category_theory.monoidal.functor | 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

3d7987cd

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

ef7acf40

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -589,8 +589,8 @@ noncomputable def monoidalAdjoint (F : MonoidalFunctor C D) {G : D ⥤ C} (h : F
 #print CategoryTheory.monoidalInverse /-
 /-- If a monoidal functor `F` is an equivalence of categories then its inverse is also monoidal. -/
 @[simps]
-noncomputable def monoidalInverse (F : MonoidalFunctor C D) [IsEquivalence F.toFunctor] :
-    MonoidalFunctor D C
+noncomputable def monoidalInverse (F : MonoidalFunctor C D)
+    [CategoryTheory.Functor.IsEquivalence F.toFunctor] : MonoidalFunctor D C
     where
   toLaxMonoidalFunctor := monoidalAdjoint F (asEquivalence _).toAdjunction
   ε_isIso := by dsimp [equivalence.to_adjunction]; infer_instance

ef7acf40

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) 2018 Michael Jendrusch. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Jendrusch, Scott Morrison, Bhavik Mehta
 -/
-import Mathbin.CategoryTheory.Monoidal.Category
-import Mathbin.CategoryTheory.Adjunction.Basic
-import Mathbin.CategoryTheory.Products.Basic
+import CategoryTheory.Monoidal.Category
+import CategoryTheory.Adjunction.Basic
+import CategoryTheory.Products.Basic
 
 #align_import category_theory.monoidal.functor from "leanprover-community/mathlib"@"ef7acf407d265ad4081c8998687e994fa80ba70c"

ef7acf40

bump to nightly-2023-09-06-06

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

f3106448

Diff

@@ -101,20 +101,12 @@ structure LaxMonoidalFunctor extends C ⥤ D where
 #align category_theory.lax_monoidal_functor CategoryTheory.LaxMonoidalFunctor
 -/
 
-restate_axiom lax_monoidal_functor.μ_natural'
-
 attribute [simp, reassoc] lax_monoidal_functor.μ_natural
 
-restate_axiom lax_monoidal_functor.left_unitality'
-
 attribute [simp] lax_monoidal_functor.left_unitality
 
-restate_axiom lax_monoidal_functor.right_unitality'
-
 attribute [simp] lax_monoidal_functor.right_unitality
 
-restate_axiom lax_monoidal_functor.associativity'
-
 attribute [simp, reassoc] lax_monoidal_functor.associativity
 
 -- When `rewrite_search` lands, add @[search] attributes to

ef7acf40

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) 2018 Michael Jendrusch. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Jendrusch, Scott Morrison, Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.monoidal.functor
-! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Monoidal.Category
 import Mathbin.CategoryTheory.Adjunction.Basic
 import Mathbin.CategoryTheory.Products.Basic
 
+#align_import category_theory.monoidal.functor from "leanprover-community/mathlib"@"ef7acf407d265ad4081c8998687e994fa80ba70c"
+
 /-!
 # (Lax) monoidal functors

ef7acf40

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -128,25 +128,30 @@ section
 variable {C D}
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.LaxMonoidalFunctor.left_unitality_inv /-
 @[simp, reassoc]
 theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
     (λ_ (F.obj X)).inv ≫ (F.ε ⊗ 𝟙 (F.obj X)) ≫ F.μ (𝟙_ C) X = F.map (λ_ X).inv := by
   rw [iso.inv_comp_eq, F.left_unitality, category.assoc, category.assoc, ← F.to_functor.map_comp,
     iso.hom_inv_id, F.to_functor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.left_unitality_inv CategoryTheory.LaxMonoidalFunctor.left_unitality_inv
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.LaxMonoidalFunctor.right_unitality_inv /-
 @[simp, reassoc]
 theorem LaxMonoidalFunctor.right_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
     (ρ_ (F.obj X)).inv ≫ (𝟙 (F.obj X) ⊗ F.ε) ≫ F.μ X (𝟙_ C) = F.map (ρ_ X).inv := by
   rw [iso.inv_comp_eq, F.right_unitality, category.assoc, category.assoc, ← F.to_functor.map_comp,
     iso.hom_inv_id, F.to_functor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.right_unitality_inv CategoryTheory.LaxMonoidalFunctor.right_unitality_inv
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.LaxMonoidalFunctor.associativity_inv /-
 @[simp, reassoc]
 theorem LaxMonoidalFunctor.associativity_inv (F : LaxMonoidalFunctor C D) (X Y Z : C) :
     (𝟙 (F.obj X) ⊗ F.μ Y Z) ≫ F.μ X (Y ⊗ Z) ≫ F.map (α_ X Y Z).inv =
@@ -155,6 +160,7 @@ theorem LaxMonoidalFunctor.associativity_inv (F : LaxMonoidalFunctor C D) (X Y Z
   rw [iso.eq_inv_comp, ← F.associativity_assoc, ← F.to_functor.map_comp, iso.hom_inv_id,
     F.to_functor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.associativity_inv CategoryTheory.LaxMonoidalFunctor.associativity_inv
+-/
 
 end
 
@@ -174,21 +180,25 @@ attribute [instance] monoidal_functor.ε_is_iso monoidal_functor.μ_is_iso
 
 variable {C D}
 
+#print CategoryTheory.MonoidalFunctor.εIso /-
 /-- The unit morphism of a (strong) monoidal functor as an isomorphism.
 -/
 noncomputable def MonoidalFunctor.εIso (F : MonoidalFunctor.{v₁, v₂} C D) :
     tensorUnit D ≅ F.obj (tensorUnit C) :=
   asIso F.ε
 #align category_theory.monoidal_functor.ε_iso CategoryTheory.MonoidalFunctor.εIso
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalFunctor.μIso /-
 /-- The tensorator of a (strong) monoidal functor as an isomorphism.
 -/
 noncomputable def MonoidalFunctor.μIso (F : MonoidalFunctor.{v₁, v₂} C D) (X Y : C) :
     F.obj X ⊗ F.obj Y ≅ F.obj (X ⊗ Y) :=
   asIso (F.μ X Y)
 #align category_theory.monoidal_functor.μ_iso CategoryTheory.MonoidalFunctor.μIso
+-/
 
 end
 
@@ -225,11 +235,14 @@ variable (F : MonoidalFunctor.{v₁, v₂} C D)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalFunctor.map_tensor /-
 theorem map_tensor {X Y X' Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') :
     F.map (f ⊗ g) = inv (F.μ X X') ≫ (F.map f ⊗ F.map g) ≫ F.μ Y Y' := by simp
 #align category_theory.monoidal_functor.map_tensor CategoryTheory.MonoidalFunctor.map_tensor
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalFunctor.map_leftUnitor /-
 theorem map_leftUnitor (X : C) :
     F.map (λ_ X).Hom = inv (F.μ (𝟙_ C) X) ≫ (inv F.ε ⊗ 𝟙 (F.obj X)) ≫ (λ_ (F.obj X)).Hom :=
   by
@@ -239,8 +252,10 @@ theorem map_leftUnitor (X : C) :
     simp
   simp
 #align category_theory.monoidal_functor.map_left_unitor CategoryTheory.MonoidalFunctor.map_leftUnitor
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalFunctor.map_rightUnitor /-
 theorem map_rightUnitor (X : C) :
     F.map (ρ_ X).Hom = inv (F.μ X (𝟙_ C)) ≫ (𝟙 (F.obj X) ⊗ inv F.ε) ≫ (ρ_ (F.obj X)).Hom :=
   by
@@ -250,6 +265,7 @@ theorem map_rightUnitor (X : C) :
     simp
   simp
 #align category_theory.monoidal_functor.map_right_unitor CategoryTheory.MonoidalFunctor.map_rightUnitor
+-/
 
 #print CategoryTheory.MonoidalFunctor.μNatIso /-
 /-- The tensorator as a natural isomorphism. -/
@@ -260,49 +276,65 @@ noncomputable def μNatIso :
 #align category_theory.monoidal_functor.μ_nat_iso CategoryTheory.MonoidalFunctor.μNatIso
 -/
 
+#print CategoryTheory.MonoidalFunctor.μIso_hom /-
 @[simp]
 theorem μIso_hom (X Y : C) : (F.μIso X Y).Hom = F.μ X Y :=
   rfl
 #align category_theory.monoidal_functor.μ_iso_hom CategoryTheory.MonoidalFunctor.μIso_hom
+-/
 
+#print CategoryTheory.MonoidalFunctor.μ_inv_hom_id /-
 @[simp, reassoc]
 theorem μ_inv_hom_id (X Y : C) : (F.μIso X Y).inv ≫ F.μ X Y = 𝟙 _ :=
   (F.μIso X Y).inv_hom_id
 #align category_theory.monoidal_functor.μ_inv_hom_id CategoryTheory.MonoidalFunctor.μ_inv_hom_id
+-/
 
+#print CategoryTheory.MonoidalFunctor.μ_hom_inv_id /-
 @[simp]
 theorem μ_hom_inv_id (X Y : C) : F.μ X Y ≫ (F.μIso X Y).inv = 𝟙 _ :=
   (F.μIso X Y).hom_inv_id
 #align category_theory.monoidal_functor.μ_hom_inv_id CategoryTheory.MonoidalFunctor.μ_hom_inv_id
+-/
 
+#print CategoryTheory.MonoidalFunctor.εIso_hom /-
 @[simp]
 theorem εIso_hom : F.εIso.Hom = F.ε :=
   rfl
 #align category_theory.monoidal_functor.ε_iso_hom CategoryTheory.MonoidalFunctor.εIso_hom
+-/
 
+#print CategoryTheory.MonoidalFunctor.ε_inv_hom_id /-
 @[simp, reassoc]
 theorem ε_inv_hom_id : F.εIso.inv ≫ F.ε = 𝟙 _ :=
   F.εIso.inv_hom_id
 #align category_theory.monoidal_functor.ε_inv_hom_id CategoryTheory.MonoidalFunctor.ε_inv_hom_id
+-/
 
+#print CategoryTheory.MonoidalFunctor.ε_hom_inv_id /-
 @[simp]
 theorem ε_hom_inv_id : F.ε ≫ F.εIso.inv = 𝟙 _ :=
   F.εIso.hom_inv_id
 #align category_theory.monoidal_functor.ε_hom_inv_id CategoryTheory.MonoidalFunctor.ε_hom_inv_id
+-/
 
+#print CategoryTheory.MonoidalFunctor.commTensorLeft /-
 /-- Monoidal functors commute with left tensoring up to isomorphism -/
 @[simps]
 noncomputable def commTensorLeft (X : C) :
     F.toFunctor ⋙ tensorLeft (F.toFunctor.obj X) ≅ tensorLeft X ⋙ F.toFunctor :=
   NatIso.ofComponents (fun Y => F.μIso X Y) fun Y Z f => by convert F.μ_natural' (𝟙 _) f; simp
 #align category_theory.monoidal_functor.comm_tensor_left CategoryTheory.MonoidalFunctor.commTensorLeft
+-/
 
+#print CategoryTheory.MonoidalFunctor.commTensorRight /-
 /-- Monoidal functors commute with right tensoring up to isomorphism -/
 @[simps]
 noncomputable def commTensorRight (X : C) :
     F.toFunctor ⋙ tensorRight (F.toFunctor.obj X) ≅ tensorRight X ⋙ F.toFunctor :=
   NatIso.ofComponents (fun Y => F.μIso Y X) fun Y Z f => by convert F.μ_natural' f (𝟙 _); simp
 #align category_theory.monoidal_functor.comm_tensor_right CategoryTheory.MonoidalFunctor.commTensorRight
+-/
 
 end
 
@@ -375,7 +407,6 @@ def comp : LaxMonoidalFunctor.{v₁, v₃} C E :=
 #align category_theory.lax_monoidal_functor.comp CategoryTheory.LaxMonoidalFunctor.comp
 -/
 
--- mathport name: «expr ⊗⋙ »
 infixr:80 " ⊗⋙ " => comp
 
 end LaxMonoidalFunctor
@@ -437,13 +468,17 @@ theorem prod'_toFunctor : (F.prod' G).toFunctor = F.toFunctor.prod' G.toFunctor
 #align category_theory.lax_monoidal_functor.prod'_to_functor CategoryTheory.LaxMonoidalFunctor.prod'_toFunctor
 -/
 
+#print CategoryTheory.LaxMonoidalFunctor.prod'_ε /-
 @[simp]
 theorem prod'_ε : (F.prod' G).ε = (F.ε, G.ε) := by dsimp [prod']; simp
 #align category_theory.lax_monoidal_functor.prod'_ε CategoryTheory.LaxMonoidalFunctor.prod'_ε
+-/
 
+#print CategoryTheory.LaxMonoidalFunctor.prod'_μ /-
 @[simp]
 theorem prod'_μ (X Y : C) : (F.prod' G).μ X Y = (F.μ X Y, G.μ X Y) := by dsimp [prod']; simp
 #align category_theory.lax_monoidal_functor.prod'_μ CategoryTheory.LaxMonoidalFunctor.prod'_μ
+-/
 
 end LaxMonoidalFunctor
 
@@ -463,7 +498,6 @@ def comp : MonoidalFunctor.{v₁, v₃} C E :=
 #align category_theory.monoidal_functor.comp CategoryTheory.MonoidalFunctor.comp
 -/
 
--- mathport name: monoidal_functor.comp
 infixr:80
   " ⊗⋙ " =>-- We overload notation; potentially dangerous, but it seems to work.
   comp

ef7acf40

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -255,8 +255,8 @@ theorem map_rightUnitor (X : C) :
 /-- The tensorator as a natural isomorphism. -/
 noncomputable def μNatIso :
     Functor.prod F.toFunctor F.toFunctor ⋙ tensor D ≅ tensor C ⋙ F.toFunctor :=
-  NatIso.ofComponents (by intros ; apply F.μ_iso)
-    (by intros ; apply F.to_lax_monoidal_functor.μ_natural)
+  NatIso.ofComponents (by intros; apply F.μ_iso)
+    (by intros; apply F.to_lax_monoidal_functor.μ_natural)
 #align category_theory.monoidal_functor.μ_nat_iso CategoryTheory.MonoidalFunctor.μNatIso
 -/

ef7acf40

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -127,9 +127,6 @@ section
 
 variable {C D}
 
-/- warning: category_theory.lax_monoidal_functor.left_unitality_inv -> CategoryTheory.LaxMonoidalFunctor.left_unitality_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.left_unitality_inv CategoryTheory.LaxMonoidalFunctor.left_unitality_invₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp, reassoc]
 theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
@@ -138,9 +135,6 @@ theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X :
     iso.hom_inv_id, F.to_functor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.left_unitality_inv CategoryTheory.LaxMonoidalFunctor.left_unitality_inv
 
-/- warning: category_theory.lax_monoidal_functor.right_unitality_inv -> CategoryTheory.LaxMonoidalFunctor.right_unitality_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.right_unitality_inv CategoryTheory.LaxMonoidalFunctor.right_unitality_invₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp, reassoc]
 theorem LaxMonoidalFunctor.right_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
@@ -149,9 +143,6 @@ theorem LaxMonoidalFunctor.right_unitality_inv (F : LaxMonoidalFunctor C D) (X :
     iso.hom_inv_id, F.to_functor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.right_unitality_inv CategoryTheory.LaxMonoidalFunctor.right_unitality_inv
 
-/- warning: category_theory.lax_monoidal_functor.associativity_inv -> CategoryTheory.LaxMonoidalFunctor.associativity_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.associativity_inv CategoryTheory.LaxMonoidalFunctor.associativity_invₓ'. -/
 /- ./././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 -/
@@ -183,12 +174,6 @@ attribute [instance] monoidal_functor.ε_is_iso monoidal_functor.μ_is_iso
 
 variable {C D}
 
-/- warning: category_theory.monoidal_functor.ε_iso -> CategoryTheory.MonoidalFunctor.εIso is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.MonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4), CategoryTheory.Iso.{u2, u4} D _inst_3 (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2))
-but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.MonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4), CategoryTheory.Iso.{u2, u4} D _inst_3 (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2))
-Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.ε_iso CategoryTheory.MonoidalFunctor.εIsoₓ'. -/
 /-- The unit morphism of a (strong) monoidal functor as an isomorphism.
 -/
 noncomputable def MonoidalFunctor.εIso (F : MonoidalFunctor.{v₁, v₂} C D) :
@@ -196,12 +181,6 @@ noncomputable def MonoidalFunctor.εIso (F : MonoidalFunctor.{v₁, v₂} C D) :
   asIso F.ε
 #align category_theory.monoidal_functor.ε_iso CategoryTheory.MonoidalFunctor.εIso
 
