The Yoneda isomorphism commutes with homology

TL;DR

This paper demonstrates that Yoneda's isomorphism interacts compatibly with homology in abelian and semiabelian categories, leading to new insights in higher torsion theories and universal extensions.

Contribution

It establishes that Yoneda's isomorphism commutes with homology in abelian and semiabelian categories, extending the understanding of functor derivation and higher extensions.

Findings

Yoneda's isomorphism commutes with homology in abelian categories.

Extension of the result to semiabelian categories.

Development of semiabelian higher torsion theories and universal extensions.

Abstract

We show that, for a right exact functor from an abelian category to abelian groups, Yoneda's isomorphism commutes with homology and, hence, with functor derivation. Then we extend this result to semiabelian domains. An interpretation in terms of satellites and higher central extensions follows. As an application, we develop semiabelian (higher) torsion theories and the associated theory of (higher) universal (central) extensions.