\begin{definition}[Definition:Representable Functor]
Let $\mathbf C$ be a locally small category.
Let $\mathbf{Set}$ be the category of sets.
Let $F : \mathbf C \to \mathbf{Set}$ be a covariant functor.
Then $F$ is '''representable''' if there exists an object $C \in \mathbf C$ such that $F$ is naturally isomorphic to the covariant hom functor $\operatorname{Hom} \paren {C, \cdot}$.
That is, $F$ is '''representable''' if $F$ has a representation.
{{DefinitionWanted|contravariant}}
\end{definition}