-/- warning: category_theory.monoidal_functor.μ_iso -> CategoryTheory.MonoidalFunctor.μIso is a dubious translation:
-lean 3 declaration is
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The tensorator of a (strong) monoidal functor as an isomorphism.
@@ -244,18 +223,12 @@ variable {D : Type u₂} [Category.{v₂} D] [MonoidalCategory.{v₂} D]
 
 variable (F : MonoidalFunctor.{v₁, v₂} C D)
 
-/- warning: category_theory.monoidal_functor.map_tensor -> CategoryTheory.MonoidalFunctor.map_tensor is a dubious translation:
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem map_tensor {X Y X' Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') :
     F.map (f ⊗ g) = inv (F.μ X X') ≫ (F.map f ⊗ F.map g) ≫ F.μ Y Y' := by simp
 #align category_theory.monoidal_functor.map_tensor CategoryTheory.MonoidalFunctor.map_tensor
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem map_leftUnitor (X : C) :
     F.map (λ_ X).Hom = inv (F.μ (𝟙_ C) X) ≫ (inv F.ε ⊗ 𝟙 (F.obj X)) ≫ (λ_ (F.obj X)).Hom :=
@@ -267,9 +240,6 @@ theorem map_leftUnitor (X : C) :
   simp
 #align category_theory.monoidal_functor.map_left_unitor CategoryTheory.MonoidalFunctor.map_leftUnitor
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem map_rightUnitor (X : C) :
     F.map (ρ_ X).Hom = inv (F.μ X (𝟙_ C)) ≫ (𝟙 (F.obj X) ⊗ inv F.ε) ≫ (ρ_ (F.obj X)).Hom :=
@@ -290,72 +260,36 @@ noncomputable def μNatIso :
 #align category_theory.monoidal_functor.μ_nat_iso CategoryTheory.MonoidalFunctor.μNatIso
 -/
 
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 @[simp]
 theorem μIso_hom (X Y : C) : (F.μIso X Y).Hom = F.μ X Y :=
   rfl
 #align category_theory.monoidal_functor.μ_iso_hom CategoryTheory.MonoidalFunctor.μIso_hom
 
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 @[simp, reassoc]
 theorem μ_inv_hom_id (X Y : C) : (F.μIso X Y).inv ≫ F.μ X Y = 𝟙 _ :=
   (F.μIso X Y).inv_hom_id
 #align category_theory.monoidal_functor.μ_inv_hom_id CategoryTheory.MonoidalFunctor.μ_inv_hom_id
 
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 @[simp]
 theorem μ_hom_inv_id (X Y : C) : F.μ X Y ≫ (F.μIso X Y).inv = 𝟙 _ :=
   (F.μIso X Y).hom_inv_id
 #align category_theory.monoidal_functor.μ_hom_inv_id CategoryTheory.MonoidalFunctor.μ_hom_inv_id
 
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 @[simp]
 theorem εIso_hom : F.εIso.Hom = F.ε :=
   rfl
 #align category_theory.monoidal_functor.ε_iso_hom CategoryTheory.MonoidalFunctor.εIso_hom
 
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 @[simp, reassoc]
 theorem ε_inv_hom_id : F.εIso.inv ≫ F.ε = 𝟙 _ :=
   F.εIso.inv_hom_id
 #align category_theory.monoidal_functor.ε_inv_hom_id CategoryTheory.MonoidalFunctor.ε_inv_hom_id
 
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 @[simp]
 theorem ε_hom_inv_id : F.ε ≫ F.εIso.inv = 𝟙 _ :=
   F.εIso.hom_inv_id
 #align category_theory.monoidal_functor.ε_hom_inv_id CategoryTheory.MonoidalFunctor.ε_hom_inv_id
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.comm_tensor_left CategoryTheory.MonoidalFunctor.commTensorLeftₓ'. -/
 /-- Monoidal functors commute with left tensoring up to isomorphism -/
 @[simps]
 noncomputable def commTensorLeft (X : C) :
@@ -363,12 +297,6 @@ noncomputable def commTensorLeft (X : C) :
   NatIso.ofComponents (fun Y => F.μIso X Y) fun Y Z f => by convert F.μ_natural' (𝟙 _) f; simp
 #align category_theory.monoidal_functor.comm_tensor_left CategoryTheory.MonoidalFunctor.commTensorLeft
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.comm_tensor_right CategoryTheory.MonoidalFunctor.commTensorRightₓ'. -/
 /-- Monoidal functors commute with right tensoring up to isomorphism -/
 @[simps]
 noncomputable def commTensorRight (X : C) :
@@ -509,16 +437,10 @@ theorem prod'_toFunctor : (F.prod' G).toFunctor = F.toFunctor.prod' G.toFunctor
 #align category_theory.lax_monoidal_functor.prod'_to_functor CategoryTheory.LaxMonoidalFunctor.prod'_toFunctor
 -/
 
-/- warning: category_theory.lax_monoidal_functor.prod'_ε -> CategoryTheory.LaxMonoidalFunctor.prod'_ε is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.prod'_ε CategoryTheory.LaxMonoidalFunctor.prod'_εₓ'. -/
 @[simp]
 theorem prod'_ε : (F.prod' G).ε = (F.ε, G.ε) := by dsimp [prod']; simp
 #align category_theory.lax_monoidal_functor.prod'_ε CategoryTheory.LaxMonoidalFunctor.prod'_ε
 
-/- warning: category_theory.lax_monoidal_functor.prod'_μ -> CategoryTheory.LaxMonoidalFunctor.prod'_μ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.prod'_μ CategoryTheory.LaxMonoidalFunctor.prod'_μₓ'. -/
 @[simp]
 theorem prod'_μ (X Y : C) : (F.prod' G).μ X Y = (F.μ X Y, G.μ X Y) := by dsimp [prod']; simp
 #align category_theory.lax_monoidal_functor.prod'_μ CategoryTheory.LaxMonoidalFunctor.prod'_μ

ef7acf40

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -285,13 +285,8 @@ theorem map_rightUnitor (X : C) :
 /-- The tensorator as a natural isomorphism. -/
 noncomputable def μNatIso :
     Functor.prod F.toFunctor F.toFunctor ⋙ tensor D ≅ tensor C ⋙ F.toFunctor :=
-  NatIso.ofComponents
-    (by
-      intros
-      apply F.μ_iso)
-    (by
-      intros
-      apply F.to_lax_monoidal_functor.μ_natural)
+  NatIso.ofComponents (by intros ; apply F.μ_iso)
+    (by intros ; apply F.to_lax_monoidal_functor.μ_natural)
 #align category_theory.monoidal_functor.μ_nat_iso CategoryTheory.MonoidalFunctor.μNatIso
 -/
 
@@ -365,10 +360,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.monoid
 @[simps]
 noncomputable def commTensorLeft (X : C) :
     F.toFunctor ⋙ tensorLeft (F.toFunctor.obj X) ≅ tensorLeft X ⋙ F.toFunctor :=
-  NatIso.ofComponents (fun Y => F.μIso X Y) fun Y Z f =>
-    by
-    convert F.μ_natural' (𝟙 _) f
-    simp
+  NatIso.ofComponents (fun Y => F.μIso X Y) fun Y Z f => by convert F.μ_natural' (𝟙 _) f; simp
 #align category_theory.monoidal_functor.comm_tensor_left CategoryTheory.MonoidalFunctor.commTensorLeft
 
 /- warning: category_theory.monoidal_functor.comm_tensor_right -> CategoryTheory.MonoidalFunctor.commTensorRight is a dubious translation:
@@ -381,10 +373,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.monoid
 @[simps]
 noncomputable def commTensorRight (X : C) :
     F.toFunctor ⋙ tensorRight (F.toFunctor.obj X) ≅ tensorRight X ⋙ F.toFunctor :=
-  NatIso.ofComponents (fun Y => F.μIso Y X) fun Y Z f =>
-    by
-    convert F.μ_natural' f (𝟙 _)
-    simp
+  NatIso.ofComponents (fun Y => F.μIso Y X) fun Y Z f => by convert F.μ_natural' f (𝟙 _); simp
 #align category_theory.monoidal_functor.comm_tensor_right CategoryTheory.MonoidalFunctor.commTensorRight
 
 end
@@ -524,20 +513,14 @@ theorem prod'_toFunctor : (F.prod' G).toFunctor = F.toFunctor.prod' G.toFunctor
 <too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.prod'_ε CategoryTheory.LaxMonoidalFunctor.prod'_εₓ'. -/
 @[simp]
-theorem prod'_ε : (F.prod' G).ε = (F.ε, G.ε) :=
-  by
-  dsimp [prod']
-  simp
+theorem prod'_ε : (F.prod' G).ε = (F.ε, G.ε) := by dsimp [prod']; simp
 #align category_theory.lax_monoidal_functor.prod'_ε CategoryTheory.LaxMonoidalFunctor.prod'_ε
 
 /- warning: category_theory.lax_monoidal_functor.prod'_μ -> CategoryTheory.LaxMonoidalFunctor.prod'_μ is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.prod'_μ CategoryTheory.LaxMonoidalFunctor.prod'_μₓ'. -/
 @[simp]
-theorem prod'_μ (X Y : C) : (F.prod' G).μ X Y = (F.μ X Y, G.μ X Y) :=
-  by
-  dsimp [prod']
-  simp
+theorem prod'_μ (X Y : C) : (F.prod' G).μ X Y = (F.μ X Y, G.μ X Y) := by dsimp [prod']; simp
 #align category_theory.lax_monoidal_functor.prod'_μ CategoryTheory.LaxMonoidalFunctor.prod'_μ
 
 end LaxMonoidalFunctor
@@ -553,12 +536,8 @@ def comp : MonoidalFunctor.{v₁, v₃} C E :=
   {
     F.toLaxMonoidalFunctor.comp
       G.toLaxMonoidalFunctor with
-    ε_isIso := by
-      dsimp
-      infer_instance
-    μ_isIso := by
-      dsimp
-      infer_instance }
+    ε_isIso := by dsimp; infer_instance
+    μ_isIso := by dsimp; infer_instance }
 #align category_theory.monoidal_functor.comp CategoryTheory.MonoidalFunctor.comp
 -/
 
@@ -669,12 +648,8 @@ noncomputable def monoidalInverse (F : MonoidalFunctor C D) [IsEquivalence F.toF
     MonoidalFunctor D C
     where
   toLaxMonoidalFunctor := monoidalAdjoint F (asEquivalence _).toAdjunction
-  ε_isIso := by
-    dsimp [equivalence.to_adjunction]
-    infer_instance
-  μ_isIso X Y := by
-    dsimp [equivalence.to_adjunction]
-    infer_instance
+  ε_isIso := by dsimp [equivalence.to_adjunction]; infer_instance
+  μ_isIso X Y := by dsimp [equivalence.to_adjunction]; infer_instance
 #align category_theory.monoidal_inverse CategoryTheory.monoidalInverse
 -/

ef7acf40

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -128,10 +128,7 @@ section
 variable {C D}
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.left_unitality_inv CategoryTheory.LaxMonoidalFunctor.left_unitality_invₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp, reassoc]
@@ -142,10 +139,7 @@ theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X :
 #align category_theory.lax_monoidal_functor.left_unitality_inv CategoryTheory.LaxMonoidalFunctor.left_unitality_inv
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.right_unitality_inv CategoryTheory.LaxMonoidalFunctor.right_unitality_invₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp, reassoc]
@@ -156,10 +150,7 @@ theorem LaxMonoidalFunctor.right_unitality_inv (F : LaxMonoidalFunctor C D) (X :
 #align category_theory.lax_monoidal_functor.right_unitality_inv CategoryTheory.LaxMonoidalFunctor.right_unitality_inv
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.associativity_inv CategoryTheory.LaxMonoidalFunctor.associativity_invₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -254,10 +245,7 @@ variable {D : Type u₂} [Category.{v₂} D] [MonoidalCategory.{v₂} D]
 variable (F : MonoidalFunctor.{v₁, v₂} C D)
 
 /- warning: category_theory.monoidal_functor.map_tensor -> CategoryTheory.MonoidalFunctor.map_tensor is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.map_tensor CategoryTheory.MonoidalFunctor.map_tensorₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -266,10 +254,7 @@ theorem map_tensor {X Y X' Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') :
 #align category_theory.monoidal_functor.map_tensor CategoryTheory.MonoidalFunctor.map_tensor
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.map_left_unitor CategoryTheory.MonoidalFunctor.map_leftUnitorₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem map_leftUnitor (X : C) :
@@ -283,10 +268,7 @@ theorem map_leftUnitor (X : C) :
 #align category_theory.monoidal_functor.map_left_unitor CategoryTheory.MonoidalFunctor.map_leftUnitor
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.map_right_unitor CategoryTheory.MonoidalFunctor.map_rightUnitorₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem map_rightUnitor (X : C) :
@@ -325,10 +307,7 @@ theorem μIso_hom (X Y : C) : (F.μIso X Y).Hom = F.μ X Y :=
 #align category_theory.monoidal_functor.μ_iso_hom CategoryTheory.MonoidalFunctor.μIso_hom
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.μ_inv_hom_id CategoryTheory.MonoidalFunctor.μ_inv_hom_idₓ'. -/
 @[simp, reassoc]
 theorem μ_inv_hom_id (X Y : C) : (F.μIso X Y).inv ≫ F.μ X Y = 𝟙 _ :=
@@ -336,10 +315,7 @@ theorem μ_inv_hom_id (X Y : C) : (F.μIso X Y).inv ≫ F.μ X Y = 𝟙 _ :=
 #align category_theory.monoidal_functor.μ_inv_hom_id CategoryTheory.MonoidalFunctor.μ_inv_hom_id
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.μ_hom_inv_id CategoryTheory.MonoidalFunctor.μ_hom_inv_idₓ'. -/
 @[simp]
 theorem μ_hom_inv_id (X Y : C) : F.μ X Y ≫ (F.μIso X Y).inv = 𝟙 _ :=
@@ -545,10 +521,7 @@ theorem prod'_toFunctor : (F.prod' G).toFunctor = F.toFunctor.prod' G.toFunctor
 -/
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.prod'_ε CategoryTheory.LaxMonoidalFunctor.prod'_εₓ'. -/
 @[simp]
 theorem prod'_ε : (F.prod' G).ε = (F.ε, G.ε) :=
@@ -558,10 +531,7 @@ theorem prod'_ε : (F.prod' G).ε = (F.ε, G.ε) :=
 #align category_theory.lax_monoidal_functor.prod'_ε CategoryTheory.LaxMonoidalFunctor.prod'_ε
 
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(CategoryTheory.LaxMonoidalFunctor.μ.{u1, u2, u4, u5} C _inst_1 _inst_2 D _inst_3 _inst_4 F X Y) (CategoryTheory.LaxMonoidalFunctor.μ.{u1, u3, u4, u6} C _inst_1 _inst_2 E _inst_5 _inst_6 G X Y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.prod'_μ CategoryTheory.LaxMonoidalFunctor.prod'_μₓ'. -/
 @[simp]
 theorem prod'_μ (X Y : C) : (F.prod' G).μ X Y = (F.μ X Y, G.μ X Y) :=

ef7acf40

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -106,7 +106,7 @@ structure LaxMonoidalFunctor extends C ⥤ D where
 
 restate_axiom lax_monoidal_functor.μ_natural'
 
-attribute [simp, reassoc.1] lax_monoidal_functor.μ_natural
+attribute [simp, reassoc] lax_monoidal_functor.μ_natural
 
 restate_axiom lax_monoidal_functor.left_unitality'
 
@@ -118,7 +118,7 @@ attribute [simp] lax_monoidal_functor.right_unitality
 
 restate_axiom lax_monoidal_functor.associativity'
 
-attribute [simp, reassoc.1] lax_monoidal_functor.associativity
+attribute [simp, reassoc] lax_monoidal_functor.associativity
 
