Model categories with simple homotopy categories

Abstract

In the present article we describe constructions of model structures on general bicomplete categories. We are motivated by the following question: given a category C with a suitable subcategory wC, when is there a model structure on C with wC as the subcategory of weak equivalences? We begin exploring this question in the case where wC = F-1(isoD) for some functor F: C → D. We also prove properness of our constructions under minor assumptions and examine an application to the category of in finite graphs.