  The aim of this paper is first to introduce and study Rota-Baxter cosystems
and bisystems as generalization of Rota-Baxter coalgebras and bialgebras,
respectively, with various examples. The second purpose is to provide an
alternative definition of covariant bialgebras via coderivations. Furthermore,
we consider coquasitriangular covariant bialgebras which are generalization of
coquasitriangular infinitesimal bialgebras, coassociative Yang-Baxter pairs,
coassociative Yang-Baxter equation, double coalgebras and dendriform
coalgebras. We study some of their properties and relationships with
Rota-Baxter cosystems and bisystems.
