Theorems · Theorem · category theory

CategoryTheory.Dial.hexagon_forward

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasFiniteProducts C]
  [inst_2 : CategoryTheory.Limits.HasPullbacks C] (X Y Z : CategoryTheory.Dial C),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).hom
      (CategoryTheory.CategoryStruct.comp (X.braiding (CategoryTheory.MonoidalCategoryStruct.tensorObj Y Z)).hom
        (CategoryTheory.MonoidalCategoryStruct.associator Y Z X).hom) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom (X.braiding Y).hom (CategoryTheory.CategoryStruct.id Z))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator Y X Z).hom
        (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.CategoryStruct.id Y) (X.braiding Z).hom))

Defined in

Mathlib.CategoryTheory.Dialectica.Monoidal

Cited by

0 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasPullbacks