Lemma 98.13.5 (07XV)—The Stacks project

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Part 7: Algebraic Stacks
Chapter 98: Artin's Axioms
Section 98.13: Openness of versality
Lemma 98.13.5 (cite)

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Lemma 98.13.5. Let $S$ be a locally Noetherian scheme. Let $f : \mathcal{X} \to \mathcal{Y}$ and $\mathcal{Z} \to \mathcal{Y}$ be $1$ -morphisms of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$ . If $f$ satisfies (98.13.2.1) so does the projection $\mathcal{X} \times _\mathcal {Y} \mathcal{Z} \to \mathcal{Z}$ .

Proof. Follows immediately from Lemma 98.3.3 and Formal Deformation Theory, Lemma 90.8.7. $\square$

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