## 2008.112: Structure sheaves of definable additive categories

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

*This is the latest version of this eprint.*

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 251 Kb |

## Abstract

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 |

### Available Versions of this Item

- Structure sheaves of definable additive categories (deposited 20 October 2009)
**[Currently Displayed]**

Download Statistics: last 4 weeks

Repository Staff Only: edit this item