The aim of this paper is to characterize the notion of internal category (groupoid) in the category of Leibniz algebras and investigate some properties of well-known notions such as covering groupoids and groupoid operations (actions) in this category. Further, for a fixed internal groupoid G in the category of Leibniz algebras, we prove that the category of covering groupoids of G and the category of internal groupoid actions of G on Leibniz algebras are equivalent. Finally, we interpret the corresponding notion of covering groupoids in the category of crossed modules of Leibniz algebras.
Birincil Dil | İngilizce |
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Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 1 Şubat 2019 |
Gönderilme Tarihi | 20 Aralık 2017 |
Kabul Tarihi | 31 Mart 2018 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 68 Sayı: 1 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
This work is licensed under a Creative Commons Attribution 4.0 International License.