Overcategories and undercategories of model categories
Algebraic Topology
2015-07-08 v1
Abstract
If M is a model category and Z is an object of M, then there are model category structures on the category of objects of M over Z and the category of objects of M under Z under which a map is a cofibration, fibration, or weak equivalence if and only if its image in M under the forgetful functor is, respectively, a cofibration, fibration, or weak equivalence. It is asserted without proof in "Model categories and their localizations" that if M is cofibrantly generated, cellular, or proper, then so is the category of objects of M over Z. The purpose of this note is to fill in the proofs of those assertions and to state and prove the analogous results for undercategories.
Keywords
Cite
@article{arxiv.1507.01624,
title = {Overcategories and undercategories of model categories},
author = {Philip S. Hirschhorn},
journal= {arXiv preprint arXiv:1507.01624},
year = {2015}
}
Comments
6 pages