Remark 9.1.3.7. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a left fibration of $\infty $-categories, where $\operatorname{\mathcal{C}}$ is $\kappa $-filtered. Then $\operatorname{\mathcal{E}}$ is $\kappa $-filtered if and only if it is filtered: by virtue of Variant 9.1.3.6 and Theorem 9.1.3.2, both conditions are equivalent to the requirement that $\operatorname{\mathcal{E}}$ is weakly contractible.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$