The Yoneda embedding is a functor よ : 𝒞 → 𝒞 ^ : よ → 𝒞 ^ 𝒞 \yo:\mathcal{C}\to\widehat{\mathcal{C}} from a Category 𝒞 𝒞 \mathcal{C} to the Presheaf Category on 𝒞 𝒞 \mathcal{C} given by X ↦ − → X X\mapsto{{-}\to{X}} .