Corollary 9.1.3.14. Let $U_{0}: \operatorname{\mathcal{E}}_{0} \rightarrow \operatorname{\mathcal{C}}$ and $U_{1}: \operatorname{\mathcal{E}}_{1} \rightarrow \operatorname{\mathcal{C}}$ be cocartesian fibrations of $\infty $-categories. If $\operatorname{\mathcal{E}}_{0}$, $\operatorname{\mathcal{E}}_{1}$, and $\operatorname{\mathcal{C}}$ are filtered, then the fiber product $\operatorname{\mathcal{E}}_{0} \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}_{1}$ is also filtered.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$