∀ {C : Type u_2} {D : Type u_4} [inst : CategoryTheory.Category.{u_1, u_2} C]
  [inst_1 : CategoryTheory.Category.{u_3, u_4} D] [inst_2 : CategoryTheory.MonoidalCategory C]
  [inst_3 : CategoryTheory.MonoidalCategory D] (F : CategoryTheory.Functor C D) [inst_4 : F.Monoidal] [F.Faithful]
  [inst_6 : CategoryTheory.BraidedCategory D]
  (β :
    (X Y : C) →
      CategoryTheory.MonoidalCategoryStruct.tensorObj X Y ≅ CategoryTheory.MonoidalCategoryStruct.tensorObj Y X),
  (∀ (X Y : C),
      CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.LaxMonoidal.μ F X Y) (F.map (β X Y).hom) =
        CategoryTheory.CategoryStruct.comp (β_ (F.obj X) (F.obj Y)).hom (CategoryTheory.Functor.LaxMonoidal.μ F Y X)) →
    ∀ {X Y : C} (f : X ⟶ Y) (Z : C),
      CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f Z) (β Y Z).hom =
        CategoryTheory.CategoryStruct.comp (β X Z).hom (CategoryTheory.MonoidalCategoryStruct.whiskerLeft Z f)