Remark 9.2.3.12. 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. If $C$ is weakly $W$-local, then any retract of $C$ is also weakly $W$-local. In particular, the condition that $C$ is weakly $W$-local depends only on the isomorphism class of $C$.
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