# Kerodon

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

Corollary 5.6.5.16. Let $\operatorname{\mathcal{C}}$ be a small category. Then passage to the homotopy coherent nerve induces a bijection

$\xymatrix { \{ \textnormal{Functors of ordinary categories \operatorname{\mathcal{C}}\rightarrow \operatorname{QCat}} \} / \textnormal{Levelwise equivalence} \ar [d] \\ \{ \textnormal{Functors of \infty -categories \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{QC}}} \} / \textnormal{Isomorphism}. }$