COMBINATORIAL MODELS FOR COALGEBRAIC STRUCTURES

We introduce a convenient category of combinatorial objects, known as cell-sets. on which we study the properties of the appropriate free ab elian roup Functor. We obtain a versatile generalization of the notion of incidence coalgebra, giving rise to an abundance of coalgebras, Ho pf algebras, and comodules, all of whose structure constants are posit ive integers with respect to certain preferred bases. Our category uni fies and extends existing constructions in algebraic combinatorics, pr oviding proper functorial descriptions; it is inspired in part by the notion of CW-complex, and is also geared to Future applications in alg ebraic topology and the theory of formal group laws. (C) 1998 Academic Press.