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The Categories of Yetter—Drinfel’d Modules, Doi—Hopf Modules and Two-sided Two-cosided Hopf Modules

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Abstract

We show that the two-sided two-cosided Hopf modules are in some case generalized Hopf modules in the sense of Doi. Then the equivalence between two-sided two-cosided Hopf modules and Yetter—Drinfel’d modules, proved in [8], becomes an equivalence between categories of Doi—Hopf modules. This equivalence induces equivalences between the underlying categories of (co)modules. We study the relation between this equivalence and the one given by the induced functor.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Mount Allison University, Sackville, N.B., Canada, E4L IE6

    M. Beattie

  2. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, RO-70109, Bucharest 1, Romania

    S. Dăscălescu & ş. Raianu

  3. Department of Mathematics, University of Antwerp (UIA), Universiteitsplein 1, B-2610, Wilrijk, Belgium

    F. Van Oystaeyen

Authors
  1. M. Beattie
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  2. S. Dăscălescu
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  3. ş. Raianu
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  4. F. Van Oystaeyen
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Beattie, M., Dăscălescu, S., Raianu, ş. et al. The Categories of Yetter—Drinfel’d Modules, Doi—Hopf Modules and Two-sided Two-cosided Hopf Modules. Applied Categorical Structures 6, 223–237 (1998). https://doi.org/10.1023/A:1008660029543

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