Coalgebraic algebra
type: Item
instance of: scholarly article
title: Coalgebraic algebra
zbMATH Open document ID: 0935.16028
DOI: 10.1016/S0022-4049(97)00076-5
author: Paul Turner
author: John Hunton
published in: Journal of Pure and Applied Algebra
publication date: 2000-02-08T00:00:00Z
review text: From a purely algebraic point of view, a Hopf algebra over a commutative ring \(R\) is a group object in the category of associative and counitary \(R\)-coalgebras. Thus, Hopf algebras are referred by the authors as coalgebraic groups. This leads to the notions of (commutative and cocommutative) coalgebraic ring and coalgebraic module, which are assumed to be bigraded for homological purposes (the paper has its motivation in Algebraic Topology). The authors establish two main results. Theorem 3.4 says that the category of finite-type coalgebraic modules over a coalgebraic ring \(A_{*,*}\) is Abelian. Theorem 5.3 establishes that the category of coalgebraic \(A_{*,*}\)-modules is a symmetric monoidal category under a tensor product functor \(\otimes_{A_{*,*}}\) which is explicitly constructed. Its derived functors are considered in Section 6. The topological background of the paper is explained in the Introduction.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 18G15
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 55N20
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 1308199
zbMATH Keywords: Hopf algebras
zbMATH Keywords: coalgebraic groups
zbMATH Keywords: coalgebraic rings
zbMATH Keywords: coalgebraic modules
zbMATH Keywords: coalgebraic module tensor products
zbMATH Keywords: derived functors
zbMATH Keywords: symmetric monoidal categories
reviewed by: José Gómez-Torrecillas
MaRDI profile type: Publication
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full work available at URL: s0022-4049(97)00076-5
OpenAlex ID: W4213232597
description: scientific article; zbMATH DE number 1308199