  Gaussian elimination answers any question about a finitely presented vector
space. However, a "uniform family" of such presentations--given as generic
relations among an unspecified number of generators--is susceptible to
elimination only once the number of generators is fixed. We develop a theory of
"uniformly presented vector spaces" to compute with these uniform families,
introducing a formalism of finitely generated functors from the category of
finite sets to the category of finite dimensional Q-vector spaces. We show that
these representations have finite length and polynomial dimension away from the
empty set, and produce finite leftward resolutions by manageable functors.
