Flows in graphs and the homology of free categories
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...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/957 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543045717065728 |
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| author | Husainov, Ahmet A. Calısıcı, Hamza |
| author_facet | Husainov, Ahmet A. Calısıcı, Hamza |
| author_sort | Husainov, Ahmet A. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-13T07:14:40Z |
| description | 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. |
| first_indexed | 2025-12-02T15:41:33Z |
| format | Article |
| id | admjournalluguniveduua-article-957 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:41:33Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-9572018-05-13T07:14:40Z Flows in graphs and the homology of free categories Husainov, Ahmet A. Calısıcı, Hamza homology of categories, derived of colimit, flows in graphs, Kirchhoff laws 18G10, 68R10 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. Lugansk National Taras Shevchenko University 2018-05-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/957 Algebra and Discrete Mathematics; Vol 2, No 2 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/957/486 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | homology of categories derived of colimit flows in graphs Kirchhoff laws 18G10 68R10 Husainov, Ahmet A. Calısıcı, Hamza Flows in graphs and the homology of free categories |
| title | Flows in graphs and the homology of free categories |
| title_full | Flows in graphs and the homology of free categories |
| title_fullStr | Flows in graphs and the homology of free categories |
| title_full_unstemmed | Flows in graphs and the homology of free categories |
| title_short | Flows in graphs and the homology of free categories |
| title_sort | flows in graphs and the homology of free categories |
| topic | homology of categories derived of colimit flows in graphs Kirchhoff laws 18G10 68R10 |
| topic_facet | homology of categories derived of colimit flows in graphs Kirchhoff laws 18G10 68R10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/957 |
| work_keys_str_mv | AT husainovahmeta flowsingraphsandthehomologyoffreecategories AT calısıcıhamza flowsingraphsandthehomologyoffreecategories |