Corollary 4.5.2.27. Suppose we are given a pullback diagram of $\infty $-categories
4.28
\begin{equation} \begin{gathered}\label{equation:categorical-pullback-square44} \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}' \ar [r] \ar [d] & \operatorname{\mathcal{C}}\ar [d]^{U} \\ \operatorname{\mathcal{D}}' \ar [r] & \operatorname{\mathcal{D}}. } \end{gathered} \end{equation}
If $U$ is an isofibration, then (4.28) is a categorical pullback square.