Kerodon

Remark 9.2.1.3. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $W$ be a collection of morphisms of $\operatorname{\mathcal{C}}$, which we also view as a collection of morphisms in the opposite $\infty $-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$. Then an object $Z \in \operatorname{\mathcal{C}}$ is $W$-local (in the sense of Definition 9.2.1.1) if and only if it is $W$-colocal when viewed as an object of $\operatorname{\mathcal{C}}^{\operatorname{op}}$.