  We deal with the symmetries of a (2-term) graded vector space or bundle. Our
first theorem shows that they define a (strict) Lie 2-groupoid in a natural
way. Our second theorem explores the construction of nerves for Lie
2-categories, showing that it yields simplicial manifolds if the 2-cells are
invertible. Finally, our third and main theorem shows that smooth
pseudofunctors into our general linear 2-groupoid classify 2-term
representations up to homotopy of Lie groupoids.
