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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| Datum: | 2024 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2024
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7371 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
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| DOI: | 10.3842/umzh.v74i4.7371 |