Homology, Homotopy and Applications

Volume 25 (2023)

Number 2

When Bousfield localizations and homotopy idempotent functors meet again

Pages: 187 – 218

DOI: https://dx.doi.org/10.4310/HHA.2023.v25.n2.a9


Victor Carmona (Facultad de Matemáticas, Departamento de Álgebra, Universidad de Sevilla, Spain)


We generalize Bousfield–Friedlander’s Theorem and Hirschhorn’s Localization Theorem to settings where the hypotheses are not satisfied at the expense of obtaining semi-model categories instead of model categories. We use such results to answer, in the world of semi-model categories, an open problem posed by May–Ponto about the existence of Bousfield localizations for Hurewicz and mixed type model structures (on spaces and chain complexes). We also provide new applications that were not available before, e.g. stabilization of non-cofibrantly generated model structures or applications to mathematical physics.


Bousfield localization, idempotent functor, model category, Hurewicz and mixed model structures, stable model category, homological algebra

2010 Mathematics Subject Classification

18G30, 18G55, 55U35

The author was partially supported by grant PID2020-117971GB-C21 of the Spanish Ministry of Science and Innovation, and grant FQM-213 of the Junta de Andalucía. He was also partly supported by Spanish Ministry of Science, Innovation and Universities grant FPU17/01871.

Received 23 May 2022

Received revised 30 August 2022

Accepted 14 September 2022

Published 1 November 2023