  It has been an open problem to identify classes of Gibbs measures less
regular then H\"older continuous on the full shift which are closed under
factor maps. In this article we show that in fact all of the classical
uniqueness regimes (Bowen, Walters, and H\"older) from thermodynamic formalism
are closed under factor maps between full shifts. In fact we show more
generally that the classical uniqueness regimes are closed under factors
between shifts of finite type provided the factor map satisfies a suitable
mixing in fibers condition.
