Are all cofibrantly generated model categories combinatorial?

Details Are all cofibrantly generated model categories combinatorial? Are all cofibrantly generated model categories combinatorial?

2009-05-05

arxiv.org/abs/0905.0595v2

Mathematics

Category Theory

Scientific paper

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.

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