# Kerodon

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

Corollary 4.6.7.17. Let $K$ be a simplicial set and let $\operatorname{\mathcal{C}}$ be a simplicial category containing objects $X$ and $Y$. Then we have a canonical bijection

$\{ \textnormal{Morphisms K \rightarrow \operatorname{Hom}_{\operatorname{N}_{\bullet }^{\operatorname{hc}}(\operatorname{\mathcal{C}})}^{\mathrm{L}}(X,Y)} \} \simeq \{ \textnormal{Morphisms \Phi (K) \rightarrow \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)_{\bullet }} \} .$