Remark 1.1.1.3. The category $\operatorname{{\bf \Delta }}$ is equivalent to the category of *all* nonempty finite linearly ordered sets, with morphisms given by nondecreasing maps. In fact, we can say something even better: for every nonempty finite linearly ordered set $I$, there is a *unique* order-preserving bijection $I \simeq [n]$, for some $n \geq 0$.

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$