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Model categories with simple homotopy categories

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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.

http://www.tac.mta.ca/tac/volumes/30/2/30-02.pdf

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