Kerodon

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

Example 5.5.7.3. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $2$-categories. By virtue of Theorem 2.3.4.1 and Corollary 2.3.4.5, passage to the Duskin nerve induces a bijection

\[ \xymatrix@R =50pt@C=50pt{ \{ \textnormal{Strictly unitary functors of $2$-categories $\operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$} \} \ar [d] \\ \{ \textnormal{Functors of $(\infty ,2)$-categories $\operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{D}})$} \} . } \]