Are all cofibrantly generated model categories combinatorial?
Abstract
G. Raptis has recently proved that, assuming Vopenka'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 Vopenka's principle is equivalent to this claim. The set-theoretical status of the original Raptis' result is open.
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