  The purpose of this paper is to give information on the FI-homology of the
standard injective cogenerators of the category of FI-modules, where FI is the
category of finite sets and injections.
  Working over a field k of characteristic zero, a full calculation is given in
homological degree zero and a conjectural description in higher homological
degree.
  The proof of the main theorem reduces to a calculation in representation
theory of the symmetric groups, exploiting the Young orthonormal basis.
