Example 4.5.6.7 (Isofibrant Squares). A square diagram of $\infty $-categories
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{E}}_{01} \ar [r]^-{F'_{1}} \ar [d]^{F'_{0}} & \operatorname{\mathcal{E}}_0 \ar [d]^{F_0} \\ \operatorname{\mathcal{E}}_1 \ar [r]^-{F_1} & \operatorname{\mathcal{E}}} \]
is isofibrant (when regarded as a functor $[1] \times [1] \rightarrow \operatorname{Set_{\Delta }}$) if and only if it satisfies the following conditions:
The functors $F_0: \operatorname{\mathcal{E}}_0 \rightarrow \operatorname{\mathcal{E}}$ and $F_1: \operatorname{\mathcal{E}}_1 \rightarrow \operatorname{\mathcal{E}}$ are isofibrations of $\infty $-categories.
The functor $(F'_1, F'_0): \operatorname{\mathcal{E}}_{01} \rightarrow \operatorname{\mathcal{E}}_0 \times _{\operatorname{\mathcal{E}}} \operatorname{\mathcal{E}}_1$ is an isofibration of $\infty $-categories.