Lemma 4.37.4. Let $\mathcal{C}$ be a category. The 2-category of categories fibred in sets over $\mathcal{C}$ has 2-fibre products. More precisely, the 2-fibre product described in Lemma 4.31.3 returns a category fibred in sets if one starts out with such.

**Proof.**
Omitted.
$\square$

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