Internal Bousfield Localizations
Renaud Gauthier
TL;DR
This paper introduces a new approach to Bousfield localizations in certain model categories, utilizing internal Hom objects to define homotopy function complexes, enhancing the theoretical framework of localization.
Contribution
It develops the concepts of left and right Bousfield localizations using internal Hom objects in proper, cellular symmetric monoidal model categories.
Findings
Defines Bousfield localizations via internal Hom objects
Extends localization theory to new categorical contexts
Provides a foundation for further homotopical algebra research
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons