Lemma 90.9.5. Let $S$ be an object of $\mathit{Sch}_{fppf}$. Let $a : F \to G$ be a map of presheaves of sets on $(\mathit{Sch}/S)_{fppf}$. Denote $a' : \mathcal{S}_ F \to \mathcal{S}_ G$ the associated map of categories fibred in sets. Then $a$ is representable by algebraic spaces (see Bootstrap, Definition 76.3.1) if and only if $a'$ is representable by algebraic spaces.

**Proof.**
Omitted.
$\square$

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