Remark 4.1.5.9. Let $f: X_{} \rightarrow S_{}$ be a morphism of simplicial sets. The following conditions are equivalent:
- $(a)$
The morphism $f$ is an inner covering map (Definition 4.1.5.1).
- $(b)$
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 inner anodyne, there exists a unique dotted arrow rendering the diagram commutative.