Crossed modules for Leibniz n-algebras

Abstract

We introduce crossed modules for the category of Leibniz n-algebras and prove that they are equivalent to cat1-Leibniz n-algebras and internal categories in Leibniz n-algebras. We interpret the set of equivalence classes of crossed extensions as the second cohomology of Leibniz n-algebras developed in [Casas J. M., Loday J.-L., Pirashvili T.: Leibniz n-algebras. Forum Math. 14 (2002), 189–207].