  Examples of exact categories in representation theory are given by the
category of Delta-filtered modules over quasi-hereditary algebras, but also by
various categories related to matrix problems, such as poset representations or
representations of bocses. Motivated by the matrix problem background, we study
in this article the reduction of exact structures, and consider the poset Ex(A)
of all exact structures on a fixed additive category A. This poset turns out to
be a complete lattice, and under suitable conditions results of Enomoto's imply
that it is boolean.
  We initiate in this article a detailed study of exact structures E by
generalizing notions from abelian categories such as the length of an object
relative to E and the quiver of an exact category (A,E). We investigate the
Gabriel-Roiter measure for (A,E), and further study how these notions change
when the exact structure varies.
