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Mar 14, 2013 at 14:24 comment added Leonid Positselski Having a discrete $G$-module $M$ means that to every element of $M$ you have assigned a locally constant function on $G$ with values in $M$. So does having a $\mathbb Z(G)$-comodule $M$. (One still has to check that the associativity and unity equations are the same in these two points of view, of course.)
Mar 13, 2013 at 21:58 comment added KBuck Why is a discrete $G$-module the same as a comodule over the coalgebra $\mathbb{Z}G$ ?
Mar 13, 2013 at 19:46 history answered Leonid Positselski CC BY-SA 3.0