Geodesic
On the path homology theory of digraphs and Eilenberg–Steenrod axioms
Homology, homotopy, and applications, Tome 20 (2018) no. 2, pp. 179-205.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2018.v20.n2.a9
Classification : 05C20, 05C25, 05C38, 05C76, 18G60, 55N35, 55N40, 55P10, 55P40, 57M15
Keywords: homology of digraphs, paths in digraphs, homotopy theory for digraphs, Eilenberg–Steenrod axioms 
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Alexander Grigor’yan; Rolando Jimenez; Yuri Muranov; Shing-Tung Yau. On the path homology theory of digraphs and Eilenberg–Steenrod axioms. Homology, homotopy, and applications, Tome 20 (2018) no. 2, pp. 179-205. doi : 10.4310/HHA.2018.v20.n2.a9. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n2.a9/

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