Lemma 97.13.4. Let $S$ be a locally Noetherian scheme. Let $f : \mathcal{X} \to \mathcal{Y}$ and $g : \mathcal{Y} \to \mathcal{Z}$ be composable $1$-morphisms of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. If $f$ and $g$ satisfy (97.13.2.1) so does $g \circ f$.

**Proof.**
This follows formally from Formal Deformation Theory, Lemma 89.8.7.
$\square$

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