On Frobenius algebras in rigid monoidal categories

Details On Frobenius algebras in rigid monoidal categories On Frobenius algebras in rigid monoidal categories

2009-01-30

arxiv.org/abs/0901.4886v1

Arabian Journal for Science and Engineering 33-2C (2008) 175 - 191

Mathematics

Category Theory

Scientific paper

We show that the equivalence between several possible characterizations of Frobenius algebras, and of symmetric Frobenius algebras, carries over from the category of vector spaces to more general monoidal categories. For Frobenius algebras, the appropriate setting is the one of rigid monoidal categories, and for symmetric Frobenius algebras it is the one of sovereign monoidal categories. We also discuss some properties of Nakayama automorphisms.

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