Proposition 3.4.2.6. A commutative diagram of simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ A \ar [r] \ar [d] & A_0 \ar [d] \\ A_1 \ar [r] & A_{01} } \]
is a homotopy pushout square if and only if the induced diagram of opposite simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ A^{\operatorname{op}} \ar [r] \ar [d] & A_{0}^{\operatorname{op}} \ar [d] \\ A_1^{\operatorname{op}} \ar [r] & A_{01}^{\operatorname{op}} } \]
is a homotopy pushout square.