Remark 2.2.8.25. A bicategory $\operatorname{\mathcal{C}}$ is a $2$-groupoid if and only if it is a $2$-category and the homotopy category $\operatorname {h}\! \mathit{\operatorname{\mathcal{C}}}$ is a groupoid.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$