Theorems · Theorem · category theory

CategoryTheory.eComp_eHomWhiskerRight

∀ (V : Type u') [inst : CategoryTheory.Category.{v', u'} V] [inst_1 : CategoryTheory.MonoidalCategory V] {C : Type u}
  [inst_2 : CategoryTheory.Category.{v, u} C] [inst_3 : CategoryTheory.EnrichedOrdinaryCategory V C] {X X' : C}
  (f : X ⟶ X') (Y Z : C),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.eComp V X' Y Z) (CategoryTheory.eHomWhiskerRight V f Z) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.eHomWhiskerRight V f Y) (Y ⟶[V] Z))
      (CategoryTheory.eComp V X Y Z)

Whiskering commutes with the enriched composition.

Defined in

Mathlib.CategoryTheory.Enriched.Ordinary.Basic

Cited by

1 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.EnrichedOrdinaryCategory