Theorems · Definition · category theory

CategoryTheory.OverPresheafAux.OverArrows.val

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {A F : CategoryTheory.Functor Cᵒᵖ (Type v)} →
      {η : F ⟶ A} →
        {X : C} →
          {s : CategoryTheory.yoneda.obj X ⟶ A} → CategoryTheory.OverPresheafAux.OverArrows η s → F.obj (Opposite.op X)

Since OverArrows η s can be thought of to contain certain morphisms yoneda.obj X ⟶ F, the Yoneda lemma yields elements F.obj (op X).

Defined in

Mathlib.CategoryTheory.Comma.Presheaf.Basic

Cited by

19 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category