The universal Hopf-cyclic theory

We define a Hopf cyclic (co)homology theory in an arbitrary symmetric strictmonoidal category. Thus we unify all different types of Hopf cyclic(co)homologies under one single universal theory. We recover Hopf cyclic(co)homology of module algebras, comodule algebras and module coalgebras alongwith Hopf-Hochschild (co)homology of module algebras. This universal theoryalso allows us to define the missing Hopf cyclic theory for comodulecoalgebras.