Kerodon

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

Remark 2.4.3.7. The homotopy coherent nerve of Definition 2.4.3.5 determines a functor $\operatorname{N}_{\bullet }^{\operatorname{hc}}(-)$ from the category $\operatorname{Cat_{\Delta }}$ of simplicial categories (Definition 2.4.1.11) to the category $\operatorname{Set_{\Delta }}$ of simplicial sets (Definition 1.1.1.12). This is a special case of the general construction described in Variant 1.1.7.7, associated to the cosimplicial object of $\operatorname{Cat_{\Delta }}$ given by

\[ \operatorname{{\bf \Delta }}\rightarrow \operatorname{Cat_{\Delta }}\quad \quad [n] \mapsto \operatorname{Path}[n]_{\bullet }. \]