A classification of nullity classes in abelian categories

TL;DR

This paper classifies nullity (torsion) classes in abelian categories using a spectrum of premonoform objects, providing a new perspective similar to Kanda's classification of Serre subcategories.

Contribution

It introduces a novel classification framework for nullity classes in abelian categories via a spectrum of equivalence classes of premonoform objects.

Findings

Nullity classes are classified by a spectrum of premonoform objects.

The classification parallels Kanda's work on Serre subcategories.

Provides a new structural understanding of abelian categories.

Abstract

We give a classification of nullity classes (or torsion classes) in an abelian category by forming a spectrum of equivalence classes of premonoform objects. This is parallel to Kanda's classification of Serre subcategories.