Brown functors of directed graphs
Algebraic Topology
2025-08-04 v2 Combinatorics
Category Theory
Abstract
We prove that any digraph Brown functor -- i.e. a contravariant functor from the homotopy category of finite directed graphs to the category of abelian groups, satisfying the triviality axiom, the additivity axiom, and the Mayer-Vietoris axiom -- is representable. Furthermore, we show that the first path cohomology functor is a digraph Brown functor.
Keywords
Cite
@article{arxiv.2503.14865,
title = {Brown functors of directed graphs},
author = {Hsuan-Yi Liao and Zachary McGuirk and Dang Khoa Nguyen and Byungdo Park},
journal= {arXiv preprint arXiv:2503.14865},
year = {2025}
}
Comments
20 pages, 4 figures, simplified proofs, and additional references. arXiv admin note: significant text overlap with a part of arXiv:2003.07426