Cyclic homology arising from adjunctions

Kowalzig, N., Krähmer, U. and Slevin, P. (2015) Cyclic homology arising from adjunctions. Theory and Applications of Categories, 30(32), pp. 1067-1095.

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Given a monad and a comonad, one obtains a distributive law between them from lifts of one through an adjunction for the other. In particular, this yields for any bialgebroid the Yetter-Drinfel'd distributive law between the comonad given by a module coalgebra and the monad given by a comodule algebra. It is this self-dual setting that reproduces the cyclic homology of associative and of Hopf algebras in the monadic framework of Bohm and Stefan. In fact, their approach generates two duplicial objects and morphisms between them which are mutual inverses if and only if the duplicial objects are cyclic. A 2-categorical perspective on the process of twisting coefficients is provided and the r^ole of the two notions of bimonad studied in the literature is clarfied.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Kowalzig, Dr Niels and Kraehmer, Dr Ulrich
Authors: Kowalzig, N., Krähmer, U., and Slevin, P.
College/School:College of Science and Engineering
College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Theory and Applications of Categories
Publisher:Mount Allison University
ISSN (Online):1201-561X
Copyright Holders:Copyright © 2015 The Authors
First Published:First published in Theory and Applications of Categories 30(32):1067-1095
Publisher Policy:Reproduced with the permission of the publisher

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
586201Homological algebra in monoidal categories: From Hopf algebroids to operads and back.Ulrich KraehmerEngineering & Physical Sciences Research Council (EPSRC)EP/J012718/1M&S - MATHEMATICS