Abstract

The aim of the talk is to show that magnitude cohomology yields finitely generated functors onthe category of directed graphs with bounded genus. We wil use the framework of quasi-Groebnercategories, as developed by Sam and Snowden, and show how to use it to obtain structural resultsof homology theories of (directed) graphs. We will discuss two main applications of the generaltheory, the first about the rank growth, and the second about the order of torsion, of magnitudecohomology groups.