On coherent systems of subobjects with application to torsion theory

TL;DR

This paper explores the properties of subobject systems in coherent categories and their extensions to general categories, applying these insights to the study of torsion theories and their universal associations.

Contribution

It generalizes properties of subobject posets from coherent categories to broader classes and applies this to analyze torsion theories in category theory.

Findings

Subobject posets exhibit strong properties in coherent categories.

These properties extend to well-behaved classes of subobjects in general categories.

The paper characterizes universal associations of torsion theories with pretorsion theories.

Abstract

In a coherent category, the posets of subobjects have very strong properties. We emphasize the validity of these properties, in general categories, for well-behaved classes of subobjects. As an example of application, we investigate the problem of the various torsion theories which can be universally associated with a pretorsion one.