  An infinite magmatic bialgebra is a vector space endowed with an n-ary
operation, and an n-ary cooperation, for each n, verifying some compatibility
relations. We prove a rigidity theorem, analogue to the Hopf-Borel theorem for
commutative bialgebras: any connected infinite magmatic bialgebra is of the
form $Mag^\infty(Prim H)$, where $Mag^\infty(V)$ is the free infinite magmatic
algebra over the vector space V.
