Example 2.2.8.20. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between (small) categories. Then $F$ is an equivalence of categories if and only if it is an isomorphism when regarded as a $1$-morphism in the $2$-category $\mathbf{Cat}$ of Example 2.2.0.4.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$