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- Title
THE HAMMOCK LOCALIZATION PRESERVES HOMOTOPIES.
- Authors
RAVENTÓS, ORIOL
- Abstract
The hammock localization provides a model for a homotopy function complex in any Quillen model category. We prove that a homotopy between a pair of morphisms induces a homotopy between the maps induced by taking the hammock localization. We also show that, under Vopěnka’s principle, every homotopy idempotent functor in a cofibrantly generated model category is determined by simplicial orthogonality with respect to a set of morphisms. Finally, we give a new proof of the fact that left Bousfield localizations with respect to a class of morphisms always exist in any left proper combinatorial model category under Vopěnka’s principle.
- Subjects
LOCALIZATION (Mathematics); HOMOTOPY theory; MATHEMATICAL functions; CATEGORIES (Mathematics); MORPHISMS (Mathematics); MATHEMATICAL mappings
- Publication
Homology, Homotopy & Applications, 2015, Vol 17, Issue 2, p191
- ISSN
1532-0073
- Publication type
Article
- DOI
10.4310/HHA.2015.v17.n2.a10