  The paper studies the problem of the cofibrant generation of a model
category. We prove that, assuming Vop\v{e}nka's principle, every cofibrantly
generated model category is Quillen equivalent to a combinatorial model
category. We discuss cases where this result implies that the class of weak
equivalences in a cofibrantly generated model category is accessibly embedded.
We also prove a necessary condition for a model category to be cofibrantly
generated by a set of generating cofibrations between cofibrant objects.

Algebraic Topology;Category Theory