The Yoneda isomorphism commutes with homology

George Peschke, Tim Van der Linden
<span title="">2016</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/74pjbehpfraq5ogj3loetdwp7m" style="color: black;">Journal of Pure and Applied Algebra</a> </i> &nbsp;
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.
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