When Bousfield localizations and homotopy idempotent functors meet again

TL;DR

This paper extends key theorems on Bousfield localizations to semimodel categories, addressing open problems and broadening the applicability of localization techniques in homotopy theory.

Contribution

It generalizes classical localization theorems to semimodel categories and solves an open problem about Bousfield localizations for specific model structures.

Findings

Generalized Bousfield-Friedlander and Hirschhorn Localization Theorems

Extended localization results to semimodel categories

Resolved open problem on Bousfield localizations for Hurewicz and mixed structures

Abstract

We adopt semimodel categories to extend fundamental results related to Bousfield localizations of model categories. More specifically, we generalize Bousfield-Friedlander Theorem and Hirschhorn Localization Theorem of cellular model categories to settings where their classical formulation does not apply. We use such results to answer, in the world of semimodel categories, an open problem posed by May-Ponto about the existence of Bousfield localizations for Hurewicz and mixed type model structures.