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Aug 28, 2012 at 19:30 vote accept Wolfgang Jeltsch
Aug 27, 2012 at 22:29 comment added Todd Trimble Qiaochu: I'm aware of that.
Aug 27, 2012 at 22:07 comment added Qiaochu Yuan There's no need to restrict to abelian groups. The natural transformations from the identity functor $G\text{-Set} \to G\text{-Set}$ are in natural bijection with $Z(G)$ for arbitrary $G$.
Aug 27, 2012 at 20:52 comment added Wolfgang Jeltsch Hmm, I need more time to think about this. Will continue tomorrow.
Aug 27, 2012 at 17:14 comment added Todd Trimble I added an edit which hopefully settles this to the OP's satisfaction.
Aug 27, 2012 at 17:13 history edited Todd Trimble CC BY-SA 3.0
added 572 characters in body
Aug 27, 2012 at 15:11 history edited Todd Trimble CC BY-SA 3.0
added observations on the enriched case
Aug 27, 2012 at 14:13 history answered Todd Trimble CC BY-SA 3.0