Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 2.3.1.3. Let $\operatorname{\mathcal{C}}$ be an ordinary category, viewed as a $2$-category having only identity $2$-morphisms (Example 2.2.0.6). Then the Duskin nerve $\operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}})$ can be identified with the nerve $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ of $\operatorname{\mathcal{C}}$ as an ordinary category (Construction 1.2.1.1).