  Suppose that $(\mathcal{F},\mathcal{M})$ is an injective structure of $R$-Mod
such that the class $\mathcal{F}$ is closed for direct limits, then two modules
in $\mathcal{M}$ are isomorphic if there are maps in $\mathcal{F}$ from each
one of the modules into the other. Examples of module classes in such injective
structures include (pure, coneat, and RD-) injective modules, as well as
$\tau$-injective modules for a hereditary torsion theory $\tau$. Thus providing
a generalization of a classical result of Bumby's and two recent ones by
Mac\'{i}as-D\'{i}az.
