Lemma 94.9.5 (0458)—The Stacks project

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Part 7: Algebraic Stacks
Chapter 94: Algebraic Stacks
Section 94.9: Morphisms representable by algebraic spaces
Lemma 94.9.5 (cite)

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Lemma 94.9.5. 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 80.3.1) if and only if $a'$ is representable by algebraic spaces.

Proof. Omitted. $\square$

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