Definition 94.8.1 (04SV)—The Stacks project

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Table of contents
Part 7: Algebraic Stacks
Chapter 94: Algebraic Stacks
Section 94.8: Categories fibred in groupoids representable by algebraic spaces
Definition 94.8.1 (cite)

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Definition 94.8.1. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$ . A category fibred in groupoids $p : \mathcal{X} \to (\mathit{Sch}/S)_{fppf}$ is called representable by an algebraic space over $S$ if there exists an algebraic space $F$ over $S$ and an equivalence $j : \mathcal{X} \to \mathcal{S}_ F$ of categories over $(\mathit{Sch}/S)_{fppf}$ .

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