Mediterranean Journal of Mathematics

, Volume 13, Issue 6, pp 3863–3886 | Cite as

Towers and Fibered Products of Model Structures

  • Javier J. Gutiérrez
  • Constanze Roitzheim
Open Access


Given a left Quillen presheaf of localized model structures, we study the homotopy limit model structure on the associated category of sections. We focus specifically on towers and fibered products (pullbacks) of model categories. As applications we consider Postnikov towers of model categories, chromatic towers of spectra and Bousfield arithmetic squares of spectra. For stable model categories, we show that the homotopy fiber of a stable left Bousfield localization is a stable right Bousfield localization.


Localization model category Postnikov tower homotopy fibered product homotopy pullback 

Mathematics Subject Classification

55P42 55P60 55S45 


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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute for Mathematics, Astrophysics and Particle PhysicsRadboud Universiteit NijmegenNijmegenNetherlands
  2. 2.School of Mathematics, Statistics and Actuarial ScienceUniversity of KentCanterbury, KentUK

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