The orthogonal subcategory problem in homotopy theory

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It is known that the existence of localization with respect to an arbitrary (possibly proper) class of maps in the category of simplicial sets is implied by a large-cardinal axiom called Vopenka's principle.In this article we extend the validity of this result to any left proper, combinatorial, simplicial model category $\cat M$ and show that, under additional assumptions on $\cat M$, every homotopy idempotent functor is in fact a localization with respect to some set of maps. These results are valid for the homotopy category of spectra, among other applications.
9 pages

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Algebraic Topology, Category Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/74216

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0502329
 http://arxiv.org/abs/math/0502329

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arXiv