Theorems · Definition · category theory

CategoryTheory.Functor.representableByEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {F : CategoryTheory.Functor Cᵒᵖ (Type v₁)} → {Y : C} → F.RepresentableBy Y ≃ (CategoryTheory.yoneda.obj Y ≅ F)

The obvious bijection F.RepresentableBy Y ≃ (yoneda.obj Y ≅ F) when F : Cᵒᵖ ⥤ Type v₁ and [Category.{v₁} C].

Defined in

Mathlib.CategoryTheory.Yoneda

Cited by

5 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category