 Let formula_2 be a graded manifold.There exists a vector bundle formula_20 with an formula_7-dimensional typical fiber formula_22 such that the structure sheaf formula_5 of formula_2 is isomorphic to the structure sheaf of sections of the exterior product formula_25 of formula_26, whose typical fibre is the Grassmann algebra formula_27.Let formula_3 be a smooth manifold.