Remark 6.2.3.4. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $W$ be a collection of morphisms of $\operatorname{\mathcal{C}}$, and let $C,C' \in \operatorname{\mathcal{C}}$ be objects which are isomorphic. Then $C$ is $W$-local if and only if $C'$ is $W$-local. In other words, the collection of $W$-local objects span a replete full subcategory of $\operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$