Lemma 80.4.2 (046F)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 80: Bootstrap
Section 80.4: Properties of maps of presheaves representable by algebraic spaces
Lemma 80.4.2 (cite)

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Lemma 80.4.2. Let $S$ be a scheme. Let $\mathcal{P}$ be a property as in Definition 80.4.1. Let

$\xymatrix{ G' \times _ G F \ar[r] \ar[d]^{a'} & F \ar[d]^ a \\ G' \ar[r] & G }$

be a fibre square of presheaves on $(\mathit{Sch}/S)_{fppf}$ . If $a$ is representable by algebraic spaces and has $\mathcal{P}$ so does $a'$ .

Proof. Omitted. Hint: This is formal. $\square$

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