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Abstract: Let G be a simply connected lie group. We denote by C(G) the differential graded Hopf algebra of smooth singular chains on G. We will explain how the category of representations of C(G) can be described infinitesimally in terms of representations of the differential graded Lie algebra Tg, which is universal for the Cartan relations. We will also explain how this correspondence is related to Chern-Weil theory and higher local systems on the classifying space BG. This talk is based on joint work with Alexander Quintero Vélez.