A category theory approach using preradicals to model information flows in networks

TL;DR

This paper introduces a category theory framework using preradicals to model and generalize various types of information flow persistence in networks with directed acyclic graph structures.

Contribution

It demonstrates that preradicals can unify and extend existing persistence concepts in network information flow modeling using category theory.

Findings

Preradicals generalize persistence in directed acyclic graphs.

A specific $mbda$ preradical models persistence of G-modules.

Preradicals preserve the underlying structure of the modeled system.

Abstract

Category theory has been recently used as a tool for constructing and modeling an information flow framework. Here, we show that the flow of information can be described using preradicals. We prove that preradicals generalize the notion of persistence in spaces where the underlying structure forms a directed acyclic graph. We show that a particular $\alpha$ preradical describes the persistence of a commutative $G$-module associated with a directed acyclic graph. Furthermore, given how preradicals are defined, they are able to preserve the modeled system's underlying structure. This allows us to generalize the notions of standard persistence, zigzag persistence, and multidirectional persistence.