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Our paper just hit arXiv: https://arxiv.org/abs/2109.00589
It's essentially a categorification of a traced monoidal category, and some nice things you can do with it. It has been accepted into MFPS, and I gave a talk about it yesterday (I also gave a shorter talk about it at CT).
This is awesome: super interesting! I'm working on trace monoidal categories with Hassei (Hasegawa), and I think this might be very useful to us.