# Kerodon

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

Remark 3.1.4.6. Let $f: X_{} \rightarrow S_{}$ be a morphism of simplicial sets. The following conditions are equivalent:

$(a)$

The morphism $f$ is a covering map (Definition 3.1.4.1).

$(b)$

For every square diagram of simplicial sets

$\xymatrix@R =50pt@C=50pt{ A_{} \ar [d]^{i} \ar [r] & X_{} \ar [d]^{f} \\ B_{} \ar [r] \ar@ {-->}[ur] & S_{} }$

where $i$ is anodyne, there exists a unique dotted arrow rendering the diagram commutative.

This follows by combining Remarks 3.1.2.7 and 3.1.4.3.