  On one hand, together with Pelle Steffens, we recently characterized the
infinity category of derived manifolds up to equivalence by a universal
property. On the other hand, it is shown in recent work of Behrend-Liao-Xu that
the category of differential graded manifolds admits a homotopy theory. In this
paper, we prove that the associated infinity category of dg-manifolds is
equivalent to that of derived manifolds. This allows the well developed theory
of dg-geometry to live in symbiosis with infinity categorical approach to
derived differential geometry. As a consequence, we prove that a
dg-C-infinity-algebra is homotopically finitely presented if and only if it is
quasi-isomorphic to smooth functions on a dg-manifold.
