Proposition 7.6.3.14. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\sigma : \Delta ^1 \times \Delta ^1 \rightarrow \operatorname{\mathcal{C}}$ be a commutative square, which we represent by a diagram
\[ \xymatrix@R =50pt@C=50pt{ X_{01} \ar [r] \ar [d] & X_0 \ar [d] \\ X_1 \ar [r] & X. } \]
Then $\sigma $ is a pullback diagram in $\operatorname{\mathcal{C}}$ if and only if it exhibits $X_{01}$ as a product of $X_0$ with $X_1$ in the slice $\infty $-category $\operatorname{\mathcal{C}}_{/X}$.