Exercise 9.2.3.16. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $w: X \rightarrow Y$ be a morphism of $\operatorname{\mathcal{C}}$ which admits a relative codiagonal $\gamma _{X/Y}: Y \coprod _{X} Y \rightarrow Y$. Show that an object $C \in \operatorname{\mathcal{C}}$ is $w$-local if and only if it is both $\gamma _{X/Y}$-local and weakly $w$-local.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$