Kerodon

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

Remark 5.4.5.7 (Comparison with Categories). Let $\mathbf{Cat}$ denote the strict $2$-category of small categories (Example 2.2.0.4). By virtue of Proposition 1.4.3.3, the construction $\operatorname{\mathcal{C}}\mapsto \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ induces an isomorphism from the Duskin nerve $\operatorname{N}_{\bullet }^{\operatorname{D}}( \mathbf{Cat} )$ to the full subcategory of $\operatorname{ \pmb {\mathcal{QC}} }$ spanned by those $\infty $-categories of the form $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$, where $\operatorname{\mathcal{C}}$ is an ordinary category.