We define a Hopf cyclic (co)homology theory in an arbitrary symmetric strict monoidal 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 along with Hopf–Hochschild (co)homology of module algebras, and describe the missing theory for comodule coalgebras.
Cite this article
Atabey Kaygun, The universal Hopf-cyclic theory. J. Noncommut. Geom. 2 (2008), no. 3, pp. 333–351DOI 10.4171/JNCG/23