Definable additive categories: purity and model theory

Prest, Mike (2008) Definable additive categories: purity and model theory. [MIMS Preprint]

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Abstract

Definable additive categories and their model theory are the topic of this paper. We begin with background and preliminary results on additive categories. Then definable subcategories, their properties and the morphisms between them are investigated, as are certain associated topological spaces (``spectra"). It was in the model theory of modules that these categories were first considered and model theory provides some of the tools for exploring them. Some general model-theoretic background is presented, then various aspects of the model theory of definable categories are considered.

Item Type:	MIMS Preprint
Additional Information:	This version incorporates various corrections (which don't affect the main results); in particular more care is taken in the background material in Section 5 over when a category should be assumed to be abelian, not just additive.
Uncontrolled Keywords:	additive definable categories modules purity model theory finitely accessible
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:	15 Feb 2010
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1412

Available Versions of this Item

• Definable additive categories: purity and model theory. (deposited 16 Jul 2008)
  • Definable additive categories: purity and model theory. (deposited 27 Sep 2008)
    • Definable additive categories: purity and model theory. (deposited 15 Feb 2010) [Currently Displayed]

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