Kerodon

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

Example 3.3.4.5. Let $Q$ be a partially ordered set, so that we can identify the subdivision of $\operatorname{N}_{\bullet }(Q)$ with the nerve of the partially ordered set $\operatorname{Chain}[Q]$ (Example 3.3.3.16). Under this identification, the last vertex map $\lambda _{ \operatorname{N}_{\bullet }(Q)}$ corresponds to the morphism $\operatorname{N}_{\bullet }( \operatorname{Chain}[Q] ) \rightarrow \operatorname{N}_{\bullet }( Q)$ induced by $\mathrm{Max}: \operatorname{Chain}[Q] \rightarrow Q$.