Is it true the formula$\newcommand{\Hom}{\operatorname{Hom}}$ $\Hom(\varprojlim G_\alpha ;I) \simeq \varinjlim \Hom(G_\alpha ;I),$ if the group $I$ is injective? We can assume that $G_\alpha$ is finite generated as well.
Commutativity of $\operatorname{Hom}$ and $\varprojlim$
Andrey
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