On Frobenius algebras in rigid monoidal categories
Jurgen Fuchs, Carl Stigner
TL;DR
This paper extends the characterization of Frobenius and symmetric Frobenius algebras from vector spaces to rigid and sovereign monoidal categories, broadening their theoretical framework.
Contribution
It generalizes the equivalence of Frobenius algebra characterizations to rigid and sovereign monoidal categories, including properties of Nakayama automorphisms.
Findings
Equivalence of Frobenius algebra characterizations in rigid monoidal categories
Extension of symmetric Frobenius algebra properties to sovereign monoidal categories
Discussion of Nakayama automorphisms in this broader context
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry