String diagrams, adjunction and autonomous categories.

[John Baez <baez@math.ucr.edu>]

Mike Shulman wrote:

On the other hand, am I right that you (John) have also written about
> string diagrams in closed (non-autonomous) monoidal categories?


Right.


> Those are a bit subtler, and I don't recall them in the work of Joyal and
> Street (am I wrong?).


I think you're right - they're subtler, and I haven't seen anyone else using
them.  I never proved any *theorems* about them.   But I used them
extensively in my course on "Classical versus quantum computation", starting
here:

http://math.ucr.edu/home/baez/qg-fall2006/index.html#computation

I wanted to explain how beta-reduction in the lambda calculus is like
"straightening a zig-zag".

There's a quick summary of this material in that "Rosetta Stone" paper with
Mike Stay, mentioned earlier:

http://arxiv.org/abs/0903.0340


>  The original question used the word "autonomous" but the notation used
> suggested a merely closed monoidal category, so perhaps that's what he had
> in mind.
>

Oh, okay.  Yeah, I was sort of disappointed that Micah credited me for
string diagrams in the autonomous case, where I didn't invent them, instead
of the closed case, where maybe I did.

Best,
jb


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