Theorems · Definition · category theory

CategoryTheory.Limits.IsColimit.OfNatIso.colimitCocone

{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} → F.cocones.CorepresentableBy X → CategoryTheory.Limits.Cocone F

If F.cocones is corepresented by X, the cocone corresponding to the identity morphism on X will be a colimit cocone.

Defined in: Mathlib.CategoryTheory.Limits.IsLimit
Cited by: 3 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category

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Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Limits.Coconestatement · cited by 746
CategoryTheory.Functor.CorepresentableBystatement and proof · cited by 27
CategoryTheory.Functor.coconesstatement and proof · cited by 9
CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHomproof · cited by 4

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_facstatement · cited by 1
CategoryTheory.Limits.IsColimit.ofCorepresentableBystatement and proof · cited by 1
CategoryTheory.Limits.HasColimit.ofCoconesIsoproof · cited by 0
CategoryTheory.Limits.IsColimit.OfNatIso.cocone_facstatement and proof · cited by 0