# Kerodon

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

Example 4.1.5.2. Every covering map of simplicial sets (in the sense of Definition 3.1.4.1) is an inner covering map. In particular, if $f: X \rightarrow S$ is a covering map of topological spaces, then the induced map $\operatorname{Sing}_{\bullet }(f): \operatorname{Sing}_{\bullet }(X) \rightarrow \operatorname{Sing}_{\bullet }(S)$ is an inner covering of simplicial sets (Proposition 3.1.4.9).