Remark 9.2.5.12. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing a morphism $g: X \rightarrow Y$, which we identify with an object $\widetilde{X}$ of the slice $\infty $-category $\operatorname{\mathcal{C}}_{/Y}$. Let $S$ be a collection of morphisms of $\operatorname{\mathcal{C}}$, and let $\widetilde{S}$ denote its inverse image in $\operatorname{\mathcal{C}}_{/Y}$. The following conditions are equivalent:
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$