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Aug 27, 2012 at 14:47 comment added Chris Schommer-Pries I think Todd's excellent answer addresses your followup question.
Aug 27, 2012 at 14:06 comment added Wolfgang Jeltsch Thank you. So there may be multiple natural transformations from $\times$ to $\times$ and from $+$ to $+$. But what happens if I require the category to be cartesian closed? Does this change anything? After all, the category of vector spaces over real numbers doesn’t have all exponentials, right?
Aug 27, 2012 at 13:52 history edited Chris Schommer-Pries CC BY-SA 3.0
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Aug 27, 2012 at 13:45 history answered Chris Schommer-Pries CC BY-SA 3.0