Lemma 97.18.3. 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 97.5.3.
$\square$

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