Kerodon

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

Definition 4.1.2.2. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. A subcategory of $\operatorname{\mathcal{C}}$ is a simplicial subset $\operatorname{\mathcal{C}}' \subseteq \operatorname{\mathcal{C}}$ for which the inclusion map $\operatorname{\mathcal{C}}' \hookrightarrow \operatorname{\mathcal{C}}$ is an inner fibration.