Monobricks in extriangulated length categories

TL;DR

This paper introduces monobricks in extriangulated length categories, establishing bijections with left Schur subcategories and torsion-free classes, extending known results from abelian categories.

Contribution

It generalizes the concept of semibricks to extriangulated categories and proves new bijections with important subcategory classes.

Findings

Bijection between monobricks and left Schur subcategories

Extension of Enomoto's results to extriangulated categories

Characterization of cofinally closed monobricks as torsion-free classes

Abstract

In this paper, we introduce the notation of monobricks in an extriangulated length category as a generalization of the semibricks. We prove that there is a bijection between monobricks and left Schur subcategories. Then we show that this bijection restricts to bijection between cofinally closed monobricks and torsion-free classes. These extend the results of Enomoto for abelian length categories.