Title: Further remarks on liftings of crossed modules,
Abstract: In this paper we define the notion of pullback lifting of a lifting crossed
module over a crossed module morphism and interpret this notion in the category
of group-groupoid actions as pullback action. Moreover, we give a criterion for
the lifting of homotopic crossed module morphisms to be homotopic, which will
be called homotopy lifting property for crossed module morphisms. Finally, we
investigate some properties of derivations of lifting crossed modules according
to base crossed module derivations.