Any monoid can be presented as an algebra (X in Set, h:TX->X) for the monad T:Set->Set for monoids. There's a 2-category with - one object - morphisms are lists of elements of X - 2-morphisms out of a list f are all the different ways of collapsing sublists of f using h This construction works for algebras of any monad, not just the one for monoids. Does it have a name? -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com