  We show that direct summands of certain additive functors arising as
bifunctors with a fixed argument in an abelian category are again of that form
whenever the fixed argument has finite length or, more generally, satisfies the
descending chain condition on images of nested endomorphisms. In particular,
this provides a positive answer to a conjecture of M. Auslander in the case of
categories of finite modules over artin algebras. This implies that the
covariant Ext functors are the only injectives in the category of defect-zero
finitely presented functors on such categories.
