Theorems · Definition · category theory

CategoryTheory.Enriched.FunctorCategory.functorEnrichedComp

(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 : CategoryTheory.Functor J C) →
                  [inst_5 : CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom V F₁ F₂] →
                    [inst_6 : CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom V F₂ F₃] →
                      [inst_7 : CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom V F₁ F₃] →
                        CategoryTheory.MonoidalCategoryStruct.tensorObj
                            (CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom V F₁ F₂)
                            (CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom V F₂ F₃) ⟶
                          CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom V F₁ F₃

The composition for the J ⥤ V-enrichment of the category J ⥤ C.

Defined in

Mathlib.CategoryTheory.Enriched.FunctorCategory

Cited by

9 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.EnrichedOrdinaryCategoryCategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHomCategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHomCategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom