Geodesic
Model categories with simple homotopy categories
Theory and applications of categories, Tome 30 (2015), pp. 15-39
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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.

Publié le :
Classification : 18G55
Keywords: model category, graph 
@article{TAC_2015_30_a1,
     author = {Jean-Marie Droz and Inna Zakharevich},
     title = {Model categories with simple homotopy categories},
     journal = {Theory and applications of categories},
     pages = {15--39},
     year = {2015},
     volume = {30},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a1/}
}
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Jean-Marie Droz; Inna Zakharevich. Model categories with simple homotopy categories. Theory and applications of categories, Tome 30 (2015), pp. 15-39. http://geodesic.mathdoc.fr/item/TAC_2015_30_a1/