Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 9.2.1.6. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $W$ be a collection of morphisms of $\operatorname{\mathcal{C}}$. If $C$ is a $W$-local object of $\operatorname{\mathcal{C}}$, then any retract of $C$ is also $W$-local. In particular, the condition that $C$ is $W$-local depends only on the isomorphism class of $C$.