Geodesic
Flows in graphs and the homology of free categories
Algebra and discrete mathematics, no. 2 (2003), pp. 36-46

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the $R$-module of generalized flows in a graph with coefficients in the $R$-representation of the graph over a ring $R$ with 1 and show that this $R$-module is isomorphic to the first derived functor of the colimit. We generalize Kirchhoff's laws and build an exact sequence for calculating the $R$-module of flows in the union of graphs.
Keywords: homology of categories, derived of colimit, flows in graphs, Kirchhoff laws. 
@article{ADM_2003_2_a2,
     author = {Ahmet A. Husainov and Hamza \c{C}ali\c{s}ici},
     title = {Flows in graphs and the homology of free categories},
     journal = {Algebra and discrete mathematics},
     pages = {36--46},
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     number = {2},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2003_2_a2/}
}
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Ahmet A. Husainov; Hamza Çalişici. Flows in graphs and the homology of free categories. Algebra and discrete mathematics, no. 2 (2003), pp. 36-46. http://geodesic.mathdoc.fr/item/ADM_2003_2_a2/