Exact Structures and Purity
Representation Theory
2026-02-16 v3 Category Theory
Abstract
We relate the theory of purity of a locally finitely presented category with products to the study of exact structures on the full subcategory of finitely presented objects. Properties in the context of purity are translated to properties about exact structures. We specialize to the case of a module category over an Artin algebra and show that generic modules are in one to one correspondence with particular maximal exact structures.
Cite
@article{arxiv.2406.19952,
title = {Exact Structures and Purity},
author = {Kevin Schlegel},
journal= {arXiv preprint arXiv:2406.19952},
year = {2026}
}