Remark 3.5.3.22. Let $X$ be a simplicial set and let $n$ be an integer. Then the tautological map $u: X \rightarrow \operatorname{cosk}_{n}(X)$ is bijective on $m$-simplices for $m \leq n$. Applying Corollary 3.5.2.2, we deduce that $u$ is $n$-connective.
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