Actions of internal groupoids in the category of Leibniz algebras

Tunçar Şahan; Ayhan Erciyes

doi:10.31801/cfsuasmas.453582

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arXiv · 1703.10426

Actions of internal groupoids in the category of Leibniz algebras

Tunçar Şahan·Ayhan Erciyes

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Abstract

The aim of this paper is to characterize the notion of internal category (groupoid) in the category of Leibniz algebras and investigate the properties of well-known notions such as covering groupoid and groupoid operations (actions) in this category. Further, for a fixed internal groupoid $G$, 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.

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Tunçar Şahan, Ayhan Erciyes. 2017-03-30. Actions of internal groupoids in the category of Leibniz algebras. https://doi.org/10.31801/cfsuasmas.453582

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