Overcategories and undercategories of model categories

@inproceedings{Hirschhorn2016OvercategoriesAU,
  title={Overcategories and undercategories of model categories},
  author={Philip S. Hirschhorn},
  year={2016}
}
If M is a model category and Z is an object of M, then there are model category structures on the categories (M ↓Z) (the category of objects of M over Z) and (Z ↓M) (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 [1] that if M is cofibrantly generated, cellular, or proper, then so is… CONTINUE READING