  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.