 -- When `rewrite_search` lands, add @[search] attributes to
 -- lax_monoidal_functor.μ_natural lax_monoidal_functor.left_unitality
@@ -134,7 +134,7 @@ but is expected to have type
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D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3) (CategoryTheory.MonoidalCategory.tensorObj.{u2, u4} D _inst_3 _inst_4 (CategoryTheory.MonoidalCategory.tensorUnit'.{u2, u4} D _inst_3 _inst_4) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X)) (CategoryTheory.MonoidalCategory.tensorObj.{u2, u4} D _inst_3 _inst_4 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2) X)) (CategoryTheory.MonoidalCategory.tensorHom.{u2, u4} D _inst_3 _inst_4 (CategoryTheory.MonoidalCategory.tensorUnit'.{u2, u4} D _inst_3 _inst_4) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (CategoryTheory.LaxMonoidalFunctor.ε.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F) (CategoryTheory.CategoryStruct.id.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X))) (CategoryTheory.LaxMonoidalFunctor.μ.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2) X))) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 (CategoryTheory.MonoidalCategory.tensorUnit'.{u1, u3} C _inst_1 _inst_2) X) (CategoryTheory.Iso.inv.{u1, u3} C _inst_1 (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 (CategoryTheory.MonoidalCategory.tensorUnit'.{u1, u3} C _inst_1 _inst_2) X) X (CategoryTheory.MonoidalCategory.leftUnitor.{u1, u3} C _inst_1 _inst_2 X)))
 Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.left_unitality_inv CategoryTheory.LaxMonoidalFunctor.left_unitality_invₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
     (λ_ (F.obj X)).inv ≫ (F.ε ⊗ 𝟙 (F.obj X)) ≫ F.μ (𝟙_ C) X = F.map (λ_ X).inv := by
   rw [iso.inv_comp_eq, F.left_unitality, category.assoc, category.assoc, ← F.to_functor.map_comp,
@@ -148,7 +148,7 @@ but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.LaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4) (X : C), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (Prefunctor.obj.{succ u1, 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u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (CategoryTheory.MonoidalCategory.tensorObj.{u2, u4} D _inst_3 _inst_4 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (CategoryTheory.MonoidalCategory.tensorUnit'.{u2, u4} D _inst_3 _inst_4)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2))) (CategoryTheory.Iso.inv.{u2, u4} D _inst_3 (CategoryTheory.MonoidalCategory.tensorObj.{u2, u4} D _inst_3 _inst_4 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (CategoryTheory.MonoidalCategory.tensorUnit'.{u2, u4} D _inst_3 _inst_4)) (Prefunctor.obj.{succ u1, 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_inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2))) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2))) (CategoryTheory.MonoidalCategory.tensorHom.{u2, u4} D _inst_3 _inst_4 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C 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_inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X)) (CategoryTheory.LaxMonoidalFunctor.ε.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.LaxMonoidalFunctor.μ.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F X (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)))) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X (CategoryTheory.MonoidalCategory.tensorUnit'.{u1, u3} C _inst_1 _inst_2)) (CategoryTheory.Iso.inv.{u1, u3} C _inst_1 (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X (CategoryTheory.MonoidalCategory.tensorUnit'.{u1, u3} C _inst_1 _inst_2)) X (CategoryTheory.MonoidalCategory.rightUnitor.{u1, u3} C _inst_1 _inst_2 X)))
 Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.right_unitality_inv CategoryTheory.LaxMonoidalFunctor.right_unitality_invₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem LaxMonoidalFunctor.right_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
     (ρ_ (F.obj X)).inv ≫ (𝟙 (F.obj X) ⊗ F.ε) ≫ F.μ X (𝟙_ C) = F.map (ρ_ X).inv := by
   rw [iso.inv_comp_eq, F.right_unitality, category.assoc, category.assoc, ← F.to_functor.map_comp,
@@ -165,7 +165,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.lax_mo
 /- ./././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 -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem LaxMonoidalFunctor.associativity_inv (F : LaxMonoidalFunctor C D) (X Y Z : C) :
     (𝟙 (F.obj X) ⊗ F.μ Y Z) ≫ F.μ X (Y ⊗ Z) ≫ F.map (α_ X Y Z).inv =
       (α_ (F.obj X) (F.obj Y) (F.obj Z)).inv ≫ (F.μ X Y ⊗ 𝟙 (F.obj Z)) ≫ F.μ (X ⊗ Y) Z :=
@@ -330,7 +330,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.MonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4) (X : C) (Y : C), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X Y)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X Y))) (CategoryTheory.CategoryStruct.comp.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X Y)) (CategoryTheory.MonoidalCategory.tensorObj.{u2, u4} D _inst_3 _inst_4 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) Y)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X Y)) (CategoryTheory.Iso.inv.{u2, u4} D _inst_3 (CategoryTheory.MonoidalCategory.tensorObj.{u2, u4} D _inst_3 _inst_4 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) Y)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X Y)) (CategoryTheory.MonoidalFunctor.μIso.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F X Y)) (CategoryTheory.LaxMonoidalFunctor.μ.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F) X Y)) (CategoryTheory.CategoryStruct.id.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X Y)))
 Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.μ_inv_hom_id CategoryTheory.MonoidalFunctor.μ_inv_hom_idₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem μ_inv_hom_id (X Y : C) : (F.μIso X Y).inv ≫ F.μ X Y = 𝟙 _ :=
   (F.μIso X Y).inv_hom_id
 #align category_theory.monoidal_functor.μ_inv_hom_id CategoryTheory.MonoidalFunctor.μ_inv_hom_id
@@ -363,7 +363,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.MonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2))) (CategoryTheory.CategoryStruct.comp.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) (CategoryTheory.Iso.inv.{u2, u4} D _inst_3 (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) (CategoryTheory.MonoidalFunctor.εIso.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.LaxMonoidalFunctor.ε.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.CategoryStruct.id.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)))
 Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.ε_inv_hom_id CategoryTheory.MonoidalFunctor.ε_inv_hom_idₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem ε_inv_hom_id : F.εIso.inv ≫ F.ε = 𝟙 _ :=
   F.εIso.inv_hom_id
 #align category_theory.monoidal_functor.ε_inv_hom_id CategoryTheory.MonoidalFunctor.ε_inv_hom_id

ef7acf40

bump to nightly-2023-02-25-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

39ef98db

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Jendrusch, Scott Morrison, Bhavik Mehta
 
 ! This file was ported from Lean 3 source module category_theory.monoidal.functor
-! leanprover-community/mathlib commit 3d7987cda72abc473c7cdbbb075170e9ac620042
+! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
 ! 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.Products.Basic
 /-!
 # (Lax) monoidal functors
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A lax monoidal functor `F` between monoidal categories `C` and `D`
 is a functor between the underlying categories equipped with morphisms
 * `ε : 𝟙_ D ⟶ F.obj (𝟙_ C)` (called the unit morphism)

3d7987cd

bump to nightly-2023-02-23-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

5ac40b03

Diff

@@ -60,6 +60,7 @@ open MonoidalCategory
 variable (C : Type u₁) [Category.{v₁} C] [MonoidalCategory.{v₁} C] (D : Type u₂) [Category.{v₂} D]
   [MonoidalCategory.{v₂} D]
 
+#print CategoryTheory.LaxMonoidalFunctor /-
 /- ./././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 -/
@@ -98,6 +99,7 @@ structure LaxMonoidalFunctor extends C ⥤ D where
   right_unitality' : ∀ X : C, (ρ_ (obj X)).Hom = (𝟙 (obj X) ⊗ ε) ≫ μ X (𝟙_ C) ≫ map (ρ_ X).Hom := by
     obviously
 #align category_theory.lax_monoidal_functor CategoryTheory.LaxMonoidalFunctor
+-/
 
 restate_axiom lax_monoidal_functor.μ_natural'
 
@@ -122,6 +124,12 @@ section
 
 variable {C D}
 
+/- warning: category_theory.lax_monoidal_functor.left_unitality_inv -> CategoryTheory.LaxMonoidalFunctor.left_unitality_inv is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.LaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4) (X : C), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F) X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2) X))) 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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.LaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4) (X : C), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (Prefunctor.obj.{succ u1, 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+Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.left_unitality_inv CategoryTheory.LaxMonoidalFunctor.left_unitality_invₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp, reassoc.1]
 theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
@@ -130,6 +138,12 @@ theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X :
     iso.hom_inv_id, F.to_functor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.left_unitality_inv CategoryTheory.LaxMonoidalFunctor.left_unitality_inv
 
+/- warning: category_theory.lax_monoidal_functor.right_unitality_inv -> CategoryTheory.LaxMonoidalFunctor.right_unitality_inv is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.LaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4) (X : C), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (Prefunctor.obj.{succ u1, 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+Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.right_unitality_inv CategoryTheory.LaxMonoidalFunctor.right_unitality_invₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp, reassoc.1]
 theorem LaxMonoidalFunctor.right_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
@@ -138,6 +152,12 @@ theorem LaxMonoidalFunctor.right_unitality_inv (F : LaxMonoidalFunctor C D) (X :
     iso.hom_inv_id, F.to_functor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.right_unitality_inv CategoryTheory.LaxMonoidalFunctor.right_unitality_inv
 
+/- warning: category_theory.lax_monoidal_functor.associativity_inv -> CategoryTheory.LaxMonoidalFunctor.associativity_inv is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.LaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4) (X : C) (Y : C) (Z : C), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.MonoidalCategory.tensorObj.{u2, u4} D _inst_3 _inst_4 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 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+Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.associativity_inv CategoryTheory.LaxMonoidalFunctor.associativity_invₓ'. -/
 /- ./././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 -/
@@ -153,6 +173,7 @@ theorem LaxMonoidalFunctor.associativity_inv (F : LaxMonoidalFunctor C D) (X Y Z
 
 end
 
+#print CategoryTheory.MonoidalFunctor /-
 /--
 A monoidal functor is a lax monoidal functor for which the tensorator and unitor as isomorphisms.
 
@@ -162,11 +183,18 @@ structure MonoidalFunctor extends LaxMonoidalFunctor.{v₁, v₂} C D where
   ε_isIso : IsIso ε := by infer_instance
   μ_isIso : ∀ X Y : C, IsIso (μ X Y) := by infer_instance
 #align category_theory.monoidal_functor CategoryTheory.MonoidalFunctor
+-/
 
 attribute [instance] monoidal_functor.ε_is_iso monoidal_functor.μ_is_iso
 
 variable {C D}
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.ε_iso CategoryTheory.MonoidalFunctor.εIsoₓ'. -/
 /-- The unit morphism of a (strong) monoidal functor as an isomorphism.
 -/
 noncomputable def MonoidalFunctor.εIso (F : MonoidalFunctor.{v₁, v₂} C D) :
@@ -174,6 +202,12 @@ noncomputable def MonoidalFunctor.εIso (F : MonoidalFunctor.{v₁, v₂} C D) :
   asIso F.ε
 #align category_theory.monoidal_functor.ε_iso CategoryTheory.MonoidalFunctor.εIso
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.μ_iso CategoryTheory.MonoidalFunctor.μIsoₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The tensorator of a (strong) monoidal functor as an isomorphism.
@@ -191,6 +225,7 @@ namespace LaxMonoidalFunctor
 
 variable (C : Type u₁) [Category.{v₁} C] [MonoidalCategory.{v₁} C]
 
+#print CategoryTheory.LaxMonoidalFunctor.id /-
 /-- The identity lax monoidal functor. -/
 @[simps]
 def id : LaxMonoidalFunctor.{v₁, v₁} C C :=
@@ -198,6 +233,7 @@ def id : LaxMonoidalFunctor.{v₁, v₁} C C :=
     ε := 𝟙 _
     μ := fun X Y => 𝟙 _ }
 #align category_theory.lax_monoidal_functor.id CategoryTheory.LaxMonoidalFunctor.id
+-/
 
 instance : Inhabited (LaxMonoidalFunctor C C) :=
   ⟨id C⟩
@@ -214,12 +250,24 @@ variable {D : Type u₂} [Category.{v₂} D] [MonoidalCategory.{v₂} D]
 
 variable (F : MonoidalFunctor.{v₁, v₂} C D)
 
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.MonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4) {X : C} {Y : C} {X' : C} {Y' : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X' Y'), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C 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+Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.map_tensor CategoryTheory.MonoidalFunctor.map_tensorₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem map_tensor {X Y X' Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') :
     F.map (f ⊗ g) = inv (F.μ X X') ≫ (F.map f ⊗ F.map g) ≫ F.μ Y Y' := by simp
 #align category_theory.monoidal_functor.map_tensor CategoryTheory.MonoidalFunctor.map_tensor
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.map_left_unitor CategoryTheory.MonoidalFunctor.map_leftUnitorₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem map_leftUnitor (X : C) :
     F.map (λ_ X).Hom = inv (F.μ (𝟙_ C) X) ≫ (inv F.ε ⊗ 𝟙 (F.obj X)) ≫ (λ_ (F.obj X)).Hom :=
@@ -231,6 +279,12 @@ theorem map_leftUnitor (X : C) :
   simp
 #align category_theory.monoidal_functor.map_left_unitor CategoryTheory.MonoidalFunctor.map_leftUnitor
 
+/- warning: category_theory.monoidal_functor.map_right_unitor -> CategoryTheory.MonoidalFunctor.map_rightUnitor is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X)) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) X (CategoryTheory.Iso.hom.{u1, u3} C _inst_1 (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) X (CategoryTheory.MonoidalCategory.rightUnitor.{u1, u3} C _inst_1 _inst_2 X))) (CategoryTheory.CategoryStruct.comp.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D 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u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2))) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (CategoryTheory.inv.{u2, u4} D _inst_3 (CategoryTheory.MonoidalCategory.tensorObj.{u2, u4} D _inst_3 _inst_4 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2))) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u3} C _inst_1 _inst_2 X (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2))) (CategoryTheory.LaxMonoidalFunctor.μ.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F) X (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) (CategoryTheory.MonoidalFunctor.μ_isIso.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F X (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2))) (CategoryTheory.CategoryStruct.comp.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3) (CategoryTheory.MonoidalCategory.tensorObj.{u2, u4} D _inst_3 _inst_4 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2))) (CategoryTheory.MonoidalCategory.tensorObj.{u2, u4} D _inst_3 _inst_4 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 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_inst_4 F)) X)) (CategoryTheory.inv.{u2, u4} D _inst_3 (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) (CategoryTheory.LaxMonoidalFunctor.ε.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalFunctor.ε_isIso.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.Iso.hom.{u2, u4} D _inst_3 (CategoryTheory.MonoidalCategory.tensorObj.{u2, u4} D _inst_3 _inst_4 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X) (CategoryTheory.MonoidalCategory.rightUnitor.{u2, u4} D _inst_3 _inst_4 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X)))))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.MonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4) (X : C), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 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+Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.map_right_unitor CategoryTheory.MonoidalFunctor.map_rightUnitorₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem map_rightUnitor (X : C) :
     F.map (ρ_ X).Hom = inv (F.μ X (𝟙_ C)) ≫ (𝟙 (F.obj X) ⊗ inv F.ε) ≫ (ρ_ (F.obj X)).Hom :=
@@ -242,6 +296,7 @@ theorem map_rightUnitor (X : C) :
   simp
 #align category_theory.monoidal_functor.map_right_unitor CategoryTheory.MonoidalFunctor.map_rightUnitor
 
+#print CategoryTheory.MonoidalFunctor.μNatIso /-
 /-- The tensorator as a natural isomorphism. -/
 noncomputable def μNatIso :
     Functor.prod F.toFunctor F.toFunctor ⋙ tensor D ≅ tensor C ⋙ F.toFunctor :=
@@ -253,37 +308,80 @@ noncomputable def μNatIso :
       intros
       apply F.to_lax_monoidal_functor.μ_natural)
 #align category_theory.monoidal_functor.μ_nat_iso CategoryTheory.MonoidalFunctor.μNatIso
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.μ_iso_hom CategoryTheory.MonoidalFunctor.μIso_homₓ'. -/
 @[simp]
 theorem μIso_hom (X Y : C) : (F.μIso X Y).Hom = F.μ X Y :=
   rfl
 #align category_theory.monoidal_functor.μ_iso_hom CategoryTheory.MonoidalFunctor.μIso_hom
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.μ_inv_hom_id CategoryTheory.MonoidalFunctor.μ_inv_hom_idₓ'. -/
 @[simp, reassoc.1]
 theorem μ_inv_hom_id (X Y : C) : (F.μIso X Y).inv ≫ F.μ X Y = 𝟙 _ :=
   (F.μIso X Y).inv_hom_id
 #align category_theory.monoidal_functor.μ_inv_hom_id CategoryTheory.MonoidalFunctor.μ_inv_hom_id
 
