Homology, Homotopy and Applications
Volume 12 (2010)
Hopf cyclic cohomology in braided monoidal categories
Pages: 111 – 155
We extend the formalism of Hopf cyclic cohomology to the context of braided categories. For a Hopf algebra in a braided monoidal abelian category we introduce the notion of stable anti-Yetter-Drinfeld module. We associate a para-cocyclic and a cocyclic object to a braided Hopf algebra endowed with a braided modular pair in involution in the sense of Connes and Moscovici. When the braiding is symmetric the full formalism of Hopf cyclic cohomology with coefficients can be extended to our categorical setting.
noncommutative geometry; Hopf algebra; braided monoidal category; Hopf cyclic cohomology
2010 Mathematics Subject Classification