Torsion Theories in a Non-pointed Context
Category Theory
2026-04-09 v2
Abstract
We study a non-pointed version of the notion of torsion theory in the framework of categories equipped with a posetal monocoreflective subcategory such that the coreflector inverts monomorphisms. We explore the connections of such torsion theories with factorization systems and categorical Galois structures. We describe several examples of these torsion theories, in the dual of elementary toposes, in varieties of universal algebras used as models for non-classical logic, and in coslices of the category of abelian groups.
Keywords
Cite
@article{arxiv.2506.13349,
title = {Torsion Theories in a Non-pointed Context},
author = {Andrea Cappelletti and Andrea Montoli},
journal= {arXiv preprint arXiv:2506.13349},
year = {2026}
}