Path homology of directed hypergraphs
Yuri Muranov, Anna Szczepkowska, Vladimir Vershinin
TL;DR
This paper develops path homology theories for directed hypergraphs, introducing a categorical framework, homotopy concepts, and demonstrating their properties and computational examples.
Contribution
It introduces a new categorical approach to path homology in directed hypergraphs, including homotopy notions and invariance properties.
Findings
Path homology theories are constructed for directed hypergraphs.
Homotopy invariance of the introduced homology groups is established.
Examples of computing these homology groups are provided.
Abstract
We describe various path homology theories constructed for a directed hypergraph. We introduce the category of directed hypergraphs and the notion of a homotopy in this category. Also, we investigate the functoriality and the homotopy invariance of the introduced path homology groups. We provide examples of computation of these homology groups.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology