Theorems · Theorem · category theory

CategoryTheory.eHomEquiv_comp

∀ (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 Z : C}
  (f : X ⟶ Y) (g : Y ⟶ Z),
  (CategoryTheory.eHomEquiv V) (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorUnit V)).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.tensorHom ((CategoryTheory.eHomEquiv V) f)
          ((CategoryTheory.eHomEquiv V) g))
        (CategoryTheory.eComp V X Y Z))

Defined in

Mathlib.CategoryTheory.Enriched.Ordinary.Basic

Cited by

5 results in Mathlib

Foundations

Depth 15 from the axioms · uses Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.EnrichedOrdinaryCategory