Lemma 97.13.6. Let $S$ be a locally Noetherian scheme. Let $f : \mathcal{X} \to \mathcal{Y}$ be a $1$-morphisms of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. If $f$ is formally smooth on objects, then $f$ satisfies (97.13.2.1). If $f$ is representable by algebraic spaces and smooth, then $f$ satisfies (97.13.2.1).

Proof. A reformulation of Lemma 97.3.2. $\square$

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