In the original definition, the fact that A --> A** is an isomorphism was part of the definition. If that is not what you're asking, then I don't understand the question. Of course you have to prove that for Chu categories, but that was relatively easy. On Sat, 3 Aug 2013, Harley D. Eades III wrote:
Hi, everyone.
I am having trouble finding a reference. I thought perhaps someone here might know.
It is well known that adding the isomorphism: d : A -> (A => 1) => 1 to a bicartisan closed category degenerates to a preorder.
In *-autonomous categories we have such an isomorphism, but is non-trivial. Where can I find a proof of this? I would like to reference it.
I think one could proof this using the category of coherence spaces and linear maps as a concrete *-autonomous category. See for example:
[1] R. a. g. Seely. Linear logic, *-autonomous categories and cofree coalgebras. In Computer Science Logic, 1989.
Any references anyone might have would be great.
Thanks, .\ Harley
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