp [Functor.comp]
         rw [mk_l_inv, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
         simp only [triangle_assoc_comp_left_inv_assoc, inv_hom_id_tensor_assoc, tensor_id,
           Category.id_comp, Category.comp_id]
         rfl
-      . ext n
+      · ext n
         dsimp
         rw [mk_ρ_hom, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
         simp only [← (Iso.inv_comp_eq _).2 (rightUnitor_tensor _ _), Category.assoc,
           ← rightUnitor_naturality, Category.comp_id]; rfl
-      . ext n
+      · ext n
         dsimp
         rw [mk_ρ_inv, NatTrans.comp_app, NatTrans.comp_app]
         dsimp [NatIso.ofComponents, normalizeMapAux, whiskeringRight, whiskerRight, Functor.comp]
         simp only [← (Iso.eq_comp_inv _).1 (rightUnitor_tensor_inv _ _), rightUnitor_conjugation,
           Category.assoc, Iso.hom_inv_id_assoc, Iso.inv_hom_id_assoc, Iso.inv_hom_id,
           Discrete.functor, Category.comp_id, Function.comp]
-      . rw [mk_comp, Functor.map_comp, Functor.map_comp, Category.assoc, h₂, reassoc_of% h₁]
-      . ext ⟨n⟩
+      · rw [mk_comp, Functor.map_comp, Functor.map_comp, Category.assoc, h₂, reassoc_of% h₁]
+      · ext ⟨n⟩
         replace h₁ := NatTrans.congr_app h₁ ⟨n⟩
         replace h₂ := NatTrans.congr_app h₂ ((Discrete.functor (normalizeObj X₁)).obj ⟨n⟩)
         have h₃ := (normalizeIsoAux _ Y₂).hom.naturality ((normalizeMapAux f).app ⟨n⟩)

f187f107

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -26,7 +26,7 @@ objects that are in normal form. A normalization procedure is then just a functo
 functoriality says that two objects which are related by associators and unitors have the
 same normal form. Another desirable property of a normalization procedure is that an object is
 isomorphic (i.e., related via associators and unitors) to its normal form. In the case of the
-specific normalization procedure we use we not only get these isomorphismns, but also that they
+specific normalization procedure we use we not only get these isomorphisms, but also that they
 assemble into a natural isomorphism `𝟭 (FreeMonoidalCategory C) ≅ fullNormalize ⋙ inclusion`.
 But this means that any two parallel morphisms in the free monoidal category factor through a
 discrete category in the same way, so they must be equal, and hence the free monoidal category

f187f107

chore: cleanup Discrete porting notes (#4780)

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

86ade6e9

Diff

@@ -109,18 +109,12 @@ section
 
 open Hom
 
---attribute [local tidy] tactic.discrete_cases
-
 -- porting note: triggers a PANIC "invalid LCNF substitution of free variable
 -- with expression CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.{u}"
 -- prevented with an initial call to dsimp...why?
--- the @[simp] attribute is removed because it also triggers a PANIC
--- `PANIC at _private.Lean.Meta.Match.MatchEqs.0.Lean.Meta.Match.SimpH.substRHS
--- Lean.Meta.Match.MatchEqs:167:2: assertion violation: (
--- __do_lift._@.Lean.Meta.Match.MatchEqs._hyg.2199.0 ).xs.contains rhs`
 /-- Auxiliary definition for `normalize`. Here we prove that objects that are related by
     associators and unitors map to the same normal form. -/
--- @[simp]
+@[simp]
 def normalizeMapAux :
     ∀ {X Y : F C}, (X ⟶ᵐ Y) →
       ((Discrete.functor (normalizeObj X) : _ ⥤  N C) ⟶ Discrete.functor (normalizeObj Y))

f187f107

feat: port CategoryTheory.Monoidal.Free.Coherence (#3769)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

149f9407

`category_theory.monoidal.free.coherence` ⟷ `Mathlib.CategoryTheory.Monoidal.Free.Coherence`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 57

category_theory.monoidal.free.coherence ⟷ Mathlib.CategoryTheory.Monoidal.Free.Coherence

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 57

`category_theory.monoidal.free.coherence` ⟷ `Mathlib.CategoryTheory.Monoidal.Free.Coherence`