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}(iso D) for some functor F : C --> D. We also prove properness of our constructions under minor assumptions and examine an application to the category of infinite graphs.
Keywords: model category, graph
2010 MSC: 18G55
Theory and Applications of Categories, Vol. 30, 2015, No. 2, pp 15-39.
Published 2015-01-08.
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