Kerodon

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

Example 3.3.3.16. Let $Q$ be a partially ordered set. Combining Proposition 3.3.3.15 with Example 3.3.3.13, we obtain a canonical isomorphism $\operatorname{Sd}( \operatorname{N}_{\bullet }(Q) ) \simeq \operatorname{N}_{\bullet }( \operatorname{Chain}[Q] )$. In the special case $Q = [n]$, this recovers the isomorphism $\operatorname{Sd}( \Delta ^{n} ) \simeq \operatorname{N}_{\bullet }( \operatorname{Chain}[n] )$ of Example 3.3.3.5.