New Models from Old Ones

Abstract

Suppose we have a category $\mathcal {C}$ along with a choice of three classes of morphisms that we want to say form the weak equivalences, fibrations, and cofibrations of a model structure on $\mathcal {C}$. It can sometimes be tedious to check if the model categorical axioms hold or not. As such, one usually relies on general methods for forming new model structures from old ones, either on the same or on a different underlying category.