Lemma 97.11.3. Let $S$ be a scheme. Let $\mathcal{X}$ be an algebraic stack over $S$. Then the following are equivalent

$\mathcal{X}$ is a stack in setoids and $\mathcal{X} \to (\mathit{Sch}/S)_{fppf}$ is limit preserving on objects,

$\mathcal{X}$ is a stack in setoids and limit preserving,

$\mathcal{X}$ is representable by an algebraic space locally of finite presentation.

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