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On The Cofibrant Generation Of Model Categories
#
On The Cofibrant Generation Of Model Categories

##
George Raptis

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 ofweak 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.

Journal of Homotopy and Related Structures, Vol. 4(2009), No. 1, pp. 245-253