  To determine whether an $n\times n$-matrix has rank at most $r$ it suffices
to check that the $(r+1)\times (r+1)$-minors have rank at most $r$. In other
words, to describe the set of $n\times n$-matrices with the property of having
rank at most $r$, we only need the description of the corresponding subset of
$(r+1)\times (r+1)$-matrices. We will generalize this observation to a large
class of subsets of tensor spaces. A description of certain subsets of a
high-dimensional tensor space can always be pulled back from a description of
the corresponding subset in a fixed lower-dimensional tensor space.
