$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Remark 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 to reduce to the case where $S = \{ s\} $ is a $0$-simplex, in which case it follows by combining Proposition with Example