# Rational homotopy theory and differential graded category - Mathematics > Algebraic Topology

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

Author: ** Syunji Moriya**

Source: https://arxiv.org/