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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