Actions of internal groupoids in the category of Leibniz algebras

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.