Purity and flatness in symmetric monoidal closed exact categories
Algebraic Geometry
2018-09-17 v1 Category Theory
Abstract
Let A be a symmetric monoidal closed exact category. This category is a natural framework to define the notions of purity and flatness. We show that an object F in A is flat if and only if any conflation ending in F is pure. Furthermore, we prove a generalization of the Lambek Theorem ([La64]) in A. In the case A is a quasi-abelian category, we prove that A has enough pure injective objects.
Cite
@article{arxiv.1809.05261,
title = {Purity and flatness in symmetric monoidal closed exact categories},
author = {Esmaeil Hosseini and Ali Zaghian},
journal= {arXiv preprint arXiv:1809.05261},
year = {2018}
}