A noetherian criterion for sequences of modules

TL;DR

This paper establishes a noetherian criterion for sequences of modules connected by linear maps, generalizing previous work on EI categories and applying it to diagram algebra categories.

Contribution

It introduces a new noetherian criterion for module sequences, extending Gan and Li's work to broader linear categories and diagram algebras.

Findings

Generalized noetherian criterion for module sequences

Extended applicability to linear categories from diagram algebras

Provided conditions ensuring noetherian properties in new contexts

Abstract

We prove a noetherian criterion for a sequence of modules with linear maps between them. This generalizes a noetherian criterion of Gan and Li for infinite EI categories. We apply our criterion to the linear categories associated to certain diagram algebras defined by Patzt.