Theorems · Theorem · category theory

CategoryTheory.BraidedCategory.braiding_tensor_right_hom_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (X Y Z : C) {Z_1 : C}
  (h : CategoryTheory.MonoidalCategoryStruct.tensorObj (CategoryTheory.MonoidalCategoryStruct.tensorObj Y Z) X ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (β_ X (CategoryTheory.MonoidalCategoryStruct.tensorObj Y Z)).hom h =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).inv
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight (β_ X Y).hom Z)
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator Y X Z).hom
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft Y (β_ X Z).hom)
            (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator Y Z X).inv h))))

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

1 results in Mathlib

Foundations

Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory