One-sided exact categories
Category Theory
2019-12-16 v1
Abstract
One-sided exact categories appear naturally as instances of Grothendieck pretopologies. In an additive setting they are given by considering the one-sided part of Keller's axioms defining Quillen exact categories. We study one-sided exact additive categories and a stronger version defined by adding the one-sided part of Quillen "obscure axiom". We show that some homological results, such as the Short Five Lemma and the 3 X 3 Lemma, can be proved in our context. We also note that the derived category of a one-sided exact additive category can be constructed.
Keywords
Cite
@article{arxiv.1106.1092,
title = {One-sided exact categories},
author = {Silvana Bazzoni and Septimiu Crivei},
journal= {arXiv preprint arXiv:1106.1092},
year = {2019}
}