Baer sums in homological categories
type: Item
instance of: scholarly article
title: Baer sums in homological categories
zbMATH Open document ID: 1134.18004
author: Dominique Bourn
published in: Journal of Algebra
publication date: 2007-02-26T00:00:00Z
review text: The author proves that the description of the abstract Baer sum defined in any Barr exact context can be simplified when the ground category \(\mathcal C\) in question is moreover protomodular and can be reduced to the classical scheme concerning the exact sequences, then, this produces a unified treatment of the Baer theory in the context of any semi-abelian variety, in particular of any category of groups with multiple operators. The author also shows that the above result does hold in the category of Hausdorff groups and more generally any category of semi-abelian Hausdorff algebras. Finally, these processes lead to a generalized ``Euclide's Postulate'' and a five terms exact sequence.
Mathematics Subject Classification ID: 18D35
Mathematics Subject Classification ID: 18E10
zbMATH DE Number: 5129726
reviewed by: Wenhuai Shen
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.07.022
OpenAlex ID: W2091446959
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DOI: 10.1016/J.JALGEBRA.2006.07.022
description: scientific article; zbMATH DE number 5129726