Example 14.11.2. For every $n \geq 0$ we denote $\Delta [n]$ the simplicial set

\[ \Delta ^{opp} \longrightarrow \textit{Sets},\quad [k] \longmapsto \mathop{\mathrm{Mor}}\nolimits _{\Delta }([k], [n]) \]

We leave it to the reader to verify the following statements. Every $m$-simplex of $\Delta [n]$ with $m > n$ is degenerate. There is a unique nondegenerate $n$-simplex of $\Delta [n]$, namely $\text{id}_{[n]}$.

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