Let $\mathcal{C}$ be a locally small category, and let $F:\mathcal{C}\to \mathbf{Set}$ be a functor. Then, for any object $C\in \mathcal{C}$, there is a natural bijection:
$$\mathrm{Nat}({\mathrm{Hom}}_{\mathcal{C}}(C,-),F)\cong F(C).$$