On the anti-Yetter-Drinfeld module-contramodule correspondence

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We study a functor from anti-Yetter Drinfeld modules to contramodules in the case of a Hopf algebra H. Some byproducts of this investigation are the establishment of sufficient conditions for this functor to be an equivalence, verification that the center of the opposite category of H-comodules is equivalent to anti-Yetter Drinfeld modules, and the observation of two types of periodicities of the generalized Yetter-Drinfeld modules introduced previously. Finally, we give an example of a symmetric 2-contratrace on H-comodules that does not arise from an anti-Yetter Drinfeld module.