Corollary 5.6.5.16. Let $\operatorname{\mathcal{C}}$ be a small category. Then passage to the homotopy coherent nerve induces a bijection
\[ \xymatrix { \{ \textnormal{Functors of ordinary categories $\operatorname{\mathcal{C}}\rightarrow \operatorname{QCat}$} \} / \textnormal{Levelwise equivalence} \ar [d] \\ \{ \textnormal{Functors of $\infty $-categories $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{QC}}$} \} / \textnormal{Isomorphism}. } \]