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 @[simp]
 theorem μ_hom_inv_id (X Y : C) : F.μ X Y ≫ (F.μIso X Y).inv = 𝟙 _ :=
   (F.μIso X Y).hom_inv_id
 #align category_theory.monoidal_functor.μ_hom_inv_id CategoryTheory.MonoidalFunctor.μ_hom_inv_id
 
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 @[simp]
 theorem εIso_hom : F.εIso.Hom = F.ε :=
   rfl
 #align category_theory.monoidal_functor.ε_iso_hom CategoryTheory.MonoidalFunctor.εIso_hom
 
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 @[simp, reassoc.1]
 theorem ε_inv_hom_id : F.εIso.inv ≫ F.ε = 𝟙 _ :=
   F.εIso.inv_hom_id
 #align category_theory.monoidal_functor.ε_inv_hom_id CategoryTheory.MonoidalFunctor.ε_inv_hom_id
 
+/- warning: category_theory.monoidal_functor.ε_hom_inv_id -> CategoryTheory.MonoidalFunctor.ε_hom_inv_id is a dubious translation:
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.MonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4) (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4)) (CategoryTheory.CategoryStruct.comp.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3) (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4) (CategoryTheory.LaxMonoidalFunctor.ε.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.Iso.inv.{u2, u4} D _inst_3 (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.MonoidalCategory.tensorUnit.{u1, u3} C _inst_1 _inst_2)) (CategoryTheory.MonoidalFunctor.εIso.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) (CategoryTheory.CategoryStruct.id.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3) (CategoryTheory.MonoidalCategory.tensorUnit.{u2, u4} D _inst_3 _inst_4))
+Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.ε_hom_inv_id CategoryTheory.MonoidalFunctor.ε_hom_inv_idₓ'. -/
 @[simp]
 theorem ε_hom_inv_id : F.ε ≫ F.εIso.inv = 𝟙 _ :=
   F.εIso.hom_inv_id
 #align category_theory.monoidal_functor.ε_hom_inv_id CategoryTheory.MonoidalFunctor.ε_hom_inv_id
 
+/- warning: category_theory.monoidal_functor.comm_tensor_left -> CategoryTheory.MonoidalFunctor.commTensorLeft is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.MonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4) (X : C), CategoryTheory.Iso.{max u3 u2, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.comp.{u1, u2, u2, u3, u4, u4} C _inst_1 D _inst_3 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorLeft.{u2, u4} D _inst_3 _inst_4 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) X))) (CategoryTheory.Functor.comp.{u1, u1, u2, u3, u3, u4} C _inst_1 C _inst_1 D _inst_3 (CategoryTheory.MonoidalCategory.tensorLeft.{u1, u3} C _inst_1 _inst_2 X) (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)))
+Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.comm_tensor_left CategoryTheory.MonoidalFunctor.commTensorLeftₓ'. -/
 /-- Monoidal functors commute with left tensoring up to isomorphism -/
 @[simps]
 noncomputable def commTensorLeft (X : C) :
@@ -294,6 +392,12 @@ noncomputable def commTensorLeft (X : C) :
     simp
 #align category_theory.monoidal_functor.comm_tensor_left CategoryTheory.MonoidalFunctor.commTensorLeft
 
+/- warning: category_theory.monoidal_functor.comm_tensor_right -> CategoryTheory.MonoidalFunctor.commTensorRight is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.MonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4) (X : C), CategoryTheory.Iso.{max u3 u2, max u1 u2 u3 u4} (CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.comp.{u1, u2, u2, u3, u4, u4} C _inst_1 D _inst_3 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorRight.{u2, u4} D _inst_3 _inst_4 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) X))) (CategoryTheory.Functor.comp.{u1, u1, u2, u3, u3, u4} C _inst_1 C _inst_1 D _inst_3 (CategoryTheory.MonoidalCategory.tensorRight.{u1, u3} C _inst_1 _inst_2 X) (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u3} C _inst_1] {D : Type.{u4}} [_inst_3 : CategoryTheory.Category.{u2, u4} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u4} D _inst_3] (F : CategoryTheory.MonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4) (X : C), CategoryTheory.Iso.{max u3 u2, max (max (max u4 u3) u2) u1} (CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.category.{u1, u2, u3, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.comp.{u1, u2, u2, u3, u4, u4} C _inst_1 D _inst_3 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorRight.{u2, u4} D _inst_3 _inst_4 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F))) X))) (CategoryTheory.Functor.comp.{u1, u1, u2, u3, u3, u4} C _inst_1 C _inst_1 D _inst_3 (CategoryTheory.MonoidalCategory.tensorRight.{u1, u3} C _inst_1 _inst_2 X) (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 (CategoryTheory.MonoidalFunctor.toLaxMonoidalFunctor.{u1, u2, u3, u4} C _inst_1 _inst_2 D _inst_3 _inst_4 F)))
+Case conversion may be inaccurate. Consider using '#align category_theory.monoidal_functor.comm_tensor_right CategoryTheory.MonoidalFunctor.commTensorRightₓ'. -/
 /-- Monoidal functors commute with right tensoring up to isomorphism -/
 @[simps]
 noncomputable def commTensorRight (X : C) :
@@ -310,6 +414,7 @@ section
 
 variable (C : Type u₁) [Category.{v₁} C] [MonoidalCategory.{v₁} C]
 
+#print CategoryTheory.MonoidalFunctor.id /-
 /-- The identity monoidal functor. -/
 @[simps]
 def id : MonoidalFunctor.{v₁, v₁} C C :=
@@ -317,6 +422,7 @@ def id : MonoidalFunctor.{v₁, v₁} C C :=
     ε := 𝟙 _
     μ := fun X Y => 𝟙 _ }
 #align category_theory.monoidal_functor.id CategoryTheory.MonoidalFunctor.id
+-/
 
 instance : Inhabited (MonoidalFunctor C C) :=
   ⟨id C⟩
@@ -335,6 +441,7 @@ namespace LaxMonoidalFunctor
 
 variable (F : LaxMonoidalFunctor.{v₁, v₂} C D) (G : LaxMonoidalFunctor.{v₂, v₃} D E)
 
+#print CategoryTheory.LaxMonoidalFunctor.comp /-
 -- The proofs here are horrendous; rewrite_search helps a lot.
 /-- The composition of two lax monoidal functors is again lax monoidal. -/
 @[simps]
@@ -370,6 +477,7 @@ def comp : LaxMonoidalFunctor.{v₁, v₃} C E :=
       rw [F.right_unitality, map_comp, ← nat_trans.id_app, ← category.assoc, ←
         lax_monoidal_functor.μ_natural, nat_trans.id_app, map_id, ← category.assoc, map_comp] }
 #align category_theory.lax_monoidal_functor.comp CategoryTheory.LaxMonoidalFunctor.comp
+-/
 
 -- mathport name: «expr ⊗⋙ »
 infixr:80 " ⊗⋙ " => comp
@@ -386,6 +494,7 @@ variable (F : LaxMonoidalFunctor.{v₀, v₁} B C) (G : LaxMonoidalFunctor.{v₂
 
 attribute [local simp] μ_natural associativity left_unitality right_unitality
 
+#print CategoryTheory.LaxMonoidalFunctor.prod /-
 /-- The cartesian product of two lax monoidal functors is lax monoidal. -/
 @[simps]
 def prod : LaxMonoidalFunctor (B × D) (C × E) :=
@@ -393,6 +502,7 @@ def prod : LaxMonoidalFunctor (B × D) (C × E) :=
     ε := (ε F, ε G)
     μ := fun X Y => (μ F X.1 Y.1, μ G X.2 Y.2) }
 #align category_theory.lax_monoidal_functor.prod CategoryTheory.LaxMonoidalFunctor.prod
+-/
 
 end LaxMonoidalFunctor
 
@@ -400,6 +510,7 @@ namespace MonoidalFunctor
 
 variable (C)
 
+#print CategoryTheory.MonoidalFunctor.diag /-
 /-- The diagonal functor as a monoidal functor. -/
 @[simps]
 def diag : MonoidalFunctor C (C × C) :=
@@ -407,6 +518,7 @@ def diag : MonoidalFunctor C (C × C) :=
     ε := 𝟙 _
     μ := fun X Y => 𝟙 _ }
 #align category_theory.monoidal_functor.diag CategoryTheory.MonoidalFunctor.diag
+-/
 
 end MonoidalFunctor
 
@@ -414,17 +526,27 @@ namespace LaxMonoidalFunctor
 
 variable (F : LaxMonoidalFunctor.{v₁, v₂} C D) (G : LaxMonoidalFunctor.{v₁, v₃} C E)
 
+#print CategoryTheory.LaxMonoidalFunctor.prod' /-
 /-- The cartesian product of two lax monoidal functors starting from the same monoidal category `C`
     is lax monoidal. -/
 def prod' : LaxMonoidalFunctor C (D × E) :=
   (MonoidalFunctor.diag C).toLaxMonoidalFunctor ⊗⋙ F.Prod G
 #align category_theory.lax_monoidal_functor.prod' CategoryTheory.LaxMonoidalFunctor.prod'
+-/
 
+#print CategoryTheory.LaxMonoidalFunctor.prod'_toFunctor /-
 @[simp]
 theorem prod'_toFunctor : (F.prod' G).toFunctor = F.toFunctor.prod' G.toFunctor :=
   rfl
 #align category_theory.lax_monoidal_functor.prod'_to_functor CategoryTheory.LaxMonoidalFunctor.prod'_toFunctor
+-/
 
+/- warning: category_theory.lax_monoidal_functor.prod'_ε -> CategoryTheory.LaxMonoidalFunctor.prod'_ε is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.prod'_ε CategoryTheory.LaxMonoidalFunctor.prod'_εₓ'. -/
 @[simp]
 theorem prod'_ε : (F.prod' G).ε = (F.ε, G.ε) :=
   by
@@ -432,6 +554,12 @@ theorem prod'_ε : (F.prod' G).ε = (F.ε, G.ε) :=
   simp
 #align category_theory.lax_monoidal_functor.prod'_ε CategoryTheory.LaxMonoidalFunctor.prod'_ε
 
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+but is expected to have type
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u4} C] [_inst_2 : CategoryTheory.MonoidalCategory.{u1, u4} C _inst_1] {D : Type.{u5}} [_inst_3 : CategoryTheory.Category.{u2, u5} D] [_inst_4 : CategoryTheory.MonoidalCategory.{u2, u5} D _inst_3] {E : Type.{u6}} [_inst_5 : CategoryTheory.Category.{u3, u6} E] [_inst_6 : CategoryTheory.MonoidalCategory.{u3, u6} E _inst_5] (F : CategoryTheory.LaxMonoidalFunctor.{u1, u2, u4, u5} C _inst_1 _inst_2 D _inst_3 _inst_4) (G : CategoryTheory.LaxMonoidalFunctor.{u1, u3, u4, u6} C _inst_1 _inst_2 E _inst_5 _inst_6) (X : C) (Y : C), Eq.{max (succ u2) (succ u3)} (Quiver.Hom.{succ (max u2 u3), max u5 u6} (Prod.{u5, u6} D E) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u5 u6} (Prod.{u5, u6} D E) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u5 u6} (Prod.{u5, u6} D E) (CategoryTheory.prod.{u2, u3, u5, u6} D _inst_3 E _inst_5))) (CategoryTheory.MonoidalCategory.tensorObj.{max u2 u3, max u5 u6} (Prod.{u5, u6} D E) 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(CategoryTheory.Category.toCategoryStruct.{u2, u5} D _inst_3)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u4, u5} C _inst_1 D _inst_3 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u2, u4, u5} C _inst_1 _inst_2 D _inst_3 _inst_4 F)) (CategoryTheory.MonoidalCategory.tensorObj.{u1, u4} C _inst_1 _inst_2 X Y))) (Quiver.Hom.{succ u3, u6} E (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} E (CategoryTheory.Category.toCategoryStruct.{u3, u6} E _inst_5)) (CategoryTheory.MonoidalCategory.tensorObj.{u3, u6} E _inst_5 _inst_6 (Prefunctor.obj.{succ u1, succ u3, u4, u6} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u4} C (CategoryTheory.Category.toCategoryStruct.{u1, u4} C _inst_1)) E (CategoryTheory.CategoryStruct.toQuiver.{u3, u6} E (CategoryTheory.Category.toCategoryStruct.{u3, u6} E _inst_5)) (CategoryTheory.Functor.toPrefunctor.{u1, u3, u4, u6} C _inst_1 E _inst_5 (CategoryTheory.LaxMonoidalFunctor.toFunctor.{u1, u3, u4, u6} C _inst_1 _inst_2 E _inst_5 _inst_6 G)) X) 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(CategoryTheory.LaxMonoidalFunctor.μ.{u1, u2, u4, u5} C _inst_1 _inst_2 D _inst_3 _inst_4 F X Y) (CategoryTheory.LaxMonoidalFunctor.μ.{u1, u3, u4, u6} C _inst_1 _inst_2 E _inst_5 _inst_6 G X Y))
+Case conversion may be inaccurate. Consider using '#align category_theory.lax_monoidal_functor.prod'_μ CategoryTheory.LaxMonoidalFunctor.prod'_μₓ'. -/
 @[simp]
 theorem prod'_μ (X Y : C) : (F.prod' G).μ X Y = (F.μ X Y, G.μ X Y) :=
   by
@@ -445,6 +573,7 @@ namespace MonoidalFunctor
 
 variable (F : MonoidalFunctor.{v₁, v₂} C D) (G : MonoidalFunctor.{v₂, v₃} D E)
 
+#print CategoryTheory.MonoidalFunctor.comp /-
 /-- The composition of two monoidal functors is again monoidal. -/
 @[simps]
 def comp : MonoidalFunctor.{v₁, v₃} C E :=
@@ -458,6 +587,7 @@ def comp : MonoidalFunctor.{v₁, v₃} C E :=
       dsimp
       infer_instance }
 #align category_theory.monoidal_functor.comp CategoryTheory.MonoidalFunctor.comp
+-/
 
 -- mathport name: monoidal_functor.comp
 infixr:80
@@ -474,6 +604,7 @@ variable {B : Type u₀} [Category.{v₀} B] [MonoidalCategory.{v₀} B]
 
 variable (F : MonoidalFunctor.{v₀, v₁} B C) (G : MonoidalFunctor.{v₂, v₃} D E)
 
+#print CategoryTheory.MonoidalFunctor.prod /-
 /-- The cartesian product of two monoidal functors is monoidal. -/
 @[simps]
 def prod : MonoidalFunctor (B × D) (C × E) :=
@@ -483,6 +614,7 @@ def prod : MonoidalFunctor (B × D) (C × E) :=
     ε_isIso := (isIso_prod_iff C E).mpr ⟨ε_isIso F, ε_isIso G⟩
     μ_isIso := fun X Y => (isIso_prod_iff C E).mpr ⟨μ_isIso F X.1 Y.1, μ_isIso G X.2 Y.2⟩ }
 #align category_theory.monoidal_functor.prod CategoryTheory.MonoidalFunctor.prod
+-/
 
 end MonoidalFunctor
 
@@ -491,17 +623,21 @@ namespace MonoidalFunctor
 variable (F : MonoidalFunctor.{v₁, v₂} C D) (G : MonoidalFunctor.{v₁, v₃} C E)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.MonoidalFunctor.prod' /-
 /-- The cartesian product of two monoidal functors starting from the same monoidal category `C`
     is monoidal. -/
 def prod' : MonoidalFunctor C (D × E) :=
   diag C ⊗⋙ F.Prod G
 #align category_theory.monoidal_functor.prod' CategoryTheory.MonoidalFunctor.prod'
+-/
 
+#print CategoryTheory.MonoidalFunctor.prod'_toLaxMonoidalFunctor /-
 @[simp]
 theorem prod'_toLaxMonoidalFunctor :
     (F.prod' G).toLaxMonoidalFunctor = F.toLaxMonoidalFunctor.prod' G.toLaxMonoidalFunctor :=
   rfl
 #align category_theory.monoidal_functor.prod'_to_lax_monoidal_functor CategoryTheory.MonoidalFunctor.prod'_toLaxMonoidalFunctor
+-/
 
 end MonoidalFunctor
 
@@ -509,6 +645,7 @@ end MonoidalFunctor
 /- ./././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.monoidalAdjoint /-
 /-- If we have a right adjoint functor `G` to a monoidal functor `F`, then `G` has a lax monoidal
 structure as well.
 -/
@@ -550,7 +687,9 @@ noncomputable def monoidalAdjoint (F : MonoidalFunctor C D) {G : D ⥤ C} (h : F
       is_iso.hom_inv_id_assoc, functor.map_comp, Functor.map_id, ← tensor_comp_assoc, assoc,
       h.counit_naturality, h.left_triangle_components_assoc, id_comp]
 #align category_theory.monoidal_adjoint CategoryTheory.monoidalAdjoint
+-/
 
