Remark 4.2.3.17. Let $f: X \rightarrow S$ be a morphism of simplicial sets which is either a left covering map or a right covering map. For each vertex $s \in S$, the fiber $X_{s} = \{ s\} \times _{S} X$ is a discrete simplicial set. To prove this, we can use Remark 4.2.3.15 to reduce to the case where $S = \{ s\} $ is a $0$-simplex, in which case it follows by combining Proposition 4.2.3.16 with Example 4.2.3.4.

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