  We show how to integrate a weak morphism of Lie algebra crossed-modules to a
weak morphism of Lie 2-groups. To do so we develop a theory of butterflies for
2-term L_infty algebras. In particular, we obtain a new description of the
bicategory of 2-term L_infty algebras. We use butterflies to give a functorial
construction of connected covers of Lie 2-groups. We also discuss the notion of
homotopy fiber of a morphism of 2-term L_infty algebras.