+#print CategoryTheory.monoidalInverse /-
 /-- If a monoidal functor `F` is an equivalence of categories then its inverse is also monoidal. -/
 @[simps]
 noncomputable def monoidalInverse (F : MonoidalFunctor C D) [IsEquivalence F.toFunctor] :
@@ -564,6 +703,7 @@ noncomputable def monoidalInverse (F : MonoidalFunctor C D) [IsEquivalence F.toF
     dsimp [equivalence.to_adjunction]
     infer_instance
 #align category_theory.monoidal_inverse CategoryTheory.monoidalInverse
+-/
 
 end CategoryTheory

3d7987cd

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

3d7987cd

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

@@ -582,7 +582,7 @@ noncomputable def monoidalAdjoint (F : MonoidalFunctor C D) {G : D ⥤ C} (h : F
 
 /-- If a monoidal functor `F` is an equivalence of categories then its inverse is also monoidal. -/
 @[simps]
-noncomputable def monoidalInverse (F : MonoidalFunctor C D) [IsEquivalence F.toFunctor] :
+noncomputable def monoidalInverse (F : MonoidalFunctor C D) [F.IsEquivalence] :
     MonoidalFunctor D C
     where
   toLaxMonoidalFunctor := monoidalAdjoint F (asEquivalence _).toAdjunction

3d7987cd

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

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -249,9 +249,7 @@ namespace MonoidalFunctor
 section
 
 variable {C : Type u₁} [Category.{v₁} C] [MonoidalCategory.{v₁} C]
-
 variable {D : Type u₂} [Category.{v₂} D] [MonoidalCategory.{v₂} D]
-
 variable (F : MonoidalFunctor.{v₁, v₂} C D)
 
 @[reassoc]
@@ -367,9 +365,7 @@ end
 end MonoidalFunctor
 
 variable {C : Type u₁} [Category.{v₁} C] [MonoidalCategory.{v₁} C]
-
 variable {D : Type u₂} [Category.{v₂} D] [MonoidalCategory.{v₂} D]
-
 variable {E : Type u₃} [Category.{v₃} E] [MonoidalCategory.{v₃} E]
 
 namespace LaxMonoidalFunctor
@@ -407,7 +403,6 @@ namespace LaxMonoidalFunctor
 universe v₀ u₀
 
 variable {B : Type u₀} [Category.{v₀} B] [MonoidalCategory.{v₀} B]
-
 variable (F : LaxMonoidalFunctor.{v₀, v₁} B C) (G : LaxMonoidalFunctor.{v₂, v₃} D E)
 
 attribute [local simp] μ_natural associativity left_unitality right_unitality
@@ -495,7 +490,6 @@ namespace MonoidalFunctor
 universe v₀ u₀
 
 variable {B : Type u₀} [Category.{v₀} B] [MonoidalCategory.{v₀} B]
-
 variable (F : MonoidalFunctor.{v₀, v₁} B C) (G : MonoidalFunctor.{v₂, v₃} D E)
 
 /-- The cartesian product of two monoidal functors is monoidal. -/

3d7987cd

chore: classify todo porting notes (#11216)

Classifies by adding issue number #11215 to porting notes claiming "TODO".

86f95a40

Diff

@@ -90,7 +90,7 @@ structure LaxMonoidalFunctor extends C ⥤ D where
     by aesop_cat
 #align category_theory.lax_monoidal_functor CategoryTheory.LaxMonoidalFunctor
 
--- Porting note: todo: remove this configuration and use the default configuration.
+-- Porting note (#11215): TODO: remove this configuration and use the default configuration.
 -- We keep this to be consistent with Lean 3.
 -- See also `initialize_simps_projections MonoidalFunctor` below.
 -- This may require waiting on https://github.com/leanprover-community/mathlib4/pull/2936

3d7987cd

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

@@ -96,7 +96,7 @@ structure LaxMonoidalFunctor extends C ⥤ D where
 -- This may require waiting on https://github.com/leanprover-community/mathlib4/pull/2936
 initialize_simps_projections LaxMonoidalFunctor (+toFunctor, -obj, -map)
 
---Porting note: was `[simp, reassoc.1]`
+-- Porting note: was `[simp, reassoc.1]`
 attribute [reassoc (attr := simp)] LaxMonoidalFunctor.μ_natural_left
 attribute [reassoc (attr := simp)] LaxMonoidalFunctor.μ_natural_right
 
@@ -104,7 +104,7 @@ attribute [simp] LaxMonoidalFunctor.left_unitality
 
 attribute [simp] LaxMonoidalFunctor.right_unitality
 
---Porting note: was `[simp, reassoc.1]`
+-- Porting note: was `[simp, reassoc.1]`
 attribute [reassoc (attr := simp)] LaxMonoidalFunctor.associativity
 
 -- When `rewrite_search` lands, add @[search] attributes to
@@ -165,7 +165,7 @@ def LaxMonoidalFunctor.ofTensorHom (F : C ⥤ D)
   right_unitality := fun X => by
     simp_rw [← id_tensorHom, right_unitality]
 
---Porting note: was `[simp, reassoc.1]`
+-- Porting note: was `[simp, reassoc.1]`
 @[reassoc (attr := simp)]
 theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
     (λ_ (F.obj X)).inv ≫ F.ε ▷ F.obj X ≫ F.μ (𝟙_ C) X = F.map (λ_ X).inv := by
@@ -173,7 +173,7 @@ theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X :
     Iso.hom_inv_id, F.toFunctor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.left_unitality_inv CategoryTheory.LaxMonoidalFunctor.left_unitality_inv
 
---Porting note: was `[simp, reassoc.1]`
+-- Porting note: was `[simp, reassoc.1]`
 @[reassoc (attr := simp)]
 theorem LaxMonoidalFunctor.right_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
     (ρ_ (F.obj X)).inv ≫ F.obj X ◁ F.ε ≫ F.μ X (𝟙_ C) = F.map (ρ_ X).inv := by
@@ -181,7 +181,7 @@ theorem LaxMonoidalFunctor.right_unitality_inv (F : LaxMonoidalFunctor C D) (X :
     Iso.hom_inv_id, F.toFunctor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.right_unitality_inv CategoryTheory.LaxMonoidalFunctor.right_unitality_inv
 
---Porting note: was `[simp, reassoc.1]`
+-- Porting note: was `[simp, reassoc.1]`
 @[reassoc (attr := simp)]
 theorem LaxMonoidalFunctor.associativity_inv (F : LaxMonoidalFunctor C D) (X Y Z : C) :
     F.obj X ◁ F.μ Y Z ≫ F.μ X (Y ⊗ Z) ≫ F.map (α_ X Y Z).inv =
@@ -304,7 +304,7 @@ theorem μIso_hom (X Y : C) : (F.μIso X Y).hom = F.μ X Y :=
   rfl
 #align category_theory.monoidal_functor.μ_iso_hom CategoryTheory.MonoidalFunctor.μIso_hom
 
---Porting note: was `[simp, reassoc.1]`
+-- Porting note: was `[simp, reassoc.1]`
 @[reassoc (attr := simp)]
 theorem μ_inv_hom_id (X Y : C) : (F.μIso X Y).inv ≫ F.μ X Y = 𝟙 _ :=
   (F.μIso X Y).inv_hom_id
@@ -320,7 +320,7 @@ theorem εIso_hom : F.εIso.hom = F.ε :=
   rfl
 #align category_theory.monoidal_functor.ε_iso_hom CategoryTheory.MonoidalFunctor.εIso_hom
 
---Porting note: was `[simp, reassoc.1]`
+-- Porting note: was `[simp, reassoc.1]`
 @[reassoc (attr := simp)]
 theorem ε_inv_hom_id : F.εIso.inv ≫ F.ε = 𝟙 _ :=
   F.εIso.inv_hom_id

3d7987cd

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

@@ -71,22 +71,22 @@ structure LaxMonoidalFunctor extends C ⥤ D where
   μ : ∀ X Y : C, obj X ⊗ obj Y ⟶ obj (X ⊗ Y)
   μ_natural_left :
     ∀ {X Y : C} (f : X ⟶ Y) (X' : C),
-      (map f ⊗ 𝟙 (obj X')) ≫ μ Y X' = μ X X' ≫ map (f ⊗ 𝟙 X') := by
+      map f ▷ obj X' ≫ μ Y X' = μ X X' ≫ map (f ▷ X') := by
     aesop_cat
   μ_natural_right :
     ∀ {X Y : C} (X' : C) (f : X ⟶ Y) ,
-      (𝟙 (obj X') ⊗ map f) ≫ μ X' Y = μ X' X ≫ map (𝟙 X' ⊗ f) := by
+      obj X' ◁ map f ≫ μ X' Y = μ X' X ≫ map (X' ◁ f) := by
     aesop_cat
   /-- associativity of the tensorator -/
   associativity :
     ∀ X Y Z : C,
-      (μ X Y ⊗ 𝟙 (obj Z)) ≫ μ (X ⊗ Y) Z ≫ map (α_ X Y Z).hom =
-        (α_ (obj X) (obj Y) (obj Z)).hom ≫ (𝟙 (obj X) ⊗ μ Y Z) ≫ μ X (Y ⊗ Z) := by
+      μ X Y ▷ obj Z ≫ μ (X ⊗ Y) Z ≫ map (α_ X Y Z).hom =
+        (α_ (obj X) (obj Y) (obj Z)).hom ≫ obj X ◁ μ Y Z ≫ μ X (Y ⊗ Z) := by
     aesop_cat
   -- unitality
-  left_unitality : ∀ X : C, (λ_ (obj X)).hom = (ε ⊗ 𝟙 (obj X)) ≫ μ (𝟙_ C) X ≫ map (λ_ X).hom :=
+  left_unitality : ∀ X : C, (λ_ (obj X)).hom = ε ▷ obj X ≫ μ (𝟙_ C) X ≫ map (λ_ X).hom :=
     by aesop_cat
-  right_unitality : ∀ X : C, (ρ_ (obj X)).hom = (𝟙 (obj X) ⊗ ε) ≫ μ X (𝟙_ C) ≫ map (ρ_ X).hom :=
+  right_unitality : ∀ X : C, (ρ_ (obj X)).hom = obj X ◁ ε ≫ μ X (𝟙_ C) ≫ map (ρ_ X).hom :=
     by aesop_cat
 #align category_theory.lax_monoidal_functor CategoryTheory.LaxMonoidalFunctor
 
@@ -118,37 +118,7 @@ variable {C D}
 theorem LaxMonoidalFunctor.μ_natural (F : LaxMonoidalFunctor C D) {X Y X' Y' : C}
     (f : X ⟶ Y) (g : X' ⟶ Y') :
       (F.map f ⊗ F.map g) ≫ F.μ Y Y' = F.μ X X' ≫ F.map (f ⊗ g) := by
-  rw [tensorHom_def, ← id_tensorHom, ← tensorHom_id]
-  simp only [assoc, μ_natural_right, μ_natural_left_assoc]
-  rw [← F.map_comp, tensor_id_comp_id_tensor]
-
-@[reassoc (attr := simp)]
-theorem  LaxMonoidalFunctor.associativity' (F : LaxMonoidalFunctor C D) (X Y Z : C) :
-    (F.μ X Y ▷ F.obj Z) ≫ F.μ (X ⊗ Y) Z ≫ F.map (α_ X Y Z).hom =
-        (α_ (F.obj X) (F.obj Y) (F.obj Z)).hom ≫ ((F.obj X) ◁ F.μ Y Z) ≫ F.μ X (Y ⊗ Z) := by
-  simp [← id_tensorHom, ← tensorHom_id]
-
-@[reassoc]
-theorem  LaxMonoidalFunctor.left_unitality' (F : LaxMonoidalFunctor C D) (X : C) :
-    (λ_ (F.obj X)).hom = (F.ε ▷ F.obj X) ≫ F.μ (𝟙_ C) X ≫ F.map (λ_ X).hom := by
-  simp [← id_tensorHom, ← tensorHom_id]
-
-@[reassoc]
-theorem  LaxMonoidalFunctor.right_unitality' (F : LaxMonoidalFunctor C D) (X : C) :
-    (ρ_ (F.obj X)).hom = (F.obj X ◁ F.ε) ≫ F.μ X (𝟙_ C) ≫ F.map (ρ_ X).hom := by
-  simp [← id_tensorHom, ← tensorHom_id]
-
-@[reassoc (attr := simp)]
-theorem LaxMonoidalFunctor.μ_natural_left' (F : LaxMonoidalFunctor C D)
-    {X Y : C} (f : X ⟶ Y) (X' : C) :
-      F.map f ▷ F.obj X' ≫ F.μ Y X' = F.μ X X' ≫ F.map (f ▷ X') := by
-  simp [← id_tensorHom, ← tensorHom_id]
-
-@[reassoc (attr := simp)]
-theorem LaxMonoidalFunctor.μ_natural_right' (F : LaxMonoidalFunctor C D)
-    {X Y : C} (X' : C) (f : X ⟶ Y) :
-      F.obj X' ◁ F.map f ≫ F.μ X' Y = F.μ X' X ≫ F.map (X' ◁ f) := by
-  simp [← id_tensorHom, ← tensorHom_id]
+  simp [tensorHom_def]
 
 /--
 A constructor for lax monoidal functors whose axioms are described by `tensorHom` instead of
@@ -185,20 +155,20 @@ def LaxMonoidalFunctor.ofTensorHom (F : C ⥤ D)
   ε := ε
   μ := μ
   μ_natural_left := fun f X' => by
-    simp_rw [← F.map_id, μ_natural]
+    simp_rw [← tensorHom_id, ← F.map_id, μ_natural]
   μ_natural_right := fun X' f => by
-    simp_rw [← F.map_id, μ_natural]
+    simp_rw [← id_tensorHom, ← F.map_id, μ_natural]
   associativity := fun X Y Z => by
-    simp_rw [associativity]
+    simp_rw [← tensorHom_id, ← id_tensorHom, associativity]
   left_unitality := fun X => by
-    simp_rw [left_unitality]
+    simp_rw [← tensorHom_id, left_unitality]
   right_unitality := fun X => by
-    simp_rw [right_unitality]
+    simp_rw [← id_tensorHom, right_unitality]
 
 --Porting note: was `[simp, reassoc.1]`
 @[reassoc (attr := simp)]
 theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
-    (λ_ (F.obj X)).inv ≫ (F.ε ⊗ 𝟙 (F.obj X)) ≫ F.μ (𝟙_ C) X = F.map (λ_ X).inv := by
+    (λ_ (F.obj X)).inv ≫ F.ε ▷ F.obj X ≫ F.μ (𝟙_ C) X = F.map (λ_ X).inv := by
   rw [Iso.inv_comp_eq, F.left_unitality, Category.assoc, Category.assoc, ← F.toFunctor.map_comp,
     Iso.hom_inv_id, F.toFunctor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.left_unitality_inv CategoryTheory.LaxMonoidalFunctor.left_unitality_inv
@@ -206,7 +176,7 @@ theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X :
 --Porting note: was `[simp, reassoc.1]`
 @[reassoc (attr := simp)]
 theorem LaxMonoidalFunctor.right_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
-    (ρ_ (F.obj X)).inv ≫ (𝟙 (F.obj X) ⊗ F.ε) ≫ F.μ X (𝟙_ C) = F.map (ρ_ X).inv := by
+    (ρ_ (F.obj X)).inv ≫ F.obj X ◁ F.ε ≫ F.μ X (𝟙_ C) = F.map (ρ_ X).inv := by
   rw [Iso.inv_comp_eq, F.right_unitality, Category.assoc, Category.assoc, ← F.toFunctor.map_comp,
     Iso.hom_inv_id, F.toFunctor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.right_unitality_inv CategoryTheory.LaxMonoidalFunctor.right_unitality_inv
@@ -214,28 +184,12 @@ theorem LaxMonoidalFunctor.right_unitality_inv (F : LaxMonoidalFunctor C D) (X :
 --Porting note: was `[simp, reassoc.1]`
 @[reassoc (attr := simp)]
 theorem LaxMonoidalFunctor.associativity_inv (F : LaxMonoidalFunctor C D) (X Y Z : C) :
-    (𝟙 (F.obj X) ⊗ F.μ Y Z) ≫ F.μ X (Y ⊗ Z) ≫ F.map (α_ X Y Z).inv =
-      (α_ (F.obj X) (F.obj Y) (F.obj Z)).inv ≫ (F.μ X Y ⊗ 𝟙 (F.obj Z)) ≫ F.μ (X ⊗ Y) Z := by
+    F.obj X ◁ F.μ Y Z ≫ F.μ X (Y ⊗ Z) ≫ F.map (α_ X Y Z).inv =
+      (α_ (F.obj X) (F.obj Y) (F.obj Z)).inv ≫ F.μ X Y ▷ F.obj Z ≫ F.μ (X ⊗ Y) Z := by
   rw [Iso.eq_inv_comp, ← F.associativity_assoc, ← F.toFunctor.map_comp, Iso.hom_inv_id,
     F.toFunctor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.associativity_inv CategoryTheory.LaxMonoidalFunctor.associativity_inv
 
