Theorems · Theorem · category theory

CategoryTheory.BraidedCategory.hexagon_reverse_inv

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

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

1 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory