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.
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  ie 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