It's well known that a preorder can be considered as a category C, such that for every two objects formula_40, there exists "at most one" morphism formula_41 in C. If there happens to be a morphism from "c" to "c' ", we could write formula_42, but in the current section we find it more convenient to express this fact in arrow form formula_41. Because there is at most one such morphism, we never have to give it a name, such as formula_44. The reflexivity and transitivity properties of an order are respectively accounted for by the identity morphism and the composition formula in C. We write formula_45 iff formula_42 and formula_47, i.e. if they are isomorphic in C. Note that in a partial order, any two isomorphic objects are in fact equal.