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arXiv · 1306.1459

On the category of weak bialgebras

Gabriella Böhm·José Gómez-Torrecillas·Esperanza López-Centella
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Abstract

Weak (Hopf) bialgebras are described as (Hopf) bimonoids in appropriate duoidal (also known as 2-monoidal) categories. This interpretation is used to define a category wba of weak bialgebras over a given field. As an application, the "free vector space" functor from the category of small categories with finitely many objects to wba is shown to possess a right adjoint, given by taking (certain) group-like elements. This adjunction is proven to restrict to the full subcategories of groupoids and of weak Hopf algebras, respectively. As a corollary, we obtain equivalences between the category of small categories with finitely many objects and the category of pointed cosemisimple weak bialgebras; and between the category of small groupoids with finitely many objects and the category of pointed cosemisimple weak Hopf algebras.

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BibTeXRIS

Gabriella Böhm, José Gómez-Torrecillas, Esperanza López-Centella. 2013-10-19. On the category of weak bialgebras. https://arxiv.org/abs/1306.1459

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