Flows in graphs and the homology of free categories

• Date: 2018
• Main Authors: Husainov, Ahmet A., Calısıcı, Hamza
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: homology of categories; derived of colimit; flows in graphs; Kirchhoff laws; 18G10; 68R10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/957
• Journal Title: Algebra and Discrete Mathematics

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 calc...