Frobenius and Separable Functors for the Category of Entwined Modules over Cowreaths, I: General Theory

  • D. Bulacu
  • S. Caenepeel
  • B. TorrecillasEmail author


Entwined modules over cowreaths in a monoidal category are introduced. They can be identified to coalgebras in an appropriate monoidal category. It is investigated when such coalgebras are Frobenius (resp. separable), and when the forgetful functor from entwined modules to representations of the underlying algebra is Frobenius (resp. separable). These properties are equivalent when the unit object of the category is a ⊗-generator.


Module category Cowreath Entwined module Frobenius functor Separable functor Frobenius coalgebra Coseparable coalgebra 


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The authors are very grateful to the referee for careful reading of the paper and valuable suggestions and comments.


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Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharest 1Romania
  2. 2.Faculty of EngineeringVrije Universiteit BrusselBrusselsBelgium
  3. 3.Department of Algebra and AnalysisUniversidad de AlmeríaAlmeríaSpain

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