  The notions of \emph{Poisson Lie group} and \emph{Poisson homogeneous space}
are extended to the Dirac category. The theorem of Drinfel$'$d
(\cite{Drinfeld93}) on the one-to-one correspondence between Poisson
homogeneous spaces of a Poisson Lie group and a special class of Lagrangian
subalgebras of the Lie bialgebra associated to the Poisson Lie group is proved
to hold in this more general setting.

Differential Geometry