A representability theorem for some huge abelian categories
Category Theory
2012-05-11 v3
Abstract
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.
Cite
@article{arxiv.1003.5937,
title = {A representability theorem for some huge abelian categories},
author = {George Ciprian Modoi},
journal= {arXiv preprint arXiv:1003.5937},
year = {2012}
}
Comments
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