A remark on a new category of supermanifolds (Q749935)

In a previous paper [J. Geom. Phys. 4, No.3, 391-404 (1987; Zbl 0658.58009)] a new category of supermanifolds, called G-supermanifolds, was introduced by two of the authors, C. Bartocci and V. Bruzzo. In this note the authors complete the analysis of that category by showing that the sheaf of a G-supermanifold is isomorphic to the sheaf of germs of G- maps between G-supermanifolds. This results is a crucial one in the theory of super vector bundles developed by the authors in other papers.