Theorems · Definition · category theory

CategoryTheory.Limits.IsColimit.ofCorepresentableBy

{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) →
              CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone h)

If F.cocones is corepresentable, then the cocone corresponding to the identity morphism on the representing object is a colimit cocone.

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category