Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Proposition 3.4.2.2 (Symmetry). A commutative diagram of simplicial sets

\[ \xymatrix { A \ar [r] \ar [d] & B \ar [d] \\ C \ar [r] & D } \]

is homotopy coCartesian if and only if the transposed diagram

\[ \xymatrix { A \ar [r] \ar [d] & C \ar [d] \\ B \ar [r] & D } \]

is homotopy coCartesian.

Proof. Apply Proposition 3.4.1.7. $\square$