Remark 4.8.6.29. Suppose we are given a pullback diagram of simplicial sets
\[ \xymatrix@C =50pt@R=50pt{ \operatorname{\mathcal{C}}' \ar [r] \ar [d]^{F'} & \operatorname{\mathcal{C}}\ar [d]^{ F } \\ \operatorname{\mathcal{D}}' \ar [r] & \operatorname{\mathcal{D}}. } \]
If $F$ is an $n$-categorical inner fibration, then $F'$ is also an $n$-categorical inner fibration.