Homology, Homotopy and Applications

Volume 14 (2012)

Number 2

A representability theorem for some huge abelian categories

Pages: 23 – 36

DOI: http://dx.doi.org/10.4310/HHA.2012.v14.n2.a2

Author

George Ciprian Modoi (Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania)

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.

Keywords

representable functor, quasi-locally presentable category, abelianization, triangulated category with coproducts

2010 Mathematics Subject Classification

18A40, 18E30

Full Text (PDF format)