Theorems · Theorem · category theory

CategoryTheory.Enriched.FunctorCategory.enriched_assoc_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 F₃ F₄ : CategoryTheory.Functor J C)
  [inst_5 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₁ F₂]
  [inst_6 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₁ F₃]
  [inst_7 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₁ F₄]
  [inst_8 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₂ F₃]
  [inst_9 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₂ F₄]
  [inst_10 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₃ F₄] {Z : V}
  (h : CategoryTheory.Enriched.FunctorCategory.enrichedHom V F₁ F₄ ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.associator (CategoryTheory.Enriched.FunctorCategory.enrichedHom V F₁ F₂)
          (CategoryTheory.Enriched.FunctorCategory.enrichedHom V F₂ F₃)
          (CategoryTheory.Enriched.FunctorCategory.enrichedHom V F₃ F₄)).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight
          (CategoryTheory.Enriched.FunctorCategory.enrichedComp V F₁ F₂ F₃)
          (CategoryTheory.Enriched.FunctorCategory.enrichedHom V F₃ F₄))
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.Enriched.FunctorCategory.enrichedComp V F₁ F₃ F₄) h)) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (CategoryTheory.Enriched.FunctorCategory.enrichedHom V F₁ F₂)
        (CategoryTheory.Enriched.FunctorCategory.enrichedComp V F₂ F₃ F₄))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Enriched.FunctorCategory.enrichedComp V F₁ F₂ F₄) h)

Defined in

Mathlib.CategoryTheory.Enriched.FunctorCategory

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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