Theorems · Theorem · category theory

CategoryTheory.BraidedCategory.yang_baxter

∀ {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 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
              (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight (β_ Y Z).hom X)
                (CategoryTheory.MonoidalCategoryStruct.associator Z Y X).hom))))) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X (β_ Y Z).hom)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X Z Y).inv
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight (β_ X Z).hom Y)
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator Z X Y).hom
            (CategoryTheory.MonoidalCategoryStruct.whiskerLeft Z (β_ X Y).hom))))

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

3 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory