# Kerodon

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

Corollary 2.3.4.5. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $2$-categories. Then passage to the Duskin nerve induces a bijection

$\xymatrix@R =50pt@C=50pt{ \{ \textnormal{Strictly unitary functors \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}} \} \ar [d] \\ \{ \textnormal{Maps \operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{N}_{\bullet }^{\operatorname{D}}(\operatorname{\mathcal{D}}) preserving thin 2-simplices} \} . }$