CYCLIC HOMOLOGY, COEFFICIENTS, AND LIMITS

Classically, coefficients for Hopf-cyclic homology were defined as objects that are both a module and a comodule with a compatibility between the two structures. This definition has been generalized to different settings with various levels of success. We will look at two cases where a limit-focused approach to cyclic-homology coefficients yields interesting descriptions of the coefficients in the style of the original definition. The difference in our approach is that it uses a general, limit-based, definition to obtain a description in a particular case without guessing. The two cases that we consider are bialgebras in vector spaces and Hopf algebras in rigid braided categories. The deduced coefficients do not agree with the existing generalizations, but do generalize the classical case.