On Frobenius algebras in rigid monoidal categories

Abstract

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.

References in corpus (4)

• TFT construction of RCFT correlators III: Simple currents
• Correspondences of ribbon categories
• Conformal Correlation Functions, Frobenius Algebras and Triangulations
• Subfactor realisation of modular invariants

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