Lemma 98.18.3 (0CXQ)—The Stacks project

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Part 7: Algebraic Stacks
Chapter 98: Artin's Axioms
Section 98.18: Strong Rim-Schlessinger
Lemma 98.18.3 (cite)

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Lemma 98.18.3. Let $S$ be a scheme. Let $p : \mathcal{X} \to \mathcal{Y}$ and $q : \mathcal{Z} \to \mathcal{Y}$ be $1$-morphisms of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. If $\mathcal{X}$, $\mathcal{Y}$, and $\mathcal{Z}$ satisfy (RS*), then so does $\mathcal{X} \times _\mathcal {Y} \mathcal{Z}$.

Proof. The proof is exactly the same as the proof of Lemma 98.5.3. $\square$

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