%0 Journal Article
%T A representability theorem for some huge abelian categories
%A George Ciprian Modoi
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1003.5937v3