Example 1.1.4.14. When $n = 1$, Proposition 1.1.4.13 asserts that we can identify maps $\operatorname{\partial \Delta }^1 \rightarrow S$ with ordered pairs $(s,t)$ of vertices of $S$. Equivalently, the boundary $\operatorname{\partial \Delta }^1$ can be identified with the coproduct of $\{ 0\} $ and $\{ 1\} $ (which we regard as simplicial subsets of $\Delta ^1$ as in Example 1.1.0.15).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$