Lemma 90.29.5. With notation and assumptions as in Situation 90.29.1. If $\mathcal{F} \to \mathcal{G}$ is a smooth morphism of categories cofibred in groupoids over $\mathcal{C}_{\Lambda , k}$, then $\mathcal{F}_{l/k} \to \mathcal{G}_{l/k}$ is a smooth morphism of categories cofibred in groupoids over $\mathcal{C}_{\Lambda , l}$.

**Proof.**
This follows immediately from the definitions and the fact that (90.29.1.1) preserves surjections.
$\square$

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