Oplax Hopf Algebras

Christina Vasilakopoulou; Joost Vercruysse; Mitchell Buckley; Timmy Fieremans

Oplax Hopf Algebras

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arxiv 1710.01465 v4 pith:2ZC6I5RF submitted 2017-10-04 math.CT math.RA

Mitchell Buckley , Timmy Fieremans , Christina Vasilakopoulou , Joost Vercruysse This is my paper · ORCID

classification math.CTmath.RA

keywords hopfmonoidalbicategoryoplaxbraidedfrobeniusintroducemonoid

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We introduce the notion of an oplax Hopf monoid in any braided monoidal bicategory, generalizing that of a Hopf monoid in a braided monoidal category in an appropriate way. We show that Hopf V-categories introduced in [BCV16] are a particular type of oplax Hopf monoids in the monoidal bicategory Span|V described in [B\"oh17]. Finally, we introduce Frobenius V-categories as the Frobenius objects in the same monoidal bicategory.

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A Larson-Sweedler Theorem for Hopf V-Categories
math.CT 2019-08 conditional novelty 7.0 of 10

A locally rigid semi-Hopf V-category is Hopf and Frobenius if and only if it has non-singular left and right integral families, equivalently if its integral spaces are the monoidal unit.

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