  In [16], a theory of universal extensions in abelian categories is developed;
in particular, the notion of Ext-universal object is presented. In the present
paper, we show that an Ab3 abelian category which is Ext-small satisfies the
Ab4 condition if, and only if, each one of its objects is Ext-universal. We
also give a characterization of the co-Ext-universal objects of the category of
torsion abelian groups. In particular, we show that such groups are the ones
admitting a decomposition $Q\oplus R$, in which $Q$ is injective and $R$ is a
reduced group on which each $p$-component is bounded.
