Example 9.2.3.9. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $w: X \rightarrow Y$ a morphism of $\operatorname{\mathcal{C}}$ which admits a left homotopy inverse $r: Y \rightarrow X$. Then every object $C \in \operatorname{\mathcal{C}}$ is weakly $w$-local. In particular, if $w$ is an isomorphism, then every object of $\operatorname{\mathcal{C}}$ is weakly $w$-local.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$