In this paper, we study operations on functors in the category of abelian groups similar to the derivation in the sense of Dold Puppe. They are defined as derived limits of a functor applied to the relation subgroup over a category of free presentations of the group. The integral homology of the Eilenberg–MacLane space K(Z,3) appears as a part of description of these operations applied to symmetric powers. Copyright © 2026, Sergei O. Ivanov, Roman Mikhailov and Fedor Pavutnitskiy. Permission to copy for private use granted.