Purity and almost split morphisms in abstract homotopy categories: A unified approach via Brown representability
type: Item
instance of: scholarly article
title: Purity and almost split morphisms in abstract homotopy categories: A unified approach via Brown representability
zbMATH Open document ID: 1040.18010
DOI: 10.1023/A:1020535022658
author: Apostolos Beligiannis
published in: Algebras and Representation Theory
publication date: 2003-03-10T00:00:00Z
review text: The main purpose of this paper is to develop a theory of purity and a theory of existence of almost split morphisms in an abstract homotopy category (an additive category which has coproducts, weak cokernels and a minimal Whitehead subcategory). The main tool for doing this is the classical Brown representability theorem. The theory is applied in the last section to important examples of abstract homotopy categories, namely those of module categories, locally finitely presented categories with products and compactly generated triangulated categories. In all these examples, the author unifies the main results on purity and the existence of almost split morphisms, sequences and triangles.
Mathematics Subject Classification ID: 18G55
Mathematics Subject Classification ID: 18E05
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 55U35
zbMATH DE Number: 1879216
zbMATH Keywords: purity
zbMATH Keywords: almost split morphisms
zbMATH Keywords: Brown representability
zbMATH Keywords: phantom maps
zbMATH Keywords: abstract homotopy categories
zbMATH Keywords: pure-injectives
zbMATH Keywords: flat functors
zbMATH Keywords: approximations
reviewed by: J. Remedios
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1879216