 Shirshov's Theorem that a Lie algebra of finite or countable dimension can be embedded into a 2-generator Lie algebra is equivalent to the statement that the 2-generator free Lie algebra is SQ-universal (in the category of Lie algebras).This can be proved by proving a version of the Higman, Neumann, Neumann theorem for Lie algebras.However versions of the HNN theorem can be proved for categories where there is no clear idea of a free object.