Theorems · Theorem · category theory

CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition_assoc

∀ (V : Type u₁) [inst : CategoryTheory.Category.{v₁, u₁} V] [inst_1 : CategoryTheory.MonoidalCategory V] {C : Type u₂}
  [inst_2 : CategoryTheory.Category.{v₂, u₂} C] {J : Type u₃} [inst_3 : CategoryTheory.Category.{v₃, u₃} J]
  [inst_4 : CategoryTheory.EnrichedOrdinaryCategory V C] (F₁ F₂ : CategoryTheory.Functor J C)
  [inst_5 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₁ F₂] {i j : J} (f : i ⟶ j) {Z : V}
  (h : (F₁.obj i ⟶[V] F₂.obj j) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Enriched.FunctorCategory.enrichedHomπ V F₁ F₂ i)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.eHomWhiskerLeft V (F₁.obj i) (F₂.map f)) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Enriched.FunctorCategory.enrichedHomπ V F₁ F₂ j)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.eHomWhiskerRight V (F₁.map f) (F₂.obj j)) h)

Defined in

Mathlib.CategoryTheory.Enriched.FunctorCategory

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.EnrichedOrdinaryCategoryCategoryTheory.Enriched.FunctorCategory.HasEnrichedHom