Dear All For a Lie group G and a vector space V, C^{\infty}(G,V) is a differentiably injective G-module (Hochschild-Mostow). Is there an analoguous construction for a Lie groupoid or, in the algebraic setting, cogroupoid object in the category of commutative algebras? Let G be a Lie groupoid, with object manifold G_o, source and target maps being supposed surjective submersions. A G-module is a vector bundle V \to G_o on G_o with a G-structure (pairing G x_G_o V to V over G_o satisfying the obvious compatiblity conditions). If we start with a vector bundle V to G_o on G_o, what corresponds to the construction C^{\infty}(G,V) for the special case where G is an ordinary Lie group? More generally, G being a Lie groupoid, does the category of G-modules have enough injectives? Where in the literature can I find answers to these questions if any? Many thanks in advance Regards Johannes HUEBSCHMANN Johannes Professeur de Mathematiques USTL, UFR de Mathematiques UMR 8524 Laboratoire Paul Painleve F-59 655 Villeneuve d'Ascq Cedex France http://math.univ-lille1.fr/~huebschm TEL. (33) 3 20 43 41 97 (33) 3 20 43 42 33 (secretariat) (33) 3 20 43 48 50 (secretariat) Fax (33) 3 20 43 43 02 e-mail Johannes.Huebschmann@math.univ-lille1.fr