Remark 2.4.5.6. Roughly speaking, one can think of the simplicial set $\operatorname{\partial \raise {0.1ex}{\square }}^{n}$ as obtained from the $n$-cube $\operatorname{\raise {0.1ex}{\square }}^{n}$ by removing its interior, while the subsets $\boldsymbol {\sqcap }^{n}_{i}, \boldsymbol {\sqcup }^{n}_{i}$ are obtained from $\operatorname{\raise {0.1ex}{\square }}^{n}$ by removing the interior together with a single face.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$