  Motivated by rational homotopy theory, we study a representable presheaf of
groups $\mathbf{\mathfrak{P}}$ on the homotopy category of cocommutative
differential graded coalgebras, its Lie algebraic counterpart and its linear
representations. We prove a Tannaka type reconstruction theorem that
$\mathbf{\mathfrak{P}}$ can be recovered from the dg-category of its linear
representations along with the forgetful dg-functor to the underlying
dg-category of chain complexes.
