Remark 4.1.5.7. Suppose we are given a pullback diagram of simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ X' \ar [r] \ar [d]^-{f'} & X \ar [d]^-{f} \\ S' \ar [r] & S. } \]
If $f$ is an inner covering map, then $f'$ is also an inner covering map.