A monoid is a set \(M\) with a monoid unit \(e \in M\) and associative monoid multiplication \(M \times M \xrightarrow{\star} M\) such that \(m \star e=m=e \star m\)
Every set \(S\) determines a discrete preorder: \(\mathbf{Disc}_S\)
It is easy to check if \((M,e,\star)\) is a commutative monoid then \((\mathbf{Disc}_M, =, e, \star)\) is a symmetric monoidal preorder.