Remark 9.2.3.11. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $W$ be a collection of morphisms of $\operatorname{\mathcal{C}}$, and let $C \in \operatorname{\mathcal{C}}$ be an object which factors as a product of some collection of objects $\{ C_ i \} _{i \in I}$ (see Definition 7.6.1.3). If each $C_ i$ is weakly $W$-local, then $C$ is weakly $W$-local. In particular, any final object of $\operatorname{\mathcal{C}}$ is weakly $W$-local.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$