  We should underline again the fact that not all categories are made of structured sets with structure-preserving maps. Thus any preordered set is a category. For given two elements \(p, q\) of a preordered set, there is a morphism \(\boldsymbol{f}: p \rightarrow q\) if and only if \(p \le q.\) Hence a preordered set is a category in which there is at most one morphism between any two objects. Any monoid (and thus any group) can be seen as a category: in this case the category has only one object, and its morphisms are the elements of the monoid. Composition of morphisms corresponds to multiplication of monoid elements. That the monoid axioms correspond to the category axioms is easily verified.