HOPF-ALGEBRAS OF COMBINATORIAL STRUCTURES

A generalization of the definition of combinatorial species is given by considering functors whose domains are categories of finite sets, with various classes of relations as morphisms. Two cases in particular correspond to species for which one has notions of restriction and quotient of structures. Coalgebras and/or Hopf algebras can be associated to such species. the duals of which provide an algebraic framework for studying invariants of structures.