Remark 9.4.1.5. Let $\mathbb {K}$ be a collection of simplicial sets and suppose we are given a pullback diagram
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{E}}' \ar [r] \ar [d]^{U'} & \operatorname{\mathcal{E}}\ar [d]^{U} \\ \operatorname{\mathcal{C}}' \ar [r] & \operatorname{\mathcal{C}}, } \]
where $U$ and $U'$ are inner fibrations. If $U$ is $\mathbb {K}$-cocomplete, then $U'$ is also $\mathbb {K}$-cocomplete.