Definition 3.5.1.1. Let $X$ be a Kan complex and let $n$ be a nonnegative integer. We say that $X$ is $n$-connective if it is nonempty and, for every vertex $x \in X$ and every integer $0 \leq m < n$, the set $\pi _{m}(X,x)$ consists of a single element.
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