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Limits via relations

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arxiv 2405.03175 v1 pith:NYZXGJG7 submitted 2024-05-06 math.KT math.AT

Sergei O. Ivanov , Roman Mikhailov , Fedor Pavutnitskiy This is my paper · ORCID
classification math.KTmath.AT
keywords appliedcategorylimitsoperationsabelianappearsdefinedderivation
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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.

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