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

On Frobenius algebras in rigid monoidal categories