Crossed modules with action
UDC 512.5 Following the idea of a group with action, in a higher dimension,  we consider crossed modules with a given crossed-module action upon itself. A category of these objects $\mathbf{XMod}^*$ is given by replacing the set of morphisms in the category $\mathbf{Gr}^*$...
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| Date: | 2024 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7371 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512660749025280 |
|---|---|
| author | Çetin, Selim Gürdal, Utku Çetin, Selim Gürdal, Utku |
| author_facet | Çetin, Selim Gürdal, Utku Çetin, Selim Gürdal, Utku |
| author_sort | Çetin, Selim |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:35:27Z |
| description | UDC 512.5
Following the idea of a group with action, in a higher dimension,  we consider crossed modules with a given crossed-module action upon itself. A category of these objects $\mathbf{XMod}^*$ is given by replacing the set of morphisms in the category $\mathbf{Gr}^*$ of groups with action by the set of a modified form of $\varphi$-crossed homomorphisms. Moreover, the connections of $\mathbf{XMod}^*$ with some other known categories, such as $\mathbf{Gr}^*$ and $\mathbf{XMod},$ are given by describing some related functors. |
| doi_str_mv | 10.3842/umzh.v74i4.7371 |
| first_indexed | 2026-03-24T03:32:19Z |
| format | Article |
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| id | umjimathkievua-article-7371 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:19Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-73712024-06-19T00:35:27Z Crossed modules with action Crossed modules with action Çetin, Selim Gürdal, Utku Çetin, Selim Gürdal, Utku Crossed module Groups with action Category of groups 18G45 20J15 19J35 UDC 512.5 Following the idea of a group with action, in a higher dimension,  we consider crossed modules with a given crossed-module action upon itself. A category of these objects $\mathbf{XMod}^*$ is given by replacing the set of morphisms in the category $\mathbf{Gr}^*$ of groups with action by the set of a modified form of $\varphi$-crossed homomorphisms. Moreover, the connections of $\mathbf{XMod}^*$ with some other known categories, such as $\mathbf{Gr}^*$ and $\mathbf{XMod},$ are given by describing some related functors. УДК 512.5 Схрещені модулі з дією За допомогою ідеї групи з дією у вищій вимірності розглянуто схрещені модулі із заданою схрещеною дією схрещеного  модуля на себе. Категорія цих об’єктів $\mathbf{XMod}^*$ задається шляхом заміни набору морфізмів у категорії $\mathbf{Gr}^*$ груп з дією на набір  $\varphi$-схрещених гомоморфізмів модифікованої форми. Крім того, зв’язки $\mathbf{XMod}^*$ з деякими іншими відомими категоріями, такими як $\mathbf{Gr}^*$ і $\mathbf{XMod},$ отримано шляхом опису деяких споріднених функторів. Institute of Mathematics, NAS of Ukraine 2024-04-26 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7371 10.3842/umzh.v74i4.7371 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 4 (2024); 581 - 598 Український математичний журнал; Том 76 № 4 (2024); 581 - 598 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7371/9918 Copyright (c) 2024 Selim Çetin |
| spellingShingle | Çetin, Selim Gürdal, Utku Çetin, Selim Gürdal, Utku Crossed modules with action |
| title | Crossed modules with action |
| title_alt | Crossed modules with action |
| title_full | Crossed modules with action |
| title_fullStr | Crossed modules with action |
| title_full_unstemmed | Crossed modules with action |
| title_short | Crossed modules with action |
| title_sort | crossed modules with action |
| topic_facet | Crossed module Groups with action Category of groups 18G45 20J15 19J35 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7371 |
| work_keys_str_mv | AT cetinselim crossedmoduleswithaction AT gurdalutku crossedmoduleswithaction AT cetinselim crossedmoduleswithaction AT gurdalutku crossedmoduleswithaction |