Theorems · Theorem · category theory

CategoryTheory.BraidedCategory.braiding_tensor_left_inv

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

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

2 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory