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Frobenius and separable functors for the category of entwined modules over cowreaths, I: General theory

Journal Contribution - Journal Article

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.

Journal: Algebras and Representation Theory
ISSN: 1386-923X
Issue: 3
Volume: 23
Pages: 1119-1157
Number of pages: 39
Publication year:2020
Keywords:Module category, cowreath, entwined module, Frobenius functor, separable functor, Frobenius coalgebra, oseparable coalgebra