Homological algebra and (semi)stable homotopy
type: Item
instance of: scholarly article
title: Homological algebra and (semi)stable homotopy
zbMATH Open document ID: 0868.18002
DOI: 10.1016/S0022-4049(96)00092-8
author: Alex Heller
published in: Journal of Pure and Applied Algebra
publication date: 1997-08-18T00:00:00Z
review text: The preceding paper [\textit{A. Heller}, ``Stable homotopy theories and stabilization'', J. Pure Appl. Algebra 115, No. 2, 113-130 (1996; Zbl 0868.18001)] considers cocontinuous/continuous stabilizations of regular/coregular homotopy theories. As well as a universal problem of spectra, the same leads, for abelian categories to the construction of chain complexes. For a (complete and cocomplete) abelian category \({\mathcal A}\) and a small category \({\mathcal C}\), the 2-functors with values in the homotopy category of chain complexes over \({\mathcal A}^{\mathcal C}\) provide homotopy theories which are in a sense universal stabilization or semistabilization.
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 18G35
Mathematics Subject Classification ID: 18E99
Mathematics Subject Classification ID: 55P42
zbMATH DE Number: 986715
zbMATH Keywords: stable homotopy theory
zbMATH Keywords: resolvent
zbMATH Keywords: stabilizations
zbMATH Keywords: homotopy theories
zbMATH Keywords: abelian categories
zbMATH Keywords: chain complexes
reviewed by: Georges Hoff
MaRDI profile type: Publication
cites work: Q5592097
cites work: The Loop-Space Functor in Homological Algebra
cites work: Stable homotopy categories
cites work: Homotopy theories
cites work: Stable homotopy theories and stabilization
cites work: Q4716145
cites work: Homotopical algebra
full work available at URL: s0022-4049(96)00092-8
OpenAlex ID: W1983610057
Recommended article: Q4893211
Recommended article: Homological algebra of homotopy algebras
Recommended article: Homotopy theory of homotopy algebras
Recommended article: Q4354363
Recommended article: Stable homotopy of algebraic theories
Recommended article: The loop-stable homotopy category of algebras
Recommended article: Q4040829
Recommended article: Q3522855
Recommended article: Hom-algebras and homology
Recommended article: Homotopical algebra in homotopical categories
description: scientific article; zbMATH DE number 986715