Theorems · Theorem · category theory

CategoryTheory.e_assoc

∀ (V : Type v) [inst : CategoryTheory.Category.{w, v} V] [inst_1 : CategoryTheory.MonoidalCategory V] {C : Type u₁}
  [inst_2 : CategoryTheory.EnrichedCategory V C] (W X Y Z : C),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.associator (W ⟶[V] X) (X ⟶[V] Y) (Y ⟶[V] Z)).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.eComp V W X Y) (Y ⟶[V] Z))
        (CategoryTheory.eComp V W Y Z)) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (W ⟶[V] X) (CategoryTheory.eComp V X Y Z))
      (CategoryTheory.eComp V W X Z)

Defined in

Mathlib.CategoryTheory.Enriched.Basic

Cited by

7 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.EnrichedCategory