Re: String diagrams, adjunction and autonomous categories.

[Michael Shulman <shulman@math.uchicago.edu>]

On the other hand, am I right that you (John) have also written about
string diagrams in closed (non-autonomous) monoidal categories? Those
are a bit subtler, and I don't recall them in the work of Joyal and
Street (am I wrong?).  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.

Mike

On Mon, Aug 30, 2010 at 10:06 PM, John Baez <baez@math.ucr.edu> wrote:
> Micah wrote:
>
> Incidentally, although I'm not sure that I'm familiar with the work of Baez
>> to which you refer, I would imagine that the use of string diagrams to
>> describe units and counits in an autonomous category is considerably older,
>> at least as far back as "Planar Diagrams and Tensor Algebra" by Joyal and
>> Street (available on the website of the latter) from 1988.
>>
>
> He was probably talking about these popularizations:
>
> A prehistory of n-categorical physics, with Aaron Lauda
> http://arxiv.org/abs/0908.2469
>
> Physics, logic, computation and topology: a Rosetta stone, with Mike Stay
> http://arxiv.org/abs/0903.0340
>
> which cite the work of Joyal and Street, though sadly not the paper you
> mention.
>
> Best,
> jb
>


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