Abstract:We develop a homotopy theory of directed graphs based on cubical homotopy groups, also known 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, denoted by ${\sf DGra}_\infty$. We prove that ${\sf DGra}_\infty$ is equivalent to the $\infty$-category of spaces, establishing a directed version of the discrete homotopy hypothesis of Carranza and Kapulkin.
From: Sergei Ivanov Olegovich [view email]
[v1]
Wed, 6 May 2026 14:21:43 UTC (43 KB)
[v2]
Thu, 10 Sep 2026 15:36:30 UTC (44 KB)
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