Brown functors of directed graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918108981100544 |
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| author | Liao, Hsuan-Yi McGuirk, Zachary Nguyen, Dang Khoa Park, Byungdo |
| author_facet | Liao, Hsuan-Yi McGuirk, Zachary Nguyen, Dang Khoa Park, Byungdo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14865 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brown functors of directed graphs Liao, Hsuan-Yi McGuirk, Zachary Nguyen, Dang Khoa Park, Byungdo Algebraic Topology Combinatorics Category Theory 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. |
| title | Brown functors of directed graphs |
| topic | Algebraic Topology Combinatorics Category Theory |
| url | https://arxiv.org/abs/2503.14865 |