2023/10/01 by Rolando Jiménez, Jimenez, Rolando, Vladimir Vershinin +3
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2310.00634
openalex publication_date 2023/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The singular cubical homology theory for the category of quivers or digraphs can be constructed similarly to the classical singular homology theory for topological spaces. The case of digraphs and quivers differs from the topological case due to the possibility of using a large number of non-isomorphic line digraphs that correspond to the unit interval in algebraic topology. In this paper we introduce several different notions of quiver realizations of a cubical set and we describe relations between them. We also define various singular cubical homology theories on quivers and digraphs. Moreover, using quiver realizations of cubical sets we define a collection of path homology theories on the category of cubical sets and we describe their properties.