Weak Lie 2-bialgebra
  We introduce the notion of weak Lie 2-bialgebra. Roughly, a weak Lie 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. 
Zhuo Chen, Mathieu Stienon, Ping Xu
math-ph math.MP math.RA