The opposite of a symmetric monoidal preorder \((X, \geq, I, \otimes)\) is still a symmetric monoidal preorder
Monotonicity: \(x_1 \geq y_1 \land x_2 \geq y_2 \implies x_1 \otimes x_2 \geq y_1 \otimes y_2\)
This holds because monotonicity holds in the original preorder (\(a\geq b \equiv b \leq a\)).
Unitality, symmetry, and associativity are not affected by the preorder.