@Jonathan – I think isomorphisms are enough – if \\(Q\\) is a preorder isomorphic to \\(P\\), then we can transplant the monoidal structure on \\(P\\) onto \\(Q\\) using the same trick (convert the \\(Q\\)-elements into \\(P\\)-elements, multiply them in \\(P\\), convert back again). The automorphism version (with \\(Q = P\\)) is just a special case of this.