A representability theorem for some huge abelian categories

Details A representability theorem for some huge abelian categories A representability theorem for some huge abelian categories

2010-03-30

arxiv.org/abs/1003.5937v2

Mathematics

Category Theory

Some examples and references added, some inconclusive remarks removed. Submitted to Homotopy, Homology and Appl

Scientific paper

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.

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