Corollary 4.6.8.19. Let $A$ and $B$ be simplicial sets, and let $\operatorname{\mathcal{E}}[B]$ be the simplicial category of Notation 4.6.8.1. Then we have a canonical bijection
\[ \{ \textnormal{Morphisms $A \rightarrow \operatorname{Hom}_{\operatorname{N}_{\bullet }^{\operatorname{hc}}(\operatorname{\mathcal{E}}[B])}^{\mathrm{L}}(x,y)$} \} \simeq \{ \textnormal{Morphisms $\Phi (A) \rightarrow B$} \} . \]