Submission date: 24 January 2018

Abstract:

We can define a module to be an exact functor on a small abelian category. This is explained and shown to be equivalent to the usual definition but it does offer a different perspective, inspired by the notions from model theory of imaginary sort and interpretation. A number of examples are worked through.

Mathematics Subject Classification: 16D90, 03C60, 16G20, 18E05

Keywords and phrases: module, model theory, multi sorted structure, interpretation, functor category, abelian category

Full text arXiv 1801.08015: pdf, ps.