Homology, Homotopy and Applications
Volume 17 (2015)
The hammock localization preserves homotopies
Pages: 191 – 204
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.
model category, homotopy function complex, localization, homotopy algebra
2010 Mathematics Subject Classification
18C35, 55P60, 55U35