Lemma 64.5.3. 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 64.5.1. 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 64.3.1. Proof omitted.
$\square$

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