Page "Category (mathematics)" Paragraph 17

Any preordered set ( P, ≤) forms a small category, where the objects are the members of P, the morphisms are arrows pointing from x to y when x ≤ y.

Between any two objects there can be at most one morphism.

The existence of identity morphisms and the composability of the morphisms are guaranteed by the reflexivity and the transitivity of the preorder.

By the same argument, any partially ordered set and any equivalence relation can be seen as a small category.

Any ordinal number can be seen as a category when viewed as an ordered set.