The right angled Artin group functor as a categorical embedding

Grossack, Chris

doi:10.2140/agt.2025.25.3035

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The right angled Artin group functor as a categorical embedding

Chris Grossack

Algebraic & Geometric Topology 25 (2025) 3035–3048

DOI: 10.2140/agt.2025.25.3035

Abstract

It has long been known that the combinatorial properties of a graph $Γ$ are closely related to the group theoretic properties of its right angled Artin group (raag). It’s natural to ask if the graph homomorphisms are similarly related to the group homomorphisms between two raags. Our main result shows that there is a purely algebraic way to characterize the raags amongst groups, and the graph homomorphisms amongst the group homomorphisms. As a corollary we present a new algorithm for recovering $Γ$ from its raag.

Keywords

geometric group theory, right angled Artin group, category theory, descent

Mathematical Subject Classification

Primary: 05C25, 18F20, 20F65

References

Publication

Received: 28 December 2023

Revised: 11 June 2024

Accepted: 10 July 2024

Published: 17 September 2025

Authors

Chris Grossack
University of California Riverside Riverside, CA United States

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Volume 25, issue 5 (2025)