Kerodon

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

Remark 6.3.3.3. 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 6.3.3.1) if and only if it is $W$-colocal when viewed as an object of $\operatorname{\mathcal{C}}^{\operatorname{op}}$. The collection of morphisms $W$ is localizing (in the sense of Definition 6.3.3.2) if and only if it is colocalizing when viewed as a collection of morphisms of $\operatorname{\mathcal{C}}^{\operatorname{op}}$.