Remark 2.2.8.25. A $2$-category $\operatorname{\mathcal{C}}$ is a $2$-groupoid if and only if it is a $(2,1)$-category and the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ is a groupoid.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$