Corollary 9.1.3.11. Let $\kappa $ be an infinite cardinal, let $\operatorname{\mathcal{C}}$ be a $\kappa $-filtered $\infty $-category, and let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration. Assume that, for each object $C \in \operatorname{\mathcal{C}}$, the $\infty $-category $\operatorname{\mathcal{E}}_{C} = \{ C\} \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}$ is $\kappa $-filtered. Then $\operatorname{\mathcal{E}}$ is $\kappa $-filtered.
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