Theorems · Theorem · category theory

CategoryTheory.Dial.pentagon

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

Defined in

Mathlib.CategoryTheory.Dialectica.Monoidal

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasPullbacks