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A structure theorem for quasi-Hopf bimodule coalgebras

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Daniel Bulacu

Let H be a quasi-Hopf algebra. We show that any H-bimodule coalgebra
C for which there exists an H-bimodule coalgebra morphism n : C ->
H is isomorphic to what we will call a smash product coalgebra. To this
end, we use an explicit monoidal equivalence between the category of
two-sided two-cosided Hopf modules over H and the category of left
Yetter-Drinfeld modules over H. This categorical method allows also to
reobtain the structure theorem for a quasi-Hopf (bi)comodule algebra given
by Panaite and Van Oystaeyen, and by Dello et al.

Keywords:
monoidal equivalence, (bi)comodule algebra, bimodule coalgebra, structure
theorem

2010 MSC:
16W30; 18D10; 16S34

*Theory and Applications of Categories,*
Vol. 32, 2017,
No. 1, pp 1-30.

Published 2017-01-03.

http://www.tac.mta.ca/tac/volumes/32/1/32-01.pdf

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