Homology, Homotopy and Applications

Volume 17 (2015)

Number 2

The hammock localization preserves homotopies

Pages: 191 – 204

DOI: http://dx.doi.org/10.4310/HHA.2015.v17.n2.a10


Oriol Raventós (Fakultät für Mathematik, Universität Regensburg, Germany)


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

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