Multisorted modules and their model theory

TL;DR

This paper explores the model theory of multisorted modules, which generalize modules and quiver representations, highlighting their structures, extensions, and examples in a comprehensive manner.

Contribution

It develops the model theory for multisorted modules, including their extensions by imaginaries, and provides detailed examples demonstrating their properties.

Findings

Multisorted modules can be viewed as representations of quivers.

The model theory for multisorted modules parallels that of 1-sorted modules.

Examples illustrate the applicability and structure of multisorted modules.

Abstract

Multisorted modules, equivalently representations of quivers, equivalently additive functors on preadditive categories, encompass a wide variety of additive structures. In addition, every module has a natural and useful multisorted extension by imaginaries. The model theory of multisorted modules works just as for the usual, 1-sorted modules. A number of examples are presented, some in considerable detail.