# Kerodon

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Proposition 3.4.2.7 (Symmetry). 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 transposed diagram

$\xymatrix@R =50pt@C=50pt{ A \ar [r] \ar [d] & A_1 \ar [d] \\ A_0 \ar [r] & A_{01} }$

is a homotopy pushout square.

Proof. Apply Proposition 3.4.1.9. $\square$