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 categories, 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.