Remark 1.1.3.6. Let $S_{\bullet }$ be a simplicial set and let $k \geq -1$. If $n \leq k$, then $\operatorname{sk}_{k}( S_{\bullet } )$ contains every $n$-simplex of $S_{\bullet }$. In particular, the union $\bigcup _{k \geq -1} \operatorname{sk}_{k}( S_{\bullet } )$ is equal to $S_{\bullet }$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$