Theorems · Definition · category theory

CategoryTheory.Enriched.FunctorCategory.precompEnrichedHom

(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] →
              {K : Type u₄} →
                [inst_4 : CategoryTheory.Category.{v₄, u₄} K] →
                  [inst_5 : CategoryTheory.EnrichedOrdinaryCategory V C] →
                    (F₁ F₂ : CategoryTheory.Functor J C) →
                      (G : CategoryTheory.Functor K J) →
                        [inst_6 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₁ F₂] →
                          [inst_7 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V (G.comp F₁) (G.comp F₂)] →
                            CategoryTheory.Enriched.FunctorCategory.enrichedHom V F₁ F₂ ⟶
                              CategoryTheory.Enriched.FunctorCategory.enrichedHom V (G.comp F₁) (G.comp F₂)

If F₁ and F₂ are functors J ⥤ C, and G : K ⥤ J, then this is the induced morphism enrichedHom V F₁ F₂ ⟶ enrichedHom V (G ⋙ F₁) (G ⋙ F₂) in V when C is a category enriched in V.

Defined in

Mathlib.CategoryTheory.Enriched.FunctorCategory

Cited by

6 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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