Remark 9.2.9.11. Let $\kappa \leq \lambda $ be regular cardinals and suppose we are given a pullback diagram of simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{E}}' \ar [r] \ar [d]^{U'} & \operatorname{\mathcal{E}}\ar [d]^{U} \\ \operatorname{\mathcal{C}}' \ar [r] & \operatorname{\mathcal{C}}. } \]
If $U$ is a $(\kappa ,\lambda )$-cocomplete inner fibration, then $U'$ is also a $(\kappa ,\lambda )$-cocomplete inner fibration.