Remark 9.3.4.25. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $f: X \hookrightarrow Y$ be a monomorphism in $\operatorname{\mathcal{C}}$. If $f': X' \rightarrow Y'$ is a retract of $f$ (in the $\infty $-category $\operatorname{Fun}(\Delta ^1, \operatorname{\mathcal{C}})$), then $f'$ is also a monomorphism. See Corollary 9.3.3.12.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$