Model-theoretic imaginaries and coherent sheaves

Rajani, Ravi and Prest, Mike (2008) Model-theoretic imaginaries and coherent sheaves. [MIMS Preprint]

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Abstract

Categories of imaginaries (imaginary sorts are the objects and definable functions are the maps) defined using positive existential formulas are shown to be equivalent to categories of finitely presented / coherent functors on the category of models. Localised/relativised versions are also proved. This is linked with interpretation functors between categories of structures. These results generalise what is already known in the additive case and include an alternative approach to an old result of Makkai and Reyes.

Item Type: MIMS Preprint
Uncontrolled Keywords: L-structure, positive existential formula, positive primitive formula, finitely presented functor, coherent functor, category, Grothendieck topology, interpretation
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations
MSC 2010, the AMS's Mathematics Subject Classification > 18 Category theory; homological algebra
Depositing User: Professor Mike Prest
Date Deposited: 27 Sep 2008
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1145

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