The Stacks project

Definition 7.49.2. Let $\mathcal{C}$ be a category. Let $J$ be a topology on $\mathcal{C}$. We say that a presheaf of sets $\mathcal{F}$ is separated if for every object $U$ and every covering sieve $S$ on $U$ the canonical map $\mathcal{F}(U) \to \mathop{\mathrm{Mor}}\nolimits _{\textit{PSh}(\mathcal{C})}(S, \mathcal{F})$ is injective.