Geodesic
Generalized Hopf modules for bimonads
Theory and applications of categories, CT2011, Tome 27 (2012), pp. 263-326.

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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).
Publié le :
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 
@article{TAC_2012_27_a12,
     author = {Marcelo Aguiar and Stephen U. Chase},
     title = {Generalized {Hopf} modules for bimonads},
     journal = {Theory and applications of categories},
     pages = {263--326},
     publisher = {mathdoc},
     volume = {27},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2012_27_a12/}
}
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Marcelo Aguiar; Stephen U. Chase. Generalized Hopf modules for bimonads. Theory and applications of categories, CT2011, Tome 27 (2012), pp. 263-326. http://geodesic.mathdoc.fr/item/TAC_2012_27_a12/