Proposition 4.5.2.16. A commutative diagram of $\infty $-categories
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}_{01} \ar [r] \ar [d] & \operatorname{\mathcal{C}}_0 \ar [d] \\ \operatorname{\mathcal{C}}_1 \ar [r] & \operatorname{\mathcal{C}}} \]
is a categorical pullback square if and only if the induced diagram of opposite $\infty $-categories
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}^{\operatorname{op}}_{01} \ar [r] \ar [d] & \operatorname{\mathcal{C}}^{\operatorname{op}}_0 \ar [d] \\ \operatorname{\mathcal{C}}^{\operatorname{op}}_1 \ar [r] & \operatorname{\mathcal{C}}^{\operatorname{op}} } \]
is a categorical pullback square.