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).

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

2010 MSC: 16T05, 16T15, 18A40, 18C15, 18D10, 18D35

*Theory and Applications of Categories,*
Vol. 27, 2013,
No. 13, pp 263-326.

Published 2013-01-28

http://www.tac.mta.ca/tac/volumes/27/13/27-13.dvi

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http://www.tac.mta.ca/tac/volumes/27/13/27-13.pdf

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Revised 2013-04-10. Original version at:

http://www.tac.mta.ca/tac/volumes/27/13/27-13a.dvi

http://www.tac.mta.ca/tac/volumes/27/13/27-13a.pdf