Definition 3.3.1.1. Let $X_{\bullet }$ be a simplicial set. We will say that $X_{\bullet }$ is braced if, for every nondegenerate simplex $\sigma \in X_{n}$ of dimension $n > 0$, the faces $\{ d^{n}_ i(\sigma ) \} _{0 \leq i \leq n}$ are also nondegenerate.
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