Abstract
We define quasi-locally presentable categories as big unions of a chain of coreflective subcategories that 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 the Brown representability theorem. Examples of functors that are not representable are also given.
Citation
George Ciprian Modoi. "A representability theorem for some huge abelian categories." Homology Homotopy Appl. 14 (2) 23 - 36, 2012.
Information