Example 1.2.4.3. The horn $\Lambda ^{1}_{0} \subset \Delta ^1$ is the vertex $\{ 0\} $, and the horn $\Lambda ^{1}_{1} \subset \Delta ^1$ is the vertex $\{ 1\} $ (see Example 1.1.0.15). In particular, $\Lambda ^{1}_{0}$ and $\Lambda ^{1}_{1}$ are abstractly isomorphic to the standard $0$-simplex $\Delta ^{0}$. Moreover, the boundary $\operatorname{\partial \Delta }^{1}$ is the disjoint union of $\Lambda ^{1}_{0}$ and $\Lambda ^{1}_{1}$.
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