Geodesic
A representability theorem for some huge abelian categories
Homology, homotopy, and applications, Tome 14 (2012) no. 2, pp. 23-36.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2012.v14.n2.a2
Classification : 18A40, 18E30
Keywords: representable functor, quasi-locally presentable category, abelianization, triangulated category with coproducts 
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     author = {George Ciprian Modoi},
     title = {A representability theorem for some huge abelian categories},
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     pages = {23--36},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2012.v14.n2.a2/}
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George Ciprian Modoi. A representability theorem for some huge abelian categories. Homology, homotopy, and applications, Tome 14 (2012) no. 2, pp. 23-36. doi : 10.4310/HHA.2012.v14.n2.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2012.v14.n2.a2/

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