  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.
