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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]