Theorems · Theorem · category theory

CategoryTheory.eComp_eHomWhiskerLeft_assoc

∀ (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 Y : C)
  {Z Z' : C} (g : Z ⟶ Z') {Z_1 : V} (h : (X ⟶[V] Z') ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.eComp V X Y Z)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.eHomWhiskerLeft V X g) h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (X ⟶[V] Y) (CategoryTheory.eHomWhiskerLeft V Y g))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.eComp V X Y Z') h)

Whiskering commutes with the enriched composition.

Defined in

Mathlib.CategoryTheory.Enriched.Ordinary.Basic

Cited by

0 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.EnrichedOrdinaryCategory