To return to our example, let N be the category whose objects are the natural numbers 0, 1, 2, ..., with a single morphism formula_62 if formula_63 in the usual ordering (and no morphisms from "i" to "j" otherwise), and a monoidal structure with the monoidal unit given by 0 and the monoidal multiplication given by the usual addition, formula_64. Then N is a monoidal preorder; in fact it is the one freely generated by a single object 1, and a single morphism 0 ≤ 1, where again 0 is the monoidal unit.