Theorems · Definition · category theory

CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom

{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 → {Y : C} → (X ⟶ Y) → CategoryTheory.Limits.Cocone F

If F.cocones is corepresented by X, each morphism f : X ⟶ Y gives a cocone with cone point Y.

Defined in: Mathlib.CategoryTheory.Limits.IsLimit
Cited by: 4 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category

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Cites8

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

DFunLike.coeproof · cited by 62,936
CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Limits.Coconestatement · cited by 746
CategoryTheory.Functor.CorepresentableBy.homEquivproof · cited by 45
CategoryTheory.Functor.CorepresentableBystatement and proof · cited by 27
CategoryTheory.Functor.coconesstatement and proof · cited by 9

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.IsColimit.OfNatIso.colimitCoconeproof · cited by 3
CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_facstatement · cited by 1
CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCoconestatement · cited by 1
CategoryTheory.Limits.IsColimit.OfNatIso.homOfCocone_coconeOfHomstatement · cited by 1
CategoryTheory.Limits.IsColimit.OfNatIso.cocone_facproof · cited by 0