Example 9.2.3.6. Let $\operatorname{\mathcal{C}}$ be a category and let $W$ be a collection of morphisms of $\operatorname{\mathcal{C}}$. Then an object $C \in \operatorname{\mathcal{C}}$ is weakly $W$-local (in the sense of Definition 9.2.3.1) if and only if it is weakly $W$-local when regarded as an object of the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ (in the sense of Definition 9.2.3.5).
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