Remark 5.1.5.5. Suppose we are given a pullback diagram of simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ X' \ar [r] \ar [d]^-{q'} & X \ar [d]^-{q} \\ S' \ar [r] & S. } \]
If $q$ is a locally cartesian fibration, then $q'$ is also a locally cartesian fibration (see Remark 5.1.1.12). If $q$ is a locally cocartesian fibration, then $q'$ is also a locally cocartesian fibration.