Theorems · Theorem · category theory

CategoryTheory.BraidedCategory.yang_baxter_iso

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (X Y Z : C),
  (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).symm ≪≫
      CategoryTheory.MonoidalCategory.whiskerRightIso (β_ X Y) Z ≪≫
        CategoryTheory.MonoidalCategoryStruct.associator Y X Z ≪≫
          CategoryTheory.MonoidalCategory.whiskerLeftIso Y (β_ X Z) ≪≫
            (CategoryTheory.MonoidalCategoryStruct.associator Y Z X).symm ≪≫
              CategoryTheory.MonoidalCategory.whiskerRightIso (β_ Y Z) X ≪≫
                CategoryTheory.MonoidalCategoryStruct.associator Z Y X =
    CategoryTheory.MonoidalCategory.whiskerLeftIso X (β_ Y Z) ≪≫
      (CategoryTheory.MonoidalCategoryStruct.associator X Z Y).symm ≪≫
        CategoryTheory.MonoidalCategory.whiskerRightIso (β_ X Z) Y ≪≫
          CategoryTheory.MonoidalCategoryStruct.associator Z X Y ≪≫
            CategoryTheory.MonoidalCategory.whiskerLeftIso Z (β_ X Y)

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

0 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory