Moduli stack of vector bundles

In algebraic geometry, the moduli stack of rank-"n" vector bundles Vect"n" is the stack parametrizing vector bundles (or locally free sheaves) of rank "n" over some reasonable spaces.
It is a smooth algebraic stack of the negative dimension formula_1. Moreover, viewing a rank-"n" vector bundle as a principal formula_2-bundle, Vect"n" is isomorphic to the classifying stack formula_3
Definition.
For the base category, let "C" be the category of schemes of finite type over a fixed field "k". Then formula_4 is the category where
Let formula_9 be the forgetful functor. Via "p", formula_4 is a prestack over "C". That it is a stack over "C" is precisely the statement "vector bundles have the descent property". Note that each fiber formula_11 over "U" is the category of rank-"n" vector bundles over "U" where every morphism is an isomorphism (i.e., each fiber of "p" is a groupoid).