On the Cofibrant Generation of Model Categories

Details On the Cofibrant Generation of Model Categories On the Cofibrant Generation of Model Categories

2009-07-16

arxiv.org/abs/0907.2726v1

J. Homotopy Relat. Struct. 4(2009)

Mathematics

Algebraic Topology

11 pages

Scientific paper

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.

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