Spectra and symmetric spectra in general model categories
type: Item
instance of: scholarly article
title: Spectra and symmetric spectra in general model categories
zbMATH Open document ID: 1008.55006
DOI: 10.1016/S0022-4049(00)00172-9
author: Mark Hovey
published in: Journal of Pure and Applied Algebra
publication date: 2003-04-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0004051
review text: Two general constructions for the passage from unstable to stable homotopy are given. The first construction is based on the standard notion of spectra [\textit{R. Vogt}, Boardman's Stable Homotopy Category, Lect. Notes Ser., Åarhus Univ. 21 (1970; Zbl 0224.55014)] and starts from a model category \({\mathcal D}\) and an endofunctor \(T\) generalizing the suspension. The second construction is based on symmetric spectra [\textit{M. Hovey}, \textit{B. Shipley} and \textit{J. Smith}, J. Am. Math. Soc. 13, No. 1, 149-208 (2000; Zbl 0931.55006)] and applies to model categories \({\mathcal C}\) witha compatible monoidal structure and an endofunctor \(T\) which is given by tensoring with a cofibrant object \({\mathcal K}\). The constructions apply not only to the homotopy theory for pointed topological spaces but also to the homotopy theory for algebraic varieties and schemes recently developed by \textit{F. Morel} and \textit{V. Voevodsky} [Publ. Math., Inst. Hautes Étud. Sci. 90, 45-143 (1999; Zbl 0983.14007); Doc. Math., J. DMV, Extra Vol. ICM Berlin 1998, vol. I, 579-604 (1998; Zbl 0907.19002)] using the affine line \(\mathbb{A}^1\) instead of the unit interval \([0,1]\).
reviewed by: Klaus Heiner Kamps
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 18G55
Mathematics Subject Classification ID: 18D99
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 55U35
zbMATH DE Number: 1698557
zbMATH Keywords: unstable homotopy
zbMATH Keywords: stable homotopy
zbMATH Keywords: localization
MaRDI profile type: Publication
arXiv ID: math/0004051
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OpenAlex ID: W1997683636
description: scientific article; zbMATH DE number 1698557