# Kerodon

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

Proposition 2.4.4.15. Let $Q$ be a partially ordered set. Then the comparison map $u: \operatorname{N}_{\bullet }(Q) \rightarrow \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{Path}[Q] )$ described above exhibits $\operatorname{Path}[Q]_{\bullet }$ as a path category for the simplicial set $\operatorname{N}_{\bullet }(Q)$ (in the sense of Definition 2.4.4.1).