Remark 3.1.4.3. Let $f: X \rightarrow S$ be a morphism of simplicial sets, and let $\delta : X \rightarrow X \times _{S} X$ be the relative diagonal of $f$. Then $f$ is a covering map if and only if both $f$ and $\delta $ are Kan fibrations. In particular, every covering map is a Kan fibration.
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