-@[reassoc (attr := simp)]
-theorem LaxMonoidalFunctor.left_unitality_inv' (F : LaxMonoidalFunctor C D) (X : C) :
-    (λ_ (F.obj X)).inv ≫ (F.ε ▷ F.obj X) ≫ F.μ (𝟙_ C) X = F.map (λ_ X).inv := by
-  simp [← id_tensorHom, ← tensorHom_id]
-
-@[reassoc (attr := simp)]
-theorem LaxMonoidalFunctor.right_unitality_inv' (F : LaxMonoidalFunctor C D) (X : C) :
-    (ρ_ (F.obj X)).inv ≫ (F.obj X ◁ F.ε) ≫ F.μ X (𝟙_ C) = F.map (ρ_ X).inv := by
-  simp [← id_tensorHom, ← tensorHom_id]
-
-@[reassoc (attr := simp)]
-theorem LaxMonoidalFunctor.associativity_inv' (F : LaxMonoidalFunctor C D) (X Y Z : C) :
-    (F.obj X ◁ F.μ Y Z) ≫ F.μ X (Y ⊗ Z) ≫ F.map (α_ X Y Z).inv =
-      (α_ (F.obj X) (F.obj Y) (F.obj Z)).inv ≫ (F.μ X Y ▷ F.obj Z) ≫ F.μ (X ⊗ Y) Z := by
-  simp [← id_tensorHom, ← tensorHom_id]
-
 end
 
 /--
@@ -300,38 +254,35 @@ variable {D : Type u₂} [Category.{v₂} D] [MonoidalCategory.{v₂} D]
 
 variable (F : MonoidalFunctor.{v₁, v₂} C D)
 
+@[reassoc]
 theorem map_tensor {X Y X' Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') :
     F.map (f ⊗ g) = inv (F.μ X X') ≫ (F.map f ⊗ F.map g) ≫ F.μ Y Y' := by simp
 #align category_theory.monoidal_functor.map_tensor CategoryTheory.MonoidalFunctor.map_tensor
 
--- Note: `𝟙 X ⊗ f` will be replaced by `X ◁ f` in #6307.
+@[reassoc]
 theorem map_whiskerLeft (X : C) {Y Z : C} (f : Y ⟶ Z) :
-    F.map (𝟙 X ⊗ f) = inv (F.μ X Y) ≫ (𝟙 (F.obj X) ⊗ F.map f) ≫ F.μ X Z := by simp
-
-theorem map_whiskerLeft' (X : C) {Y Z : C} (f : Y ⟶ Z) :
     F.map (X ◁ f) = inv (F.μ X Y) ≫ F.obj X ◁ F.map f ≫ F.μ X Z := by simp
 
--- Note: `f ⊗ 𝟙 Z` will be replaced by `f ▷ Z` in #6307.
+@[reassoc]
 theorem map_whiskerRight {X Y : C} (f : X ⟶ Y) (Z : C) :
-    F.map (f ⊗ 𝟙 Z) = inv (F.μ X Z) ≫ (F.map f ⊗ 𝟙 (F.obj Z)) ≫ F.μ Y Z := by simp
-
-theorem map_whiskerRight' {X Y : C} (f : X ⟶ Y) (Z : C) :
     F.map (f ▷ Z) = inv (F.μ X Z) ≫ F.map f ▷ F.obj Z ≫ F.μ Y Z := by simp
 
+@[reassoc]
 theorem map_leftUnitor (X : C) :
-    F.map (λ_ X).hom = inv (F.μ (𝟙_ C) X) ≫ (inv F.ε ⊗ 𝟙 (F.obj X)) ≫ (λ_ (F.obj X)).hom := by
+    F.map (λ_ X).hom = inv (F.μ (𝟙_ C) X) ≫ inv F.ε ▷ F.obj X ≫ (λ_ (F.obj X)).hom := by
   simp only [LaxMonoidalFunctor.left_unitality]
   slice_rhs 2 3 =>
-    rw [← comp_tensor_id]
+    rw [← comp_whiskerRight]
     simp
   simp
 #align category_theory.monoidal_functor.map_left_unitor CategoryTheory.MonoidalFunctor.map_leftUnitor
 
+@[reassoc]
 theorem map_rightUnitor (X : C) :
-    F.map (ρ_ X).hom = inv (F.μ X (𝟙_ C)) ≫ (𝟙 (F.obj X) ⊗ inv F.ε) ≫ (ρ_ (F.obj X)).hom := by
+    F.map (ρ_ X).hom = inv (F.μ X (𝟙_ C)) ≫ F.obj X ◁ inv F.ε ≫ (ρ_ (F.obj X)).hom := by
   simp only [LaxMonoidalFunctor.right_unitality]
   slice_rhs 2 3 =>
-    rw [← id_tensor_comp]
+    rw [← MonoidalCategory.whiskerLeft_comp]
     simp
   simp
 #align category_theory.monoidal_functor.map_right_unitor CategoryTheory.MonoidalFunctor.map_rightUnitor
@@ -384,14 +335,14 @@ theorem ε_hom_inv_id : F.ε ≫ F.εIso.inv = 𝟙 _ :=
 @[simps!]
 noncomputable def commTensorLeft (X : C) :
     F.toFunctor ⋙ tensorLeft (F.toFunctor.obj X) ≅ tensorLeft X ⋙ F.toFunctor :=
-  NatIso.ofComponents (fun Y => F.μIso X Y) fun f => F.μ_natural_right' X f
+  NatIso.ofComponents (fun Y => F.μIso X Y) fun f => F.μ_natural_right X f
 #align category_theory.monoidal_functor.comm_tensor_left CategoryTheory.MonoidalFunctor.commTensorLeft
 
 /-- Monoidal functors commute with right tensoring up to isomorphism -/
 @[simps!]
 noncomputable def commTensorRight (X : C) :
     F.toFunctor ⋙ tensorRight (F.toFunctor.obj X) ≅ tensorRight X ⋙ F.toFunctor :=
-  NatIso.ofComponents (fun Y => F.μIso Y X) fun f => F.μ_natural_left' f X
+  NatIso.ofComponents (fun Y => F.μIso Y X) fun f => F.μ_natural_left f X
 #align category_theory.monoidal_functor.comm_tensor_right CategoryTheory.MonoidalFunctor.commTensorRight
 
 end
@@ -440,14 +391,10 @@ def comp : LaxMonoidalFunctor.{v₁, v₃} C E :=
       simp_rw [comp_obj, F.comp_map, μ_natural_right_assoc, assoc, ← G.map_comp, μ_natural_right]
     associativity := fun X Y Z => by
       dsimp
-      rw [id_tensor_comp]
-      slice_rhs 3 4 => rw [← G.toFunctor.map_id, G.μ_natural]
+      simp only [comp_whiskerRight, assoc, μ_natural_left_assoc, MonoidalCategory.whiskerLeft_comp,
+        μ_natural_right_assoc]
       slice_rhs 1 3 => rw [← G.associativity]
-      rw [comp_tensor_id]
-      slice_lhs 2 3 => rw [← G.toFunctor.map_id, G.μ_natural]
-      rw [Category.assoc, Category.assoc, Category.assoc, Category.assoc, Category.assoc, ←
-        G.toFunctor.map_comp, ← G.toFunctor.map_comp, ← G.toFunctor.map_comp, ←
-        G.toFunctor.map_comp, F.associativity] }
+      simp_rw [Category.assoc, ← G.toFunctor.map_comp, F.associativity] }
 #align category_theory.lax_monoidal_functor.comp CategoryTheory.LaxMonoidalFunctor.comp
 
 @[inherit_doc]
@@ -586,43 +533,57 @@ structure as well.
 -/
 @[simp]
 noncomputable def monoidalAdjoint (F : MonoidalFunctor C D) {G : D ⥤ C} (h : F.toFunctor ⊣ G) :
-    LaxMonoidalFunctor D C := LaxMonoidalFunctor.ofTensorHom
-  (F := G)
-  (ε := h.homEquiv _ _ (inv F.ε))
-  (μ := fun X Y ↦
-    h.homEquiv _ (X ⊗ Y) (inv (F.μ (G.obj X) (G.obj Y)) ≫ (h.counit.app X ⊗ h.counit.app Y)))
-  (μ_natural := @fun X Y X' Y' f g => by
-    rw [← h.homEquiv_naturality_left, ← h.homEquiv_naturality_right, Equiv.apply_eq_iff_eq, assoc,
-      IsIso.eq_inv_comp, ← F.toLaxMonoidalFunctor.μ_natural_assoc, IsIso.hom_inv_id_assoc, ←
-      tensor_comp, Adjunction.counit_naturality, Adjunction.counit_naturality, tensor_comp])
-  (associativity := fun X Y Z ↦ by
+    LaxMonoidalFunctor D C where
+  toFunctor := G
+  ε := h.homEquiv _ _ (inv F.ε)
+  μ := fun X Y =>
+    h.homEquiv _ _ (inv (F.μ (G.obj X) (G.obj Y)) ≫ (h.counit.app X ⊗ h.counit.app Y))
+  μ_natural_left {X Y} f X' := by
+    rw [← h.homEquiv_naturality_left, ← h.homEquiv_naturality_right, Equiv.apply_eq_iff_eq,
+      assoc, IsIso.eq_inv_comp,
+      ← F.toLaxMonoidalFunctor.μ_natural_left_assoc, IsIso.hom_inv_id_assoc, tensorHom_def,
+      ← comp_whiskerRight_assoc, Adjunction.counit_naturality, comp_whiskerRight_assoc,
+      ← whisker_exchange, ← tensorHom_def_assoc]
+  μ_natural_right {X Y} X' f := by
+    rw [← h.homEquiv_naturality_left, ← h.homEquiv_naturality_right, Equiv.apply_eq_iff_eq,
+      assoc, IsIso.eq_inv_comp,
+      ← F.toLaxMonoidalFunctor.μ_natural_right_assoc, IsIso.hom_inv_id_assoc, tensorHom_def',
+      ← MonoidalCategory.whiskerLeft_comp_assoc, Adjunction.counit_naturality, whisker_exchange,
+      MonoidalCategory.whiskerLeft_comp, ← tensorHom_def_assoc]
+  associativity X Y Z := by
     dsimp only
-    rw [← h.homEquiv_naturality_right, ← h.homEquiv_naturality_left, ←
-      h.homEquiv_naturality_left, ← h.homEquiv_naturality_left, Equiv.apply_eq_iff_eq, ←
-      cancel_epi (F.toLaxMonoidalFunctor.μ (G.obj X ⊗ G.obj Y) (G.obj Z)), ←
-      cancel_epi (F.toLaxMonoidalFunctor.μ (G.obj X) (G.obj Y) ⊗ 𝟙 (F.obj (G.obj Z))),
-      F.toLaxMonoidalFunctor.associativity_assoc (G.obj X) (G.obj Y) (G.obj Z), ←
-      F.toLaxMonoidalFunctor.μ_natural_assoc, assoc, IsIso.hom_inv_id_assoc, ←
-      F.toLaxMonoidalFunctor.μ_natural_assoc, IsIso.hom_inv_id_assoc, ← tensor_comp, ←
-      tensor_comp, id_comp, Functor.map_id, Functor.map_id, id_comp, ← tensor_comp_assoc, ←
-      tensor_comp_assoc, id_comp, id_comp, h.homEquiv_unit, h.homEquiv_unit, Functor.map_comp,
-      assoc, assoc, h.counit_naturality, h.left_triangle_components_assoc, Functor.map_comp,
-      assoc, h.counit_naturality, h.left_triangle_components_assoc]
-    simp)
-  (left_unitality := fun X ↦ by
+    rw [← h.homEquiv_naturality_right, ← h.homEquiv_naturality_left, ← h.homEquiv_naturality_left,
+      ← h.homEquiv_naturality_left, Equiv.apply_eq_iff_eq,
+      ← cancel_epi (F.μ (G.obj X ⊗ G.obj Y) (G.obj Z)),
+      ← cancel_epi (F.μ (G.obj X) (G.obj Y) ▷ (F.obj (G.obj Z)))]
+    simp only [assoc]
+    calc
+      _ = (α_ _ _ _).hom ≫ (h.counit.app X ⊗ h.counit.app Y ⊗ h.counit.app Z) := by
+        rw [← F.μ_natural_left_assoc, IsIso.hom_inv_id_assoc, h.homEquiv_unit,
+          tensorHom_def_assoc (h.counit.app (X ⊗ Y)) (h.counit.app Z)]
+        dsimp only [comp_obj, id_obj]
+        simp_rw [← MonoidalCategory.comp_whiskerRight_assoc]
+        rw [F.map_comp_assoc, h.counit_naturality, h.left_triangle_components_assoc,
+          IsIso.hom_inv_id_assoc, ← tensorHom_def_assoc, associator_naturality]
+      _ = _ := by
+        rw [F.associativity_assoc, ← F.μ_natural_right_assoc, IsIso.hom_inv_id_assoc,
+          h.homEquiv_unit, tensorHom_def (h.counit.app X) (h.counit.app (Y ⊗ Z))]
+        dsimp only [id_obj, comp_obj]
+        rw [whisker_exchange_assoc, ← MonoidalCategory.whiskerLeft_comp, F.map_comp_assoc,
+          h.counit_naturality, h.left_triangle_components_assoc, whisker_exchange_assoc,
+          ← MonoidalCategory.whiskerLeft_comp, ← tensorHom_def, IsIso.hom_inv_id_assoc]
+  left_unitality X := by
     rw [← h.homEquiv_naturality_right, ← h.homEquiv_naturality_left, ← Equiv.symm_apply_eq,
-      h.homEquiv_counit, F.map_leftUnitor, h.homEquiv_unit, assoc, assoc, assoc, F.map_tensor,
-      assoc, assoc, IsIso.hom_inv_id_assoc, ← tensor_comp_assoc, Functor.map_id, id_comp,
-      Functor.map_comp, assoc, h.counit_naturality, h.left_triangle_components_assoc, ←
-      leftUnitor_naturality, ← tensor_comp_assoc, id_comp, comp_id]
-    simp)
-  (right_unitality := fun X ↦  by
+      h.homEquiv_counit, F.map_leftUnitor_assoc, h.homEquiv_unit, F.map_whiskerRight_assoc, assoc,
+      IsIso.hom_inv_id_assoc, tensorHom_def_assoc, ← MonoidalCategory.comp_whiskerRight_assoc,
+      F.map_comp_assoc, h.counit_naturality, h.left_triangle_components_assoc]
+    simp
+  right_unitality X := by
     rw [← h.homEquiv_naturality_right, ← h.homEquiv_naturality_left, ← Equiv.symm_apply_eq,
-      h.homEquiv_counit, F.map_rightUnitor, assoc, assoc, ← rightUnitor_naturality, ←
-      tensor_comp_assoc, comp_id, id_comp, h.homEquiv_unit, F.map_tensor, assoc, assoc, assoc,
-      IsIso.hom_inv_id_assoc, Functor.map_comp, Functor.map_id, ← tensor_comp_assoc, assoc,
-      h.counit_naturality, h.left_triangle_components_assoc, id_comp]
-    simp)
+      h.homEquiv_counit, F.map_rightUnitor_assoc, h.homEquiv_unit, F.map_whiskerLeft_assoc, assoc,
+      IsIso.hom_inv_id_assoc, tensorHom_def'_assoc, ← MonoidalCategory.whiskerLeft_comp_assoc,
+      F.map_comp_assoc, h.counit_naturality, h.left_triangle_components_assoc]
+    simp
 #align category_theory.monoidal_adjoint CategoryTheory.monoidalAdjoint
 
