The Stacks project

Definition 80.3.1. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$. Let $F$, $G$ be presheaves on $\mathit{Sch}_{fppf}/S$. We say a morphism $a : F \to G$ is representable by algebraic spaces if for every $U \in \mathop{\mathrm{Ob}}\nolimits ((\mathit{Sch}/S)_{fppf})$ and any $\xi : U \to G$ the fiber product $U \times _{\xi , G} F$ is an algebraic space.