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Martin Sleziak
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Comutativity Commutativity of $Hom$$\operatorname{Hom}$ and $\varprojlim$

Is it true the formula$\newcommand{\Hom}{\operatorname{Hom}}$ $Hom(\varprojlim G_\alpha ;I) \simeq \varinjlim Hom(G_\alpha ;I),$$\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.

Comutativity of $Hom$ and $\varprojlim$

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

Commutativity of $\operatorname{Hom}$ and $\varprojlim$

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.

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Comutative Comutativity of Hom$Hom$ and lim$\varprojlim$

Is it true the formula $Hom(lim G_\alpha ;I) \simeq colim Hom(G_\alpha ;I),$$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.

Comutative of Hom and lim

Is it true the formula $Hom(lim G_\alpha ;I) \simeq colim Hom(G_\alpha ;I),$ if the group $I$ is injective? We can assume that $G_\alpha$ is finite generated as well.

Comutativity of $Hom$ and $\varprojlim$

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

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Comutative of Hom and lim

Is it true the formula $Hom(lim G_\alpha ;I) \simeq colim Hom(G_\alpha ;I),$ if the group $I$ is injective? We can assume that $G_\alpha$ is finite generated as well.