 /-- If a monoidal functor `F` is an equivalence of categories then its inverse is also monoidal. -/

3d7987cd

feat(CategoryTheory/Monoidal): redefine tensorLeft by using whiskering (#10898)

Extracted from #6307

13e13156

Diff

@@ -384,14 +384,14 @@ theorem ε_hom_inv_id : F.ε ≫ F.εIso.inv = 𝟙 _ :=
 @[simps!]
 noncomputable def commTensorLeft (X : C) :
     F.toFunctor ⋙ tensorLeft (F.toFunctor.obj X) ≅ tensorLeft X ⋙ F.toFunctor :=
-  NatIso.ofComponents (fun Y => F.μIso X Y) fun f => F.μ_natural_right X f
+  NatIso.ofComponents (fun Y => F.μIso X Y) fun f => F.μ_natural_right' X f
 #align category_theory.monoidal_functor.comm_tensor_left CategoryTheory.MonoidalFunctor.commTensorLeft
 
 /-- Monoidal functors commute with right tensoring up to isomorphism -/
 @[simps!]
 noncomputable def commTensorRight (X : C) :
     F.toFunctor ⋙ tensorRight (F.toFunctor.obj X) ≅ tensorRight X ⋙ F.toFunctor :=
-  NatIso.ofComponents (fun Y => F.μIso Y X) fun f => F.μ_natural_left f X
+  NatIso.ofComponents (fun Y => F.μIso Y X) fun f => F.μ_natural_left' f X
 #align category_theory.monoidal_functor.comm_tensor_right CategoryTheory.MonoidalFunctor.commTensorRight
 
 end

3d7987cd

refactor(CategoryTheory/Monoidal/Rigid): use monoidalComp in the proofs (#10326)

Similar to #10078

cda31e7e

Diff

@@ -308,10 +308,16 @@ theorem map_tensor {X Y X' Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') :
 theorem map_whiskerLeft (X : C) {Y Z : C} (f : Y ⟶ Z) :
     F.map (𝟙 X ⊗ f) = inv (F.μ X Y) ≫ (𝟙 (F.obj X) ⊗ F.map f) ≫ F.μ X Z := by simp
 
+theorem map_whiskerLeft' (X : C) {Y Z : C} (f : Y ⟶ Z) :
+    F.map (X ◁ f) = inv (F.μ X Y) ≫ F.obj X ◁ F.map f ≫ F.μ X Z := by simp
+
 -- Note: `f ⊗ 𝟙 Z` will be replaced by `f ▷ Z` in #6307.
 theorem map_whiskerRight {X Y : C} (f : X ⟶ Y) (Z : C) :
     F.map (f ⊗ 𝟙 Z) = inv (F.μ X Z) ≫ (F.map f ⊗ 𝟙 (F.obj Z)) ≫ F.μ Y Z := by simp
 
+theorem map_whiskerRight' {X Y : C} (f : X ⟶ Y) (Z : C) :
+    F.map (f ▷ Z) = inv (F.μ X Z) ≫ F.map f ▷ F.obj Z ≫ F.μ Y Z := by simp
+
 theorem map_leftUnitor (X : C) :
     F.map (λ_ X).hom = inv (F.μ (𝟙_ C) X) ≫ (inv F.ε ⊗ 𝟙 (F.obj X)) ≫ (λ_ (F.obj X)).hom := by
   simp only [LaxMonoidalFunctor.left_unitality]

3d7987cd

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

depends on: #10061

007ad742

Diff

@@ -122,6 +122,34 @@ theorem LaxMonoidalFunctor.μ_natural (F : LaxMonoidalFunctor C D) {X Y X' Y' :
   simp only [assoc, μ_natural_right, μ_natural_left_assoc]
   rw [← F.map_comp, tensor_id_comp_id_tensor]
 
+@[reassoc (attr := simp)]
+theorem  LaxMonoidalFunctor.associativity' (F : LaxMonoidalFunctor C D) (X Y Z : C) :
+    (F.μ X Y ▷ F.obj Z) ≫ F.μ (X ⊗ Y) Z ≫ F.map (α_ X Y Z).hom =
+        (α_ (F.obj X) (F.obj Y) (F.obj Z)).hom ≫ ((F.obj X) ◁ F.μ Y Z) ≫ F.μ X (Y ⊗ Z) := by
+  simp [← id_tensorHom, ← tensorHom_id]
+
+@[reassoc]
+theorem  LaxMonoidalFunctor.left_unitality' (F : LaxMonoidalFunctor C D) (X : C) :
+    (λ_ (F.obj X)).hom = (F.ε ▷ F.obj X) ≫ F.μ (𝟙_ C) X ≫ F.map (λ_ X).hom := by
+  simp [← id_tensorHom, ← tensorHom_id]
+
+@[reassoc]
+theorem  LaxMonoidalFunctor.right_unitality' (F : LaxMonoidalFunctor C D) (X : C) :
+    (ρ_ (F.obj X)).hom = (F.obj X ◁ F.ε) ≫ F.μ X (𝟙_ C) ≫ F.map (ρ_ X).hom := by
+  simp [← id_tensorHom, ← tensorHom_id]
+
+@[reassoc (attr := simp)]
+theorem LaxMonoidalFunctor.μ_natural_left' (F : LaxMonoidalFunctor C D)
+    {X Y : C} (f : X ⟶ Y) (X' : C) :
+      F.map f ▷ F.obj X' ≫ F.μ Y X' = F.μ X X' ≫ F.map (f ▷ X') := by
+  simp [← id_tensorHom, ← tensorHom_id]
+
+@[reassoc (attr := simp)]
+theorem LaxMonoidalFunctor.μ_natural_right' (F : LaxMonoidalFunctor C D)
+    {X Y : C} (X' : C) (f : X ⟶ Y) :
+      F.obj X' ◁ F.map f ≫ F.μ X' Y = F.μ X' X ≫ F.map (X' ◁ f) := by
+  simp [← id_tensorHom, ← tensorHom_id]
+
 /--
 A constructor for lax monoidal functors whose axioms are described by `tensorHom` instead of
 `whiskerLeft` and `whiskerRight`.
@@ -192,6 +220,22 @@ theorem LaxMonoidalFunctor.associativity_inv (F : LaxMonoidalFunctor C D) (X Y Z
     F.toFunctor.map_id, comp_id]
 #align category_theory.lax_monoidal_functor.associativity_inv CategoryTheory.LaxMonoidalFunctor.associativity_inv
 
+@[reassoc (attr := simp)]
+theorem LaxMonoidalFunctor.left_unitality_inv' (F : LaxMonoidalFunctor C D) (X : C) :
+    (λ_ (F.obj X)).inv ≫ (F.ε ▷ F.obj X) ≫ F.μ (𝟙_ C) X = F.map (λ_ X).inv := by
+  simp [← id_tensorHom, ← tensorHom_id]
+
+@[reassoc (attr := simp)]
+theorem LaxMonoidalFunctor.right_unitality_inv' (F : LaxMonoidalFunctor C D) (X : C) :
+    (ρ_ (F.obj X)).inv ≫ (F.obj X ◁ F.ε) ≫ F.μ X (𝟙_ C) = F.map (ρ_ X).inv := by
+  simp [← id_tensorHom, ← tensorHom_id]
+
+@[reassoc (attr := simp)]
+theorem LaxMonoidalFunctor.associativity_inv' (F : LaxMonoidalFunctor C D) (X Y Z : C) :
+    (F.obj X ◁ F.μ Y Z) ≫ F.μ X (Y ⊗ Z) ≫ F.map (α_ X Y Z).inv =
+      (α_ (F.obj X) (F.obj Y) (F.obj Z)).inv ≫ (F.μ X Y ▷ F.obj Z) ≫ F.μ (X ⊗ Y) Z := by
+  simp [← id_tensorHom, ← tensorHom_id]
+
 end
 
 /--

3d7987cd

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

@@ -115,11 +115,11 @@ section
 variable {C D}
 
 @[reassoc (attr := simp)]
-theorem  LaxMonoidalFunctor.μ_natural (F : LaxMonoidalFunctor C D) {X Y X' Y' : C}
+theorem LaxMonoidalFunctor.μ_natural (F : LaxMonoidalFunctor C D) {X Y X' Y' : C}
     (f : X ⟶ Y) (g : X' ⟶ Y') :
       (F.map f ⊗ F.map g) ≫ F.μ Y Y' = F.μ X X' ≫ F.map (f ⊗ g) := by
-  rw [← tensor_id_comp_id_tensor_assoc]
-  rw [F.μ_natural_right, F.μ_natural_left_assoc]
+  rw [tensorHom_def, ← id_tensorHom, ← tensorHom_id]
+  simp only [assoc, μ_natural_right, μ_natural_left_assoc]
   rw [← F.map_comp, tensor_id_comp_id_tensor]
 
 /--
@@ -334,18 +334,14 @@ theorem ε_hom_inv_id : F.ε ≫ F.εIso.inv = 𝟙 _ :=
 @[simps!]
 noncomputable def commTensorLeft (X : C) :
     F.toFunctor ⋙ tensorLeft (F.toFunctor.obj X) ≅ tensorLeft X ⋙ F.toFunctor :=
-  NatIso.ofComponents (fun Y => F.μIso X Y) @fun Y Z f => by
-    convert F.μ_natural (𝟙 X) f using 2
-    simp
+  NatIso.ofComponents (fun Y => F.μIso X Y) fun f => F.μ_natural_right X f
 #align category_theory.monoidal_functor.comm_tensor_left CategoryTheory.MonoidalFunctor.commTensorLeft
 
 /-- Monoidal functors commute with right tensoring up to isomorphism -/
 @[simps!]
 noncomputable def commTensorRight (X : C) :
     F.toFunctor ⋙ tensorRight (F.toFunctor.obj X) ≅ tensorRight X ⋙ F.toFunctor :=
-  NatIso.ofComponents (fun Y => F.μIso Y X) @fun Y Z f => by
-    convert F.μ_natural f (𝟙 X) using 2
-    simp
+  NatIso.ofComponents (fun Y => F.μIso Y X) fun f => F.μ_natural_left f X
 #align category_theory.monoidal_functor.comm_tensor_right CategoryTheory.MonoidalFunctor.commTensorRight
 
 end
@@ -401,19 +397,7 @@ def comp : LaxMonoidalFunctor.{v₁, v₃} C E :=
       slice_lhs 2 3 => rw [← G.toFunctor.map_id, G.μ_natural]
       rw [Category.assoc, Category.assoc, Category.assoc, Category.assoc, Category.assoc, ←
         G.toFunctor.map_comp, ← G.toFunctor.map_comp, ← G.toFunctor.map_comp, ←
-        G.toFunctor.map_comp, F.associativity]
-    left_unitality := fun X => by
-      dsimp
-      rw [G.left_unitality, comp_tensor_id, Category.assoc, Category.assoc]
-      apply congr_arg
-      rw [F.left_unitality, map_comp, ← NatTrans.id_app, ← Category.assoc, ←
-        LaxMonoidalFunctor.μ_natural, NatTrans.id_app, map_id, ← Category.assoc, map_comp]
-    right_unitality := fun X => by
-      dsimp
-      rw [G.right_unitality, id_tensor_comp, Category.assoc, Category.assoc]
-      apply congr_arg
-      rw [F.right_unitality, map_comp, ← NatTrans.id_app, ← Category.assoc, ←
-        LaxMonoidalFunctor.μ_natural, NatTrans.id_app, map_id, ← Category.assoc, map_comp] }
+        G.toFunctor.map_comp, F.associativity] }
 #align category_theory.lax_monoidal_functor.comp CategoryTheory.LaxMonoidalFunctor.comp
 
 @[inherit_doc]

3d7987cd

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

@@ -260,6 +260,14 @@ theorem map_tensor {X Y X' Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') :
     F.map (f ⊗ g) = inv (F.μ X X') ≫ (F.map f ⊗ F.map g) ≫ F.μ Y Y' := by simp
 #align category_theory.monoidal_functor.map_tensor CategoryTheory.MonoidalFunctor.map_tensor
 
+-- Note: `𝟙 X ⊗ f` will be replaced by `X ◁ f` in #6307.
+theorem map_whiskerLeft (X : C) {Y Z : C} (f : Y ⟶ Z) :
+    F.map (𝟙 X ⊗ f) = inv (F.μ X Y) ≫ (𝟙 (F.obj X) ⊗ F.map f) ≫ F.μ X Z := by simp
+
+-- Note: `f ⊗ 𝟙 Z` will be replaced by `f ▷ Z` in #6307.
+theorem map_whiskerRight {X Y : C} (f : X ⟶ Y) (Z : C) :
+    F.map (f ⊗ 𝟙 Z) = inv (F.μ X Z) ≫ (F.map f ⊗ 𝟙 (F.obj Z)) ≫ F.μ Y Z := by simp
+
 theorem map_leftUnitor (X : C) :
     F.map (λ_ X).hom = inv (F.μ (𝟙_ C) X) ≫ (inv F.ε ⊗ 𝟙 (F.obj X)) ≫ (λ_ (F.obj X)).hom := by
   simp only [LaxMonoidalFunctor.left_unitality]

3d7987cd

refactor(CategoryTheory/Monoidal): split the naturality condition of monoidal functors (#9988)

Extracted from #6307. We replace μ_natural with μ_natural_left and μ_natural_right since we prefer to use the whiskerings to the tensor of morphisms in the refactor #6307.

2e59248d

Diff

@@ -69,9 +69,13 @@ structure LaxMonoidalFunctor extends C ⥤ D where
   ε : 𝟙_ D ⟶ obj (𝟙_ C)
   /-- tensorator -/
   μ : ∀ X Y : C, obj X ⊗ obj Y ⟶ obj (X ⊗ Y)
-  μ_natural :
-    ∀ {X Y X' Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y'),
-      (map f ⊗ map g) ≫ μ Y Y' = μ X X' ≫ map (f ⊗ g) := by
+  μ_natural_left :
+    ∀ {X Y : C} (f : X ⟶ Y) (X' : C),
+      (map f ⊗ 𝟙 (obj X')) ≫ μ Y X' = μ X X' ≫ map (f ⊗ 𝟙 X') := by
+    aesop_cat
+  μ_natural_right :
+    ∀ {X Y : C} (X' : C) (f : X ⟶ Y) ,
+      (𝟙 (obj X') ⊗ map f) ≫ μ X' Y = μ X' X ≫ map (𝟙 X' ⊗ f) := by
     aesop_cat
   /-- associativity of the tensorator -/
   associativity :
@@ -93,7 +97,8 @@ structure LaxMonoidalFunctor extends C ⥤ D where
 initialize_simps_projections LaxMonoidalFunctor (+toFunctor, -obj, -map)
 
