Cofibration category of digraphs for path homology

TL;DR

This paper establishes a cofibration category structure on directed graphs where weak equivalences are graph maps that preserve path homology, facilitating algebraic topological analysis of digraphs.

Contribution

It introduces a cofibration category framework for digraphs based on path homology, linking graph theory with algebraic topology.

Findings

Category of digraphs has a cofibration structure

Weak equivalences correspond to isomorphisms in path homology

Provides a foundation for homological analysis of directed graphs

Abstract

We prove that the category of directed graphs and graph maps carries a cofibration category structure in which the weak equivalences are the graph maps inducing isomorphisms on path homology.