Article ID Journal Published Year Pages File Type
5771895 Journal of Algebra 2017 39 Pages PDF
Abstract
The theories of (Hopf) bialgebras and weak (Hopf) bialgebras have been introduced for vector space categories over fields and make heavily use of the tensor product. As first generalisations, these notions were formulated for monoidal categories, with braidings if needed. The present authors developed a theory of bimonads and Hopf monads H on arbitrary categories A, employing distributive laws, allowing for a general form of the Fundamental Theorem for Hopf algebras. For τ-bimonads H, properties of braided (Hopf) bialgebras were captured by requiring a Yang-Baxter operator τ:HH→HH. The purpose of this paper is to extend the features of weak (Hopf) bialgebras to this general setting including an appropriate form of the Fundamental Theorem. This subsumes the theory of braided Hopf algebras (based on weak Yang-Baxter operators) as considered by Alonso Álvarez and others.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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