Remark 1.3.1.9. Let $\operatorname{\mathcal{C}}$ be a category and let $\sigma $ be an $n$-simplex of $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$, corresponding to a diagram
\[ C_0 \xrightarrow {f_1} C_1 \xrightarrow {f_2} C_2 \rightarrow \cdots \xrightarrow {f_ n} C_ n. \]
Then $\sigma $ is degenerate (Definition 1.1.2.3) if and only if some $f_ i$ is an identity morphism of $\operatorname{\mathcal{C}}$ (in which case we must have $C_{i-1} = C_{i}$).