Remark 4.5.5.11. The collection of isofibrations is closed under pullback. That is, given a pullback diagram of simplicial sets

\[ \xymatrix@R =50pt@C=50pt{ X'_{} \ar [d]^{q'} \ar [r] & X_{} \ar [d]^{q} \\ S'_{} \ar [r] & S_{} } \]

where $q$ is an isofibration, the morphism $q'$ is also an isofibration.