  We use Goncharov's coproduct of multiple polylogarithms to define a Lie
coalgebra over an arbitrary field. It is generated by symbols subject to
inductively defined relations, which we think of as functional relations for
multiple polylogarithms. In particular, we have inversion relations and shuffle
relations. We relate our definition to Goncharov's Bloch groups, and to the
concrete model in weight less than 5 by Goncharov and Rudenko.
