Model categories with simple homotopy categories

Jean-Marie Droz and Inna Zakharevich

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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