Theorems · Theorem · category theory

CategoryTheory.BraidedCategory.braiding_naturality_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] {X X' Y Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') {Z : C}
  (h : CategoryTheory.MonoidalCategoryStruct.tensorObj Y' Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom f g)
      (CategoryTheory.CategoryStruct.comp (β_ Y Y').hom h) =
    CategoryTheory.CategoryStruct.comp (β_ X X').hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom g f) h)

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

6 results in Mathlib

Foundations

Depth 10 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory