Ionescu's theorem for higher rank graphs

TL;DR

This paper extends Ionescu's theorem to higher rank graphs by introducing new constructions akin to graph systems of correspondences, connecting with topological k-graphs and tensor groupoid product systems.

Contribution

It develops a novel framework for higher rank graphs, generalizing Ionescu's theorem and linking it to existing structures like Yeend's topological k-graphs and Fowler and Sims' tensor groupoid systems.

Findings

Established a version of Ionescu's theorem for higher rank graphs

Analyzed properties of the new constructions in relation to existing theories

Connected the new framework with topological k-graphs and tensor groupoid product systems

Abstract

We will define new constructions similar to the graph systems of correspondences described by Deaconu et al. We will use these to prove a version of Ionescu's theorem for higher rank graphs. Afterwards we will examine the properties of these constructions further and make contact with Yeend's topological k-graphs and the tensor groupoid valued product systems of Fowler and Sims.