Remark 3.4.1.7. A commutative diagram of simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ X_{01} \ar [r] \ar [d] & X_0 \ar [d] \\ X_1 \ar [r] & X } \]
is a homotopy pullback square if and only if the induced diagram of opposite simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ X_{01}^{\operatorname{op}} \ar [r] \ar [d] & X_0^{\operatorname{op}} \ar [d] \\ X_1^{\operatorname{op}} \ar [r] & X^{\operatorname{op}} } \]
is a homotopy pullback square.