Internal Bousfield Localizations

Abstract

We develop the notion of left and right Bousfield localizations in proper, cellular symmetric monoidal model categories with cofibrant unit, using homotopy function complexes defined by internal Hom objects instead of Hom sets.

38 pages. References added. Expanded introduction to discuss past work on the subject. Acknowledgments added. The set $\Gamma$ with respect to which we operate a left Bousfield localization is slightly enlarged to simplify some proofs