Are all cofibrantly generated model categories combinatorial?
Category Theory
2012-05-02 v2 Algebraic Topology
Abstract
G. Raptis has recently proved that, assuming Vop\v{e}nka's principle, every cofibrantly generated model category is Quillen equivalent to a combinatorial one. His result remains true for a slightly more general concept of a cofibrantly generated model category. We show that Vop\v{e}nka's principle is equivalent to this claim. The set-theoretical status of the original Raptis' result is open.
Cite
@article{arxiv.0905.0595,
title = {Are all cofibrantly generated model categories combinatorial?},
author = {J. Rosicky},
journal= {arXiv preprint arXiv:0905.0595},
year = {2012}
}