Abstract
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.
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J. J. Gutiérrez was supported by the NWO (SPI 61-638) and the MEC-FEDER Grants MTM2010-15831 and MTM2013-42178-P. Both authors received support from the LMS Scheme 4 Grant No. 41360.
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Gutiérrez, J.J., Roitzheim, C. Towers and Fibered Products of Model Structures. Mediterr. J. Math. 13, 3863–3886 (2016). https://doi.org/10.1007/s00009-016-0719-3
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DOI: https://doi.org/10.1007/s00009-016-0719-3