Remark 3.5.1.11. Let $X$ be a simplicial set. Then $X$ is weakly contractible if and only if it is $n$-connective for every integer $n$. To prove this, we can use Corollary 3.1.7.2 to reduce to the case where $X$ is a Kan complex, in which case it is a reformulation of Proposition 3.5.1.12.
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