Example 1.2.3.8. For each $n \geq 0$, the boundary $\operatorname{\partial \Delta }^{n}$ of Construction 1.1.4.10 is given by $\Delta ^{n}_{\operatorname{\mathcal{U}}}$, where $\operatorname{\mathcal{U}}$ is the collection of all nonempty proper subsets of $[n]$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$