 --Porting note: was `[simp, reassoc.1]`
-attribute [reassoc (attr := simp)] LaxMonoidalFunctor.μ_natural
+attribute [reassoc (attr := simp)] LaxMonoidalFunctor.μ_natural_left
+attribute [reassoc (attr := simp)] LaxMonoidalFunctor.μ_natural_right
 
 attribute [simp] LaxMonoidalFunctor.left_unitality
 
@@ -109,6 +114,59 @@ section
 
 variable {C D}
 
+@[reassoc (attr := simp)]
+theorem  LaxMonoidalFunctor.μ_natural (F : LaxMonoidalFunctor C D) {X Y X' Y' : C}
+    (f : X ⟶ Y) (g : X' ⟶ Y') :
+      (F.map f ⊗ F.map g) ≫ F.μ Y Y' = F.μ X X' ≫ F.map (f ⊗ g) := by
+  rw [← tensor_id_comp_id_tensor_assoc]
+  rw [F.μ_natural_right, F.μ_natural_left_assoc]
+  rw [← F.map_comp, tensor_id_comp_id_tensor]
+
+/--
+A constructor for lax monoidal functors whose axioms are described by `tensorHom` instead of
+`whiskerLeft` and `whiskerRight`.
+-/
+@[simps]
+def LaxMonoidalFunctor.ofTensorHom (F : C ⥤ D)
+    /- unit morphism -/
+    (ε : 𝟙_ D ⟶ F.obj (𝟙_ C))
+    /- tensorator -/
+    (μ : ∀ X Y : C, F.obj X ⊗ F.obj Y ⟶ F.obj (X ⊗ Y))
+    (μ_natural :
+      ∀ {X Y X' Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y'),
+        (F.map f ⊗ F.map g) ≫ μ Y Y' = μ X X' ≫ F.map (f ⊗ g) := by
+      aesop_cat)
+    /- associativity of the tensorator -/
+    (associativity :
+      ∀ X Y Z : C,
+        (μ X Y ⊗ 𝟙 (F.obj Z)) ≫ μ (X ⊗ Y) Z ≫ F.map (α_ X Y Z).hom =
+          (α_ (F.obj X) (F.obj Y) (F.obj Z)).hom ≫ (𝟙 (F.obj X) ⊗ μ Y Z) ≫ μ X (Y ⊗ Z) := by
+      aesop_cat)
+    /- unitality -/
+    (left_unitality :
+      ∀ X : C, (λ_ (F.obj X)).hom = (ε ⊗ 𝟙 (F.obj X)) ≫ μ (𝟙_ C) X ≫ F.map (λ_ X).hom :=
+        by aesop_cat)
+    (right_unitality :
+      ∀ X : C, (ρ_ (F.obj X)).hom = (𝟙 (F.obj X) ⊗ ε) ≫ μ X (𝟙_ C) ≫ F.map (ρ_ X).hom :=
+        by aesop_cat) :
+        LaxMonoidalFunctor C D where
+  obj := F.obj
+  map := F.map
+  map_id := F.map_id
+  map_comp := F.map_comp
+  ε := ε
+  μ := μ
+  μ_natural_left := fun f X' => by
+    simp_rw [← F.map_id, μ_natural]
+  μ_natural_right := fun X' f => by
+    simp_rw [← F.map_id, μ_natural]
+  associativity := fun X Y Z => by
+    simp_rw [associativity]
+  left_unitality := fun X => by
+    simp_rw [left_unitality]
+  right_unitality := fun X => by
+    simp_rw [right_unitality]
+
 --Porting note: was `[simp, reassoc.1]`
 @[reassoc (attr := simp)]
 theorem LaxMonoidalFunctor.left_unitality_inv (F : LaxMonoidalFunctor C D) (X : C) :
@@ -320,10 +378,12 @@ def comp : LaxMonoidalFunctor.{v₁, v₃} C E :=
   { F.toFunctor ⋙ G.toFunctor with
     ε := G.ε ≫ G.map F.ε
     μ := fun X Y => G.μ (F.obj X) (F.obj Y) ≫ G.map (F.μ X Y)
-    μ_natural := @fun _ _ _ _ f g => by
-      simp only [Functor.comp_map, assoc]
-      rw [← Category.assoc, LaxMonoidalFunctor.μ_natural, Category.assoc, ← map_comp, ← map_comp,
-        ← LaxMonoidalFunctor.μ_natural]
+    μ_natural_left := by
+      intro X Y f X'
+      simp_rw [comp_obj, F.comp_map, μ_natural_left_assoc, assoc, ← G.map_comp, μ_natural_left]
+    μ_natural_right := by
+      intro X Y f X'
+      simp_rw [comp_obj, F.comp_map, μ_natural_right_assoc, assoc, ← G.map_comp, μ_natural_right]
     associativity := fun X Y Z => by
       dsimp
       rw [id_tensor_comp]
@@ -482,17 +542,18 @@ end MonoidalFunctor
 /-- If we have a right adjoint functor `G` to a monoidal functor `F`, then `G` has a lax monoidal
 structure as well.
 -/
-@[simps]
+@[simp]
 noncomputable def monoidalAdjoint (F : MonoidalFunctor C D) {G : D ⥤ C} (h : F.toFunctor ⊣ G) :
-    LaxMonoidalFunctor D C where
-  toFunctor := G
-  ε := h.homEquiv _ _ (inv F.ε)
-  μ X Y := h.homEquiv _ (X ⊗ Y) (inv (F.μ (G.obj X) (G.obj Y)) ≫ (h.counit.app X ⊗ h.counit.app Y))
-  μ_natural := @fun X Y X' Y' f g => by
+    LaxMonoidalFunctor D C := LaxMonoidalFunctor.ofTensorHom
+  (F := G)
+  (ε := h.homEquiv _ _ (inv F.ε))
+  (μ := fun X Y ↦
+    h.homEquiv _ (X ⊗ Y) (inv (F.μ (G.obj X) (G.obj Y)) ≫ (h.counit.app X ⊗ h.counit.app Y)))
+  (μ_natural := @fun X Y X' Y' f g => by
     rw [← h.homEquiv_naturality_left, ← h.homEquiv_naturality_right, Equiv.apply_eq_iff_eq, assoc,
       IsIso.eq_inv_comp, ← F.toLaxMonoidalFunctor.μ_natural_assoc, IsIso.hom_inv_id_assoc, ←
-      tensor_comp, Adjunction.counit_naturality, Adjunction.counit_naturality, tensor_comp]
-  associativity X Y Z := by
+      tensor_comp, Adjunction.counit_naturality, Adjunction.counit_naturality, tensor_comp])
+  (associativity := fun X Y Z ↦ by
     dsimp only
     rw [← h.homEquiv_naturality_right, ← h.homEquiv_naturality_left, ←
       h.homEquiv_naturality_left, ← h.homEquiv_naturality_left, Equiv.apply_eq_iff_eq, ←
@@ -505,21 +566,21 @@ noncomputable def monoidalAdjoint (F : MonoidalFunctor C D) {G : D ⥤ C} (h : F
       tensor_comp_assoc, id_comp, id_comp, h.homEquiv_unit, h.homEquiv_unit, Functor.map_comp,
       assoc, assoc, h.counit_naturality, h.left_triangle_components_assoc, Functor.map_comp,
       assoc, h.counit_naturality, h.left_triangle_components_assoc]
-    simp
-  left_unitality X := by
+    simp)
+  (left_unitality := fun X ↦ by
     rw [← h.homEquiv_naturality_right, ← h.homEquiv_naturality_left, ← Equiv.symm_apply_eq,
       h.homEquiv_counit, F.map_leftUnitor, h.homEquiv_unit, assoc, assoc, assoc, F.map_tensor,
       assoc, assoc, IsIso.hom_inv_id_assoc, ← tensor_comp_assoc, Functor.map_id, id_comp,
       Functor.map_comp, assoc, h.counit_naturality, h.left_triangle_components_assoc, ←
       leftUnitor_naturality, ← tensor_comp_assoc, id_comp, comp_id]
-    simp
-  right_unitality X := by
+    simp)
+  (right_unitality := fun X ↦  by
     rw [← h.homEquiv_naturality_right, ← h.homEquiv_naturality_left, ← Equiv.symm_apply_eq,
       h.homEquiv_counit, F.map_rightUnitor, assoc, assoc, ← rightUnitor_naturality, ←
       tensor_comp_assoc, comp_id, id_comp, h.homEquiv_unit, F.map_tensor, assoc, assoc, assoc,
       IsIso.hom_inv_id_assoc, Functor.map_comp, Functor.map_id, ← tensor_comp_assoc, assoc,
       h.counit_naturality, h.left_triangle_components_assoc, id_comp]
-    simp
+    simp)
 #align category_theory.monoidal_adjoint CategoryTheory.monoidalAdjoint
 
 /-- If a monoidal functor `F` is an equivalence of categories then its inverse is also monoidal. -/

3d7987cd

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

@@ -156,7 +156,7 @@ variable {C D}
 /-- The unit morphism of a (strong) monoidal functor as an isomorphism.
 -/
 noncomputable def MonoidalFunctor.εIso (F : MonoidalFunctor.{v₁, v₂} C D) :
-    tensorUnit D ≅ F.obj (tensorUnit C) :=
+    𝟙_ D ≅ F.obj (𝟙_ C) :=
   asIso F.ε
 #align category_theory.monoidal_functor.ε_iso CategoryTheory.MonoidalFunctor.εIso

3d7987cd

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) 2018 Michael Jendrusch. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Jendrusch, Scott Morrison, Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.monoidal.functor
-! leanprover-community/mathlib commit 3d7987cda72abc473c7cdbbb075170e9ac620042
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Monoidal.Category
 import Mathlib.CategoryTheory.Adjunction.Basic
 import Mathlib.CategoryTheory.Products.Basic
 
+#align_import category_theory.monoidal.functor from "leanprover-community/mathlib"@"3d7987cda72abc473c7cdbbb075170e9ac620042"
+
 /-!
 # (Lax) monoidal functors

3d7987cd

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

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

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

5b958613

Diff

@@ -75,21 +75,17 @@ structure LaxMonoidalFunctor extends C ⥤ D where
   μ_natural :
     ∀ {X Y X' Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y'),
       (map f ⊗ map g) ≫ μ Y Y' = μ X X' ≫ map (f ⊗ g) := by
-    --Porting note: was `obviously`
     aesop_cat
   /-- associativity of the tensorator -/
   associativity :
     ∀ X Y Z : C,
       (μ X Y ⊗ 𝟙 (obj Z)) ≫ μ (X ⊗ Y) Z ≫ map (α_ X Y Z).hom =
         (α_ (obj X) (obj Y) (obj Z)).hom ≫ (𝟙 (obj X) ⊗ μ Y Z) ≫ μ X (Y ⊗ Z) := by
-    --Porting note: was `obviously`
     aesop_cat
   -- unitality
   left_unitality : ∀ X : C, (λ_ (obj X)).hom = (ε ⊗ 𝟙 (obj X)) ≫ μ (𝟙_ C) X ≫ map (λ_ X).hom :=
-    --Porting note: was `obviously`
     by aesop_cat
   right_unitality : ∀ X : C, (ρ_ (obj X)).hom = (𝟙 (obj X) ⊗ ε) ≫ μ X (𝟙_ C) ≫ map (ρ_ X).hom :=
-    --Porting note: was `obviously`
     by aesop_cat
 #align category_theory.lax_monoidal_functor CategoryTheory.LaxMonoidalFunctor

3d7987cd

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -327,8 +327,7 @@ def comp : LaxMonoidalFunctor.{v₁, v₃} C E :=
   { F.toFunctor ⋙ G.toFunctor with
     ε := G.ε ≫ G.map F.ε
     μ := fun X Y => G.μ (F.obj X) (F.obj Y) ≫ G.map (F.μ X Y)
-    μ_natural := @fun _ _ _ _ f g =>
-      by
+    μ_natural := @fun _ _ _ _ f g => by
       simp only [Functor.comp_map, assoc]
       rw [← Category.assoc, LaxMonoidalFunctor.μ_natural, Category.assoc, ← map_comp, ← map_comp,
         ← LaxMonoidalFunctor.μ_natural]

3d7987cd

chore: fix simps projections in CategoryTheory.Monad.Basic (#3269)

This fixes a regression of @[simps] to @[simp] from #2969, per zulip.

There are a few incidental changes to @[simps] arguments in this PR, just removing arguments that had no effect on behaviour.

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

12c8e4f9

Diff

@@ -95,6 +95,8 @@ structure LaxMonoidalFunctor extends C ⥤ D where
 
 -- Porting note: todo: remove this configuration and use the default configuration.
 -- We keep this to be consistent with Lean 3.
+-- See also `initialize_simps_projections MonoidalFunctor` below.
+-- This may require waiting on https://github.com/leanprover-community/mathlib4/pull/2936
 initialize_simps_projections LaxMonoidalFunctor (+toFunctor, -obj, -map)
 
 --Porting note: was `[simp, reassoc.1]`
@@ -151,6 +153,7 @@ structure MonoidalFunctor extends LaxMonoidalFunctor.{v₁, v₂} C D where
   μ_isIso : ∀ X Y : C, IsIso (μ X Y) := by infer_instance
 #align category_theory.monoidal_functor CategoryTheory.MonoidalFunctor
 
+-- See porting note on `initialize_simps_projections LaxMonoidalFunctor`
 initialize_simps_projections MonoidalFunctor (+toLaxMonoidalFunctor, -obj, -map, -ε, -μ)
 
 attribute [instance] MonoidalFunctor.ε_isIso MonoidalFunctor.μ_isIso

3d7987cd

feat: improvements to congr! and convert (#2606)

There is now configuration for congr!, convert, and convert_to to control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas.
congr! now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first.
There is now a new HEq congruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality ⊢ ⟨a, x⟩ = ⟨b, y⟩ of sigma types, congr! turns this into goals ⊢ a = b and ⊢ a = b → HEq x y (note that congr! will also auto-introduce a = b for you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does.
congr! (and hence convert) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation of congr was being abused to unfold definitions.
With set_option trace.congr! true you can see what congr! sees when it is deciding on congruence lemmas.
There is also a bug fix in convert_to to do using 1 when there is no using clause, to match its documentation.

Note that congr! is more capable than congr at finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with a using clause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by the typeEqs option), which can help limit the depth automatically.

There is also a predefined configuration that you can invoke with, for example, convert (config := .unfoldSameFun) h, that causes it to behave more like congr, including using default transparency when unfolding.

61ca0ea8

Diff

@@ -273,7 +273,7 @@ theorem ε_hom_inv_id : F.ε ≫ F.εIso.inv = 𝟙 _ :=
 noncomputable def commTensorLeft (X : C) :
     F.toFunctor ⋙ tensorLeft (F.toFunctor.obj X) ≅ tensorLeft X ⋙ F.toFunctor :=
   NatIso.ofComponents (fun Y => F.μIso X Y) @fun Y Z f => by
-    convert F.μ_natural (𝟙 X) f
+    convert F.μ_natural (𝟙 X) f using 2
     simp
 #align category_theory.monoidal_functor.comm_tensor_left CategoryTheory.MonoidalFunctor.commTensorLeft
 
@@ -282,7 +282,7 @@ noncomputable def commTensorLeft (X : C) :
 noncomputable def commTensorRight (X : C) :
     F.toFunctor ⋙ tensorRight (F.toFunctor.obj X) ≅ tensorRight X ⋙ F.toFunctor :=
   NatIso.ofComponents (fun Y => F.μIso Y X) @fun Y Z f => by
-    convert F.μ_natural f (𝟙 X)
+    convert F.μ_natural f (𝟙 X) using 2
     simp
 #align category_theory.monoidal_functor.comm_tensor_right CategoryTheory.MonoidalFunctor.commTensorRight

3d7987cd

feat: simps uses fields of parent structures (#2042)

initialize_simps_projections now by default generates all projections of all parent structures, and doesn't generate the projections to those parent structures.
You can also rename a nested projection directly, without having to specify intermediate parent structures
Added the option to turn the default behavior off (done in e.g. TwoPointed)

Internal changes:

Move most declarations to the Simps namespace, and shorten their names
Restructure ParsedProjectionData to avoid the bug reported here (and to another bug where it seemed that the wrong data was inserted in ParsedProjectionData, but it was hard to minimize because of all the crashes). If we manage to fix the bug in that Zulip thread, I'll see if I can track down the other bug in commit 97454284

Co-authored-by: Johan Commelin <johan@commelin.net>

b21620a7

Diff

@@ -93,6 +93,10 @@ structure LaxMonoidalFunctor extends C ⥤ D where
     by aesop_cat
 #align category_theory.lax_monoidal_functor CategoryTheory.LaxMonoidalFunctor
 
+-- Porting note: todo: remove this configuration and use the default configuration.
+-- We keep this to be consistent with Lean 3.
+initialize_simps_projections LaxMonoidalFunctor (+toFunctor, -obj, -map)
+
 --Porting note: was `[simp, reassoc.1]`
 attribute [reassoc (attr := simp)] LaxMonoidalFunctor.μ_natural
 
@@ -147,6 +151,8 @@ structure MonoidalFunctor extends LaxMonoidalFunctor.{v₁, v₂} C D where
   μ_isIso : ∀ X Y : C, IsIso (μ X Y) := by infer_instance
 #align category_theory.monoidal_functor CategoryTheory.MonoidalFunctor
 
+initialize_simps_projections MonoidalFunctor (+toLaxMonoidalFunctor, -obj, -map, -ε, -μ)
+
 attribute [instance] MonoidalFunctor.ε_isIso MonoidalFunctor.μ_isIso
 
 variable {C D}

3d7987cd

feat: port CategoryTheory.Monoidal.Functor (#2445)

db3e3bdc

`category_theory.monoidal.functor` ⟷ `Mathlib.CategoryTheory.Monoidal.Functor`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 17

category_theory.monoidal.functor ⟷ Mathlib.CategoryTheory.Monoidal.Functor

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 17

`category_theory.monoidal.functor` ⟷ `Mathlib.CategoryTheory.Monoidal.Functor`