Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Construction 4.6.7.23. Let $K$ be a simplicial set, let $\operatorname{\mathcal{E}}[K]$ be the simplicial category of Notation 4.6.7.1, and let

\[ \theta : K = \operatorname{Hom}_{\operatorname{\mathcal{E}}[K]}(x,y)_{\bullet } \rightarrow \operatorname{Hom}^{\mathrm{L}}_{ \operatorname{N}_{\bullet }^{\operatorname{hc}}(\operatorname{\mathcal{E}}[K])}( x, y) \]

be the comparison map of Construction 4.6.7.3. We let $\rho _{K}: \Phi (K) \rightarrow K$ denote the image of $\theta $ under the bijection of Corollary 4.6.7.19.