Kerodon

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

Remark 7.1.2.3. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then an object $Y \in \operatorname{\mathcal{C}}$ is initial (in the sense of Definition 7.1.2.1) if and only if it is a colimit of the empty diagram $\emptyset \hookrightarrow \operatorname{\mathcal{C}}$. Similarly, $Y$ is final if and only if it is a limit of the empty diagram.