Limits via relations

TL;DR

This paper explores derived limit operations on functors in abelian groups, linking them to integral homology of Eilenberg-MacLane spaces, revealing new algebraic structures.

Contribution

It introduces a novel class of functor operations based on derived limits over relations, connecting algebraic and topological invariants.

Findings

Derived limits relate to functor operations on abelian groups.

Integral homology of $K( extbf{Z},3)$ appears in the description of these operations.

New algebraic structures are characterized through these limits.

Abstract

In this paper, we study operations on functors in the category of abelian groups simplar 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 $K(\mathbb Z,3)$ appears as a part of description of these operations applied to symmetric powers.