A categorical approach to cyclic duality
Gabriella B\"ohm, Dragos Stefan
TL;DR
This paper develops a unifying categorical framework for para-(co)cyclic modules in Hopf cyclic theory, enabling functoriality of coefficients and extending the theory to bialgebroids.
Contribution
It introduces a categorical approach to cyclic duality, broadening the scope of Hopf cyclic theory to include bialgebroids and providing a functorial perspective.
Findings
Constructed a functor for Connes's cyclic duality.
Extended Hopf cyclic theory to (Hopf) bialgebroids.
Provided a unifying categorical framework for para-(co)cyclic modules.
Abstract
The aim of this paper is to provide a unifying categorical framework for the many examples of para-(co)cyclic modules arising from Hopf cyclic theory. Functoriality of the coefficients is immediate in this approach. A functor corresponding to Connes's cyclic duality is constructed. Our methods allow, in particular, to extend Hopf cyclic theory to (Hopf) bialgebroids.
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