  We study the equivalence between the self-dual and the Maxwell-Chern-Simons
(MCS) models coupled to dynamical, U(1) charged matter, both fermionic and
bosonic. This is done through an iterative procedure of gauge embedding that
produces the dual mapping of the self-dual vector field theory into a
Maxwell-Chern-Simons version. In both cases, to establish this equivalence a
current-current interaction term is needed to render the matter sector
unchanged. Moreover, the minimal coupling of the original self-dual model is
replaced by a non-minimal magnetic like coupling in the MCS side. Unlike the
fermionic instance however, in the bosonic example the dual mapping proposed
here leads to a Maxwell-Chern-Simons theory immersed in a field dependent
medium.
