On homotopy Lie bialgebroids

A well-known result of A. Vaintrob characterizes Lie algebroids and their morphisms in terms of homological vector fields on supermanifolds. We give an interpretation of Lie bialgebroids and their morphisms in terms of odd symplectic dg-manifolds, building on the approach of D. Roytenberg. This extends naturally to the homotopy Lie case and leads to the notion of $L_{\mathrm{\infty }}$-bialgebroids and $L_{\mathrm{\infty }}$-morphisms between them.