Lemma 97.13.5. 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 (97.13.2.1) so does the projection $\mathcal{X} \times _\mathcal {Y} \mathcal{Z} \to \mathcal{Z}$.

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