Remark 1.1.4.4. Let $S$ be a simplicial set and let $k$ be an integer. If $n \leq k$, then $\operatorname{sk}_{k}( S )$ contains every $n$-simplex of $S$. In particular, the union $\bigcup _{k} \operatorname{sk}_{k}( S )$ is equal to $S$.
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