Re: Non-triviality of *-autonomous categories

[Michael Barr <barr@math.mcgill.ca>]

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
>
>

The modern conservative is engaged in one of man's oldest exercises in
moral philosophy--the search for a superior moral justification
for selfishness.  --J.K. Galbraith


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