?? so for example, consider the co-bisimplicial object in _simplicial set_ whose "realization" functor is cartesian prouct ... in other words consider cartesian product of representable simplicial sets ... ??? .... realizing a bi-simplex as the cartesian product in _simplicial set_ of the corresponding pair of simplexes ... ??? ...

?? then analog for actions of commutative monoid m ... tri-module ... just one representable m-set, namely m with cayley action .... cartesian product with itself as m^2 ... co-bi-m-set object in _m-set_ ... ??isn't this real close to part of categorified bialgebra structure that we've been looking at .... ???? ....