Definition 3.5.2.8. Let $X$ be a simplicial set and let $n$ be a nonnegative integer. We say that $X$ is $n$-reduced if the $n$-skeleton $\operatorname{sk}_{n}(X)$ is isomorphic to the standard $0$-simplex $\Delta ^0$: that is, $X$ has a single $m$-simplex for every integer $0 \leq m \leq n$.
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