Prest, Mike and Rajani, Ravi (2008) Structure sheaves of definable additive categories. [MIMS Preprint]
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Abstract
2equivalences 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 finitetype localisations and the presheaf of localisations of associated functor categories. The image of the free abelian category in ModR is described and related to special bases of the Ziegler and repZariski 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 modeltheoretic sense).
Item Type:  MIMS Preprint 

Uncontrolled Keywords:  definable category, abelian category, functor category, locally coherent category, 2category, exact functor, finitetype localisation, pureinjective, injective, free abelian category, GabrielZariski spectrum, repZariski spectrum, Ziegler spectrum, presheaf, elimination of imaginaries, pp formula 
Subjects:  MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 18 Category theory; homological algebra 
Depositing User:  Professor Mike Prest 
Date Deposited:  20 Oct 2009 
Last Modified:  08 Nov 2017 18:18 
URI:  https://eprints.maths.manchester.ac.uk/id/eprint/1339 
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Structure sheaves of definable additive categories. (deposited 21 Nov 2008)
 Structure sheaves of definable additive categories. (deposited 20 Oct 2009) [Currently Displayed]
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