2010/03/30 by George Ciprian Modoi, Modoi, George Ciprian
Mathematics · #18A40 #18E30 #Category Theory (math.CT) #FOS: Mathematics #math.CT #msc:18A40 #msc:18E30
paper · pdf · doi:10.48550/arxiv.1003.5937
In the new version it is given a stronger definition for the notion of quasi--locally presentable category. An already known result was removed. To appear Homotopy, Homology and Applications
arxiv created 2012/05/10 · arxiv updated 2012/05/11
We define quasi--locally presentable categories as big unions of coreflective subcategories which are locally presentable. Under appropriate hypotheses we prove a representability theorem for exact contravariant functors defined on a quasi--locally presentable category taking values in abelian groups. We show that the abelianization of a well generated triangulated category is quasi--locally presentable and we obtain a new proof of Brown representability theorem. Examples of functors which are not representable are also given.