Remark 4.1.1.9. Let $q: X \rightarrow Y$ be an inner fibration of simplicial sets. If $Y$ is an $\infty $-category, then $X$ is also an $\infty $-category (this follows by combining Remark 4.1.1.8 with Example 4.1.1.2).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$