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2006.218: Definable additive categories: purity and model theory

2006.218: Mike Prest (2008) Definable additive categories: purity and model theory.

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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
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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 2000 > 03 Mathematical logic and foundations
MSC 2000 > 16 Associative rings and algebras
MSC 2000 > 18 Category theory; homological algebra
MIMS number:2006.218
Deposited By:Professor Mike Prest
Deposited On:15 February 2010

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