Example 7.6.3.5. A (strictly) commutative diagram of $\infty $-categories
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}\ar [r] \ar [d] & \operatorname{\mathcal{C}}_0 \ar [d] \\ \operatorname{\mathcal{C}}_{1} \ar [r] & \operatorname{\mathcal{C}}_{01} } \]
is a categorical pushout square (in the sense of Definition 4.5.4) if and only if the induced diagram $\Delta ^1 \times \Delta ^1 \rightarrow \operatorname{N}_{\bullet }^{\operatorname{hc}}(\operatorname{QCat}) = \operatorname{\mathcal{QC}}$ is a pushout square in the $\infty $-category $\operatorname{\mathcal{QC}}$. This follows by combining Corollaries 7.5.8.5 and 7.5.8.9.