Sheaf coalgebras and duality

In this paper we construct an adjoint pair of functors between the category of sheaves on a smooth manifold M and the category of coalgebras over the ring C c ∞ ( M ) of smooth functions with compact support on M. We show that the sheaf coalgebra associated to a sheaf E on M determines the sheaf E uniquely up to an isomorphism, and that the adjoint functors restrict to an equivalence between sheaves on M and sheaf coalgebras over C c ∞ ( M ) .