Journal of Noncommutative Geometry

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Volume 2, Issue 3, 2008, pp. 333–351
DOI: 10.4171/JNCG/23

Published online: 2008-09-30

The universal Hopf-cyclic theory

Atabey Kaygun[1]

(1) Ohio State University, Columbus

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.

Keywords: Hopf-cyclic cohomology, transpositive algebras, monads

Kaygun Atabey: The universal Hopf-cyclic theory. J. Noncommut. Geom. 2 (2008), 333-351. doi: 10.4171/JNCG/23