Auslander-Reiten theory via Brown representability
type: Item
instance of: scholarly article
title: Auslander-Reiten theory via Brown representability
zbMATH Open document ID: 0970.18012
DOI: 10.1023/A:1026571214620
author: Henning Krause
published in: \(K\)-Theory
publication date: 2001-10-15T00:00:00Z
review text: Under mild assumptions, a triangulated category is known to satisfy Brown representability. That is, a covariant functor into abelian groups is representable if and only if it is exact and sends arbitrary coproducts to products. The paper under review develops some Auslander-Reiten theory for triangulated categories by using Brown representability as a basis. For example, Brown representability yields the existence of objects playing the role of Auslander-Reiten translates of given objects. It is shown that Auslander-Reiten triangles exist for compact objects. (Recall that over a finite-dimensional algebra, a compact complex is a bounded complex of finitely generated projective modules.) Moreover, pure-injective objects are discussed as well as morphisms determined by objects, and defects of triangles.
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 18G25
zbMATH DE Number: 1563904
zbMATH Keywords: Auslander-Reiten theory
zbMATH Keywords: Brown representability
zbMATH Keywords: triangulated categories
Wikidata QID: Q121301444
reviewed by: Steffen Koenig
MaRDI profile type: Publication
full work available at URL: a:1026571214620
OpenAlex ID: W2325957216
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description: scientific article; zbMATH DE number 1563904