On the path homology theory of digraphs and Eilenberg–Steenrod axioms
Alexander Asaturovich Grigor'yan, Rolando Jiménez, Yu. V. Muranov, Shing–Tung Yau · Homology Homotopy and Applications · 2018
In the paper we continue the investigation of the path homology theory of digraphs that was constructed in our previous papers.We prove basic theorems that are similar to the theorems of classical algebraic topology and introduce several natural constructions of digraphs which are very helpful to investigate the path homology theory.We describe relation of our results to the Eilenberg-Steenrod axiomatic of homology theory.