## Homology, Homotopy and Applications

- Homology Homotopy Appl.
- Volume 14, Number 2 (2012), 23-36.

### A representability theorem for some huge abelian categories

#### 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.

#### Article information

**Source**

Homology Homotopy Appl., Volume 14, Number 2 (2012), 23-36.

**Dates**

First available in Project Euclid: 12 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1355321478

**Mathematical Reviews number (MathSciNet)**

MR3007083

**Zentralblatt MATH identifier**

1263.18008

**Subjects**

Primary: 18A40: Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) 18E30: Derived categories, triangulated categories

**Keywords**

Representable functor quasi-locally presentable category abelianization triangulated category with coproducts

#### Citation

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