Example 2.2.8.26. Let $\operatorname{\mathcal{C}}$ be an ordinary category. Then $\operatorname{\mathcal{C}}$ is a groupoid if and only if it is a $2$-groupoid (when viewed as a $2$-category having only identity $2$-morphisms).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$