# Kerodon

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Proposition 4.5.3.4 (Symmetry). A commutative diagram of simplicial sets

$\xymatrix@R =50pt@C=50pt{ A \ar [r] \ar [d] & B \ar [d] \\ C \ar [r] & D }$

is a categorical pushout diagram if and only if the transposed diagram

$\xymatrix@R =50pt@C=50pt{ A \ar [r] \ar [d] & C \ar [d] \\ B \ar [r] & D }$

is a categorical pushout diagram.

Proof. Apply Proposition 3.4.1.7. $\square$