On the existence and construction of proper costratifying systems

TL;DR

This paper explores the conditions for the existence of proper costratifying systems and examines their relationship with existing stratifying systems, advancing the theoretical understanding of these algebraic structures.

Contribution

It provides new sufficient conditions for the existence of proper costratifying systems and clarifies their connection to previously studied stratifying systems.

Findings

Established new sufficient conditions for proper costratifying systems

Analyzed the relation between proper costratifying systems and Erdmann-Sáenz stratifying systems

Enhanced theoretical framework for algebraic stratification methods

Abstract

In this paper we further study the notion of proper costratifying systems, defined in \cite{MPV}. We give sufficient conditions for their existence, and investigate the relation between the stratifying systems defined by K. Erdmann and C. S\'aenz in \cite{ES} with the proper costratifying systems.