Example 3.3.3.18. Let $Q$ be a partially ordered set. Combining Proposition 3.3.3.17 with Example 3.3.3.14, 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.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$