Variant 9.2.1.7. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $w: X \rightarrow Y$ be a morphism in $\operatorname{\mathcal{C}}$, and let $C \in \operatorname{\mathcal{C}}$ be an object which is $w$-local. Then $C$ is $w'$-local, for any morphism $w': X' \rightarrow Y'$ which is a retract of $w$ (in the $\infty $-category $\operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}})$).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$