On the category of weak bialgebras

Böhm, Gabriella Eszter and Gómez-Torrecillas, J. and López-Centella, E. (2014) On the category of weak bialgebras. JOURNAL OF ALGEBRA, 399. pp. 801-844. ISSN 0021-8693

Preview

Text 1306.1459.pdf Available under License Creative Commons Attribution. Download (515kB) | Preview

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.

Actions (login required)

Edit Item