Theorems · Theorem · category theory

CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_fac

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [inst_1 : CategoryTheory.Category.{v₃, u₃} C]
  {F : CategoryTheory.Functor J C} {X : C} (h : F.cocones.CorepresentableBy X) {Y : C} (f : X ⟶ Y),
  CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom h f =
    (CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone h).extend f

If F.cocones is corepresented by X, the cocone corresponding to a morphism f : Y ⟶ X is the colimit cocone extended by f.

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

1 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category