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


The morphism $f$ is a covering map (Definition


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 and