# Kerodon

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

Corollary 4.4.3.9. Let $q: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets, where $\operatorname{\mathcal{D}}$ is a Kan complex. The following conditions are equivalent:

$(1)$

The morphism $q$ is a covering map.

$(2)$

The morphism $q$ is a left covering map.

$(3)$

The morphism $q$ is a right covering map.