Theorems · Theorem · category theory

CategoryTheory.Enriched.FunctorCategory.isLimitConeFunctorEnrichedHom.fac

∀ {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.HasFunctorEnrichedHom V F₁ F₂]
  [inst_6 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₁ F₂]
  (s : CategoryTheory.Limits.Cone (CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom V F₁ F₂)) (j : J),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Enriched.FunctorCategory.isLimitConeFunctorEnrichedHom.lift s)
      ((CategoryTheory.Enriched.FunctorCategory.coneFunctorEnrichedHom V F₁ F₂).π.app j) =
    s.π.app j

Defined in

Mathlib.CategoryTheory.Enriched.FunctorCategory

Cited by

0 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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