Lemma 64.16.4. Let $\mathit{Sch}_{fppf}$ be a big fppf site. Let $S \to S'$ be a morphism of this site. Let $F'$ be a sheaf on $(\mathit{Sch}/S')_{fppf}$. The following are equivalent:

1. The restriction $F'|_{(\mathit{Sch}/S)_{fppf}}$ is an algebraic space over $S$, and

2. the sheaf $h_ S \times F'$ is an algebraic space over $S'$.

Proof. The restriction and the product match under the equivalence of categories of Sites, Lemma 7.25.4 so that Lemma 64.16.3 above gives the result. $\square$

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