Colimits in the Crossed Modules Category in Lie Algebras

In this paper a left adjoint is constructed for the restriction (or pullback) functor associated to a morphism of Lie algebras. Colimits in the category of crossed modules in Lie algebras and a new result on crossed modules induced by a morphism of Lie algebras ι: P→ Qin the case where ιis the inclusion of an ideal, are obtained.