Year: 2025
Type: article
Abstract: 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 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.
Source: Data Analytics and Topology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4411333082