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Asad Saeeduddin (Jan 10 2022 at 03:50):Hello there. Does anyone know of a visual formalism (perhaps analogous to wiring diagrams) that allows one to work with with morphisms in a category with two simultaneous monoidal structures, such that one distributes over the other? I was imagining some kind of three dimensional diagram, but I can't envision it very clearly.
John Baez (Jan 10 2022 at 04:33):People keep asking this; this is a very popular question. I think some people here have tried coming up with something that does this.
Fabrizio Genovese (Jan 10 2022 at 09:21):@Jules Hedges ? @Antonin Delpeuch ?
Antonin Delpeuch (Jan 10 2022 at 09:40):Thanks @Fabrizio Genovese for the ping! Yes your question seems to match pretty well the paper Jules, @Cole Comfort and I wrote: https://arxiv.org/abs/2010.13361. I would be curious to know if it suits your needs! The diagrams look like this: image.png
Antonin Delpeuch (Jan 10 2022 at 09:46):We also have a renderer for those diagrams: https://wetneb.github.io/sheetshow/ if you are interested in using the diagrams in your own work (with configurable theme, export to vector graphics for LaTeX and interactive embeds in web pages)
Asad Saeeduddin (Jan 10 2022 at 09:54):@Antonin Delpeuch that looks awesome, thanks a bunch!
Asad Saeeduddin (Jan 10 2022 at 10:00):@John Baez i wonder if it is worth having a FAQ. i feel in fact that i might have asked this question or something like it before, but now i can't find it from searching my message history
Antonin Delpeuch (Jan 10 2022 at 10:07):Someone kindly added a reference to our paper to [[rig category]] on nLab but perhaps we could develop it more, including pictures, as a section of the article.
Asad Saeeduddin (Jan 10 2022 at 10:34):That would be great. I also wonder if Peter Selinger's excellent survey of graphical languages for monoidal categories could be extended with these (or if we could have some kind of analogous community maintained resource)
Jules Hedges (Jan 10 2022 at 10:37):A community-edited version of Selinger's Bible is a pretty good idea. I have a couple of graphical syntaxen I use more or less privately that I could add...
Jon Sterling (Jan 10 2022 at 10:51):Antonin Delpeuch said:
We also have a renderer for those diagrams: https://wetneb.github.io/sheetshow/ if you are interested in using the diagrams in your own work (with configurable theme, export to vector graphics for LaTeX and interactive embeds in web pages)
Wow this tool is mindblowing...
Matteo Capucci (he/him) (Jan 10 2022 at 12:54):Yeah, really outstanding! I don't know how I missed it
Matteo Capucci (he/him) (Jan 10 2022 at 12:54):(also very funny name, +1)