For the case that M is the category of sets and is the monoidal structure given by the cartesian product, the terminal single-point set, and the canonical isomorphisms they induce, then each is a set whose elements may be thought of as "individual morphisms" of C, while °, now a function, defines how consecutive morphisms compose. In this case, each path leading to in the first diagram corresponds to one of the two ways of composing three consecutive individual morphisms , i.e. elements from , and . Commutativity of the diagram is then merely the statement that both orders of composition give the same result, exactly as required for ordinary categories.