Coalgebraic models for combinatorial model categories

摘要

We show that the category of algebraically cofibrant objects in a combinatorial and simplicial model category $mathcal{A}$ has a model structure that is left-induced from that on $mathcal{A}$. In particular, it follows that any presentable model category is Quillen equivalent (via a single Quillen equivalence) to one in which all objects are cofibrant.