Lemma 65.5.3 (02WJ)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 65: Algebraic Spaces
Section 65.5: Properties of representable morphisms of presheaves
Lemma 65.5.3 (cite)

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Lemma 65.5.3. Let $S$ , $X$ , $Y$ be objects of $\mathit{Sch}_{fppf}$ . Let $f : X \to Y$ be a morphism of schemes. Let $\mathcal{P}$ be as in Definition 65.5.1. Then $h_ X \longrightarrow h_ Y$ has property $\mathcal{P}$ if and only if $f$ has property $\mathcal{P}$ .

Proof. Note that the lemma makes sense by Lemma 65.3.1. Proof omitted. $\square$

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