Modules as exact functors
Representation Theory
2018-01-25 v1 Category Theory
Logic
Rings and Algebras
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.
Cite
@article{arxiv.1801.08015,
title = {Modules as exact functors},
author = {Mike Prest},
journal= {arXiv preprint arXiv:1801.08015},
year = {2018}
}