Homology, Homotopy and Applications
- Homology Homotopy Appl.
- Volume 14, Number 2 (2012), 23-36.
A representability theorem for some huge abelian categories
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.
Homology Homotopy Appl., Volume 14, Number 2 (2012), 23-36.
First available in Project Euclid: 12 December 2012
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Modoi, George Ciprian. A representability theorem for some huge abelian categories. Homology Homotopy Appl. 14 (2012), no. 2, 23--36. https://projecteuclid.org/euclid.hha/1355321478