Geodesic
Cyclic homology arising from adjunctions
Theory and applications of categories, Tome 30 (2015), pp. 1067-1095

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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 Böhm 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 role of the two notions of bimonad studied in the literature is clarified.

Publié le :
Classification : 16T05, 18C15, 18C20, 19D55
Keywords: cyclic homology, Hopf algebroids, Hopf monads, distributive laws 
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     author = {Niels Kowalzig and Ulrich Kr\"ahmer and Paul Slevin},
     title = {Cyclic homology arising from adjunctions},
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     pages = {1067--1095},
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     volume = {30},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a31/}
}
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Niels Kowalzig; Ulrich Krähmer; Paul Slevin. Cyclic homology arising from adjunctions. Theory and applications of categories, Tome 30 (2015), pp. 1067-1095. http://geodesic.mathdoc.fr/item/TAC_2015_30_a31/