Theorems · Theorem · category theory

CategoryTheory.Functor.map_braiding_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) (X Y : C) [inst_6 : F.Braided] {Z : D}
  (h : F.obj (CategoryTheory.MonoidalCategoryStruct.tensorObj Y X) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (F.map (β_ X Y).hom) h =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OplaxMonoidal.δ F X Y)
      (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 12 from the axioms · uses Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.Functor.Braided