Hopf monoids in varieties
type: Item
instance of: scholarly article
title: Hopf monoids in varieties
zbMATH Open document ID: 1397.08006
author: Hans-E. Porst
published in: Algebra Universalis
publication date: 2018-07-16T00:00:00Z
review text: Although the natural frame for defining generalizations of Hopf algebras is that of monoidal categories, one has to add extra assumptions if one wants to obtain non-trivial results, generalizing the classical theorem on Hopf algebras over a commutative field. In this paper, the frame of commutative categories is studied. Hopf bimonoids in such a category are defined, and conditions for the existence of groups of group-like elements and of a functorial finite dual are given. This paper ends with a bunch of open questions on the monoidal structure of commutative varieties, related to the notion requested before.
reviewed by: Loïc Foissy
Mathematics Subject Classification ID: 08B99
Mathematics Subject Classification ID: 08C05
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 18B99
zbMATH DE Number: 6904403
zbMATH Keywords: commutative varieties
zbMATH Keywords: Hopf monoids
zbMATH Keywords: free and cofree Hopf monoids
zbMATH Keywords: universal measuring comonoids
zbMATH Keywords: group algebras
zbMATH Keywords: finite dual
MaRDI profile type: Publication
full work available at URL: s00012-018-0500-5
OpenAlex ID: W2801863183
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DOI: 10.1007/S00012-018-0500-5
description: scientific article; zbMATH DE number 6904403