$\mathcal{C}$-filtered modules and proper costratifying systems

TL;DR

This paper introduces proper costratifying systems, generalizing proper costandard modules from quasi-hereditary algebra theory to stratifying systems, expanding the framework for module classification.

Contribution

It defines and studies proper costratifying systems, extending the concept of proper costandard modules to a broader stratifying system context.

Findings

Established properties of proper costratifying systems

Connected these systems to existing module theory concepts

Provided foundational results for future research

Abstract

In this paper we define and study the notion of a proper costratifying system, which is a generalization of the so-called proper costandard modules to the context of stratifying systems. The proper costandard modules were defined by V. Dlab in his study of quasi-hereditary algebras (see \cite{Dlab}).