The Stacks project

Definition 4.8.2. Let $\mathcal{C}$ be a category. Let $F, G : \mathcal{C}^{opp} \to \textit{Sets}$ be functors. We say a morphism $a : F \to G$ is representable, or that $F$ is relatively representable over $G$, if for every $U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$ and any $\xi \in G(U)$ the functor $h_ U \times _ G F$ is representable.