On direct summands of homological functors on length categories. In memory of Hans-Bjørn Foxby (Q726714)

There is shown that a direct summand of a covariant Ext-functor on an abelian category \(\mathcal K\) is again of this form provided that \(\mathcal K\) is noetherian and satisfies a weak form of the descending chain condition. This generalizes the result of \textit{M. Auslander} [Topology 8, 151--166 (1969; Zbl 0204.36401)]. In fact, the result is proved in a greater generality -- for certain additive functors \(G(A,-):\mathcal K\to Ab\).