Bousfield localisations along Quillen bifunctors and applications

Gutierrez, Javier and Roitzheim, Constanze (2014) Bousfield localisations along Quillen bifunctors and applications. arxiv.org, . (Full text available)

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http://arxiv.org/abs/1411.0500

Abstract

We describe left and right Bousfield localisations along Quillen adjunctions of two variables. These localised model structures can be used to define Postnikov sections and homological localisations of arbitrary model categories, and to study the homotopy limit model structure on the category of sections of a left Quillen presheaf of localised model structures. We obtain explicit results in this direction in concrete examples of towers and fiber products of model categories. In particular, we prove that the category of simplicial sets is Quillen equivalent to the homotopy limit model structure of its Postnikov tower, and that the category of symmetric spectra is Quillen equivalent to the homotopy fiber product of its Bousfield arithmetic square. For spectral model categories, we show that the homotopy fiber of a stable left Bousfield localisation is a stable right Bousfield localisation.

Item Type: Article
Uncontrolled keywords: model categories, localisation, stable homotopy theory
Subjects: Q Science > QA Mathematics (inc Computing science) > QA440 Geometry > QA611 Topology
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Constanze Roitzheim
Date Deposited: 14 Jul 2015 15:23 UTC
Last Modified: 19 May 2018 08:17 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/44078 (The current URI for this page, for reference purposes)
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