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A Larson-Sweedler theorem for Hopf V-categories

Journal Contribution - Journal Article

The aim of this paper is to extend the classical Larson-Sweedler theorem, namely that a k-bialgebra has a non-singular integral (and in particular is Frobenius) if and only if it is a finite dimensional Hopf algebra, to the ‘many-object’ setting of Hopf categories. To this end, we provide new characterizations of Frobenius V-categories and we develop the integral theory for Hopf V-categories. Our results apply to Hopf algebras in any braided monoidal category as a special case, and also relate to Turaev's Hopf group algebras and particular cases of weak and multiplier Hopf algebras.

Journal: Advances in Mathematics
ISSN: 0001-8708
Volume: 376
Number of pages: 64
Publication year:2021
Keywords:Hopf CategoryFrobenius categoryEnriched categoryMonoidal categoryIntegral spaceHopf module, Pure mathematics