Note that if C is a partial order, the above description is simplified even more, because the associativity and unitality isomorphisms becomes equalities. Another simplification occurs if we assume that the set of objects is the free monoid on a generating set formula_60. In this case we could write formula_61, where * denotes the Kleene star and the monoidal unit "I" stands for the empty string. If we start with a set "R" of generating morphisms (facts about ≤), we recover the usual notion of semi-Thue system, where "R" is called the "rewriting rule".