The discrete homotopy hypothesis for directed graphs
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918486159130624 |
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| author | Eldridge, Briony Ivanov, Sergei O. Xu, Xiaomeng Yau, Shing-Tung Zhang, Mengmeng |
| author_facet | Eldridge, Briony Ivanov, Sergei O. Xu, Xiaomeng Yau, Shing-Tung Zhang, Mengmeng |
| contents | We develop a homotopy theory of directed graphs based on cubical homotopy groups, also referred to as A-groups or reduced GLMY homotopy groups. Localizing the category of directed graphs at morphisms that induce isomorphisms on these groups yields an $\infty$-category, which we denote by ${\sf DGra}_\infty$. Our main result shows that ${\sf DGra}_\infty$ is equivalent to the $\infty$-category of spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04959 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The discrete homotopy hypothesis for directed graphs Eldridge, Briony Ivanov, Sergei O. Xu, Xiaomeng Yau, Shing-Tung Zhang, Mengmeng Algebraic Topology Combinatorics Category Theory We develop a homotopy theory of directed graphs based on cubical homotopy groups, also referred to as A-groups or reduced GLMY homotopy groups. Localizing the category of directed graphs at morphisms that induce isomorphisms on these groups yields an $\infty$-category, which we denote by ${\sf DGra}_\infty$. Our main result shows that ${\sf DGra}_\infty$ is equivalent to the $\infty$-category of spaces. |
| title | The discrete homotopy hypothesis for directed graphs |
| topic | Algebraic Topology Combinatorics Category Theory |
| url | https://arxiv.org/abs/2605.04959 |