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2008.112: Structure sheaves of definable additive categories

2008.112: Mike Prest and Ravi Rajani (2008) Structure sheaves of definable additive categories.

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2-equivalences are described between the category of small abelian categories with exact functors, the category of definable additive categories with functors which commute with products and direct limits and the category of locally coherent Grothendieck categories with "coherent" morphisms. There is a comparison, for definable additive categories, between the presheaf of finite-type localisations and the presheaf of localisations of associated functor categories. The image of the free abelian category in Mod-R is described and related to special bases of the Ziegler and rep-Zariski spectra restricted to the set of indecomposable injectives. In the coherent case there is a particularly nice form (which is essentially elimination of imaginaries in the model-theoretic sense).

Item Type:MIMS Preprint
Uncontrolled Keywords:definable category, abelian category, functor category, locally coherent category, 2-category, exact functor, finite-type localisation, pure-injective, injective, free abelian category, Gabriel-Zariski spectrum, rep-Zariski spectrum, Ziegler spectrum, presheaf, elimination of imaginaries, pp formula
Subjects:MSC 2000 > 03 Mathematical logic and foundations
MSC 2000 > 16 Associative rings and algebras
MSC 2000 > 18 Category theory; homological algebra
MIMS number:2008.112
Deposited By:Professor Mike Prest
Deposited On:20 October 2009

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