We introduce the notion of weak Lie 2-bialgebra. Roughly, a weak LieView original: http://arxiv.org/abs/1109.2290
2-bialgebra is a pair of compatible 2-term $L_\infty$-algebra structures on a
vector space and its dual. The compatibility condition is described in terms of
the big bracket. We prove that (strict) Lie 2-bialgebras are in one-one
correspondence with crossed modules of Lie bialgebras.