Typed binary trees and generalized dendrifom algebras

We here both unify and generalize nonassociative structures on typed binary trees, that is to say plane trees which edges are decorated by elements of a set Ω. prove we obtain such structure, called an Ω-dendriform if Ω has four products satisfying certain axioms (EDS axioms), including the diassociative semigroup. This includes matching dendriform algebras introduced Zhang, Gao Guo family associated semigroup Manchon, course when reduced single element. also give examples EDS, all EDS cardinality two; combinatorial description structure but words; study Koszul dual operads; considerations existence coproduct, in order bialgebras.