Example 3.5.7.23. Let $X$ be a Kan complex and let $n$ be an integer. The coskeleton $\operatorname{cosk}_{n+1}(X)$ is a Kan complex (Proposition 3.5.3.23) which is $(n+1)$-coskeletal, and therefore $n$-truncated (Example 3.5.7.2). Remark 3.5.3.22 guarantees that the tautological map $f: X \rightarrow \operatorname{cosk}_{n+1}(X)$ is $(n+1)$-connective. It follows that $f$ exhibits $\operatorname{cosk}_{n+1}(X)$ as an $n$-truncation of $X$.
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