Homology, Homotopy and Applications

A representability theorem for some huge abelian categories

George Ciprian Modoi

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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


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