Abstract
A theory of singular cubic homology of digraphs is developed; the obtained homology groups are proved to be functorial and homotopy invariant. Commutative diagrams of exact sequences similar to the classical ones are constructed, and a relationship between the cubic homology and the path homology of a digraph is described. Carrying over the results to graphs, multigraphs, and quivers is discussed.
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Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 705-722 https://doi.org/10.4213/mzm12599.
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Grigor’yan, A.A., Muranov, Y.V. & Jimenez, R. Homology of Digraphs. Math Notes 109, 712–726 (2021). https://doi.org/10.1134/S0001434621050059
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DOI: https://doi.org/10.1134/S0001434621050059