Lie 2-bialgebras

In this paper, we study Lie 2-bialgebras, with special attention to coboundary ones, with the help of the cohomology theory of $L_{\mathrm{\infty }}$-algebras with coefficients in $L_{\mathrm{\infty }}$-modules. We construct examples of strict Lie 2-bialgebras from left-symmetric algebras and symplectic Lie algebras.