Kerodon

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

Remark 8.4.0.2. Let $\operatorname{\mathcal{C}}$ be a category. Then an object $Y \in \operatorname{\mathcal{C}}$ is initial if and only if it is a colimit of the unique diagram $\emptyset \rightarrow \operatorname{\mathcal{C}}$; here $\emptyset $ denotes the category with no objects. Similarly, an object $Y \in \operatorname{\mathcal{C}}$ is final if and only if it is a limit of the unique diagram $\emptyset \rightarrow \operatorname{\mathcal{C}}$.