Definition 1.1.2.3. Let $S_{\bullet }$ be a simplicial set. We say that an $n$-simplex $\sigma $ of $S_{\bullet }$ is degenerate if it belongs to the image of the degeneracy operator $s^{n-1}_{i}: S_{n-1} \rightarrow S_{n}$ for some integer $0 \leq i < n$. We say that $\sigma $ is nondegenerate if it is not degenerate. In particular, every $0$-simplex of $S_{\bullet }$ is nondegenerate.
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