Theorems · Theorem · category theory

CategoryTheory.Functor.LaxBraided.braided_assoc

∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.MonoidalCategory C}
  {inst_2 : CategoryTheory.BraidedCategory C} {D : Type u₂} {inst_3 : CategoryTheory.Category.{v₂, u₂} D}
  {inst_4 : CategoryTheory.MonoidalCategory D} {inst_5 : CategoryTheory.BraidedCategory D}
  {F : CategoryTheory.Functor C D} [self : F.LaxBraided] (X Y : C) {Z : D}
  (h : F.obj (CategoryTheory.MonoidalCategoryStruct.tensorObj Y X) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.LaxMonoidal.μ F X Y)
      (CategoryTheory.CategoryStruct.comp (F.map (β_ X Y).hom) h) =
    CategoryTheory.CategoryStruct.comp (β_ (F.obj X) (F.obj Y)).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.LaxMonoidal.μ F Y X) h)

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

0 results in Mathlib

Foundations

Depth 6 from the axioms · uses Quot.sound

Assumes

CategoryTheory.Functor.LaxBraided