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Matteo Capucci (he/him) (Apr 11 2024 at 15:32):I thought I knew the answer to this question but today I realized Joyal and Street only defined string diagrams for monoidal categories. What about string diagrams for 2-categories? Who defined those first?
Amar Hadzihasanovic (Apr 11 2024 at 17:33):Perhaps @Dan Marsden would know?
Dan Marsden (Apr 11 2024 at 18:01):Unfortunately I don't know. Ralf and I did some digging around but couldn't find a definitive answer if I remember correctly. Of course, I would love to know if somebody does understand the history.
Mike Shulman (Apr 11 2024 at 18:03):I think the earliest occurrence I'm aware of is in some paper by Ross Street, I don't remember which offhand.
Nathanael Arkor (Apr 11 2024 at 18:33):Street certainly mentions string diagrams for 2-categories in Categorical structures (1996). Perhaps there are earlier references.
Dan Marsden (Apr 11 2024 at 18:55):Street also mentions them in Higher Categories, Strings, Cubes and Simplex Equations (1995), which is very marginally earlier.
David Michael Roberts (Apr 12 2024 at 00:50):Perhaps someone can email Ross to see if he had the idea independently, or it came from someone else and/or in collaboration/discussion with others. It may well be that the Sydney/Australian CT seminar prompted it in discussions at talks.