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The orthogonal subcategory problem in homotopy theory

Carles Casacuberta·Boris Chorny
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Abstract

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.

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Carles Casacuberta, Boris Chorny. 2005-02-15. The orthogonal subcategory problem in homotopy theory. https://arxiv.org/abs/math/0502329

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