Remark 6.3.7.16. Let $S$ be a finite simplicial set. In this case, each of the simplicial sets $\widetilde{\operatorname{sk}}_{k}(S)$ constructed in the proof of Proposition 6.3.7.14 will also be finite. Specializing to the case $k \geq \dim (S)$, we obtain a universally localizing morphism
\[ \widetilde{\operatorname{sk}}_{k}(S) \rightarrow \operatorname{sk}_{k}(S) = S \]
where the simplicial set $\widetilde{\operatorname{sk}}_{k}(S)$ is both finite and nonsingular.