  We propose a generalization of Sullivan's de Rham homotopy theory to
non-simply connected spaces. The formulation is such that the real homotopy
type of a manifold should be the closed tensor dg-category of flat bundles on
it much the same as the real homotopy type of a simply connected manifold is
the de Rham algebra in original Sullivan's theory. We prove the existence of a
model category structure on the category of small closed tensor dg-categories
and as a most simple case, confirm an equivalence between the homotopy category
of spaces whose fundamental groups are finite and whose higher homotopy groups
are finite dimensional rational vector spaces and the homotopy category of
small closed tensor dg-categories satisfying certain conditions.
