ACTIONS OF INTERNAL GROUPOIDS IN THE CATEGORY OF LEIBNIZ ALGEBRAS

Abstract

The aim of this paper is to characterize the notion of internalcategory (groupoid) in the category of Leibniz algebras and investigate someproperties of well-known notions such as covering groupoids and groupoid operations (actions) in this category. Further, for a Öxed internal groupoid Gin the category of Leibniz algebras, we prove that the category of coveringgroupoids of G and the category of internal groupoid actions of G on Leibniz algebras are equivalent. Finally, we interpret the corresponding notion ofcovering groupoids in the category of crossed modules of Leibniz algebras.