Generalized Hopf modules for bimonads

Marcelo Aguiar ; Stephen U. Chase

Theory and applications of categories, CT2011, Tome 27 (2012), pp. 263-326

Résumé

Bruguières, Lack and Virelizier have recently obtained a vast generalization of Sweedler's Fundamental Theorem of Hopf modules, in which the role of the Hopf algebra is played by a bimonad. We present an extension of this result which involves, in addition to the bimonad, a comodule-monad and a algebra-comonoid over it. As an application we obtain a generalization of another classical theorem from the Hopf algebra literature, due to Schneider, which itself is an extension of Sweedler's result (to the setting of Hopf Galois extensions).

Détail

Publié le : 2013-01-28

Classification : 16T05, 16T15, 18A40, 18C15, 18D10, 18D35
Keywords: monad, comonad, bimonad, Beck's theorem, Hopf module, Doi-Koppinen Hopf module, Hopf Galois, Sweedler's Fundamental Theorem, Schneider's Structure Theorem, Hilbert's Theorem 90