Corollary 2.2.8.4. Let $\operatorname{Cat}$ denote the category of (small) categories and let $\operatorname{2Cat}$ denote the category of (small) $2$-categories (Definition 2.2.5.5. Then the inclusion $\operatorname{Cat}\hookrightarrow \operatorname{2Cat}$ admits a left adjoint, given on objects by the construction $\operatorname{\mathcal{C}}\mapsto \mathrm{h} \mathit{\operatorname{\mathcal{C}}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$