  We study dg-manifolds which are R[2]-bundles over R[1]-bundles over
manifolds, we calculate its symmetries, its derived symmetries and we introduce
the concept of T-dual dg-manifolds. Within this framework we construct the
T-duality map as a degree -1 map between the cohomologies of the T-dual
dg-manifolds and we show an explicit isomorphism between the differential
graded algebra of the symmetries of the T-dual dg-manifolds. We furthermore
show how the algebraic structure underlying B_n generalized geometry could be
recovered as derived dg-Leibniz algebra of the fixed points of the T-dual
automorphism acting on the symmetries of a self T-dual dg-manifold, and we show
how other types of algebraic structures underlying exceptional generalized
geometry could be obtained as derived symmetries of certain dg-manifolds.
