r${}_{\mathrm{\infty }}$-Matrices, triangular L${}_{\mathrm{\infty }}$-bialgebras, and quantum${}_{\mathrm{\infty }}$ groups

A homotopy analogue of the notion of a triangular Lie bialgebra is proposed with a goal of extending the basic notions of theory of quantum groups to the context of homotopy algebras and, in particular, introducing a homotopical generalization of the notion of a quantum group, or quantum${}_{\mathrm{\infty }}$-group.