

If you search about it you will find https://www.youtube.com/watch?v=oR_RAp73ra0 She also talked about trans-athletes https://www.youtube.com/watch?v=cZ9YAFYIBOU
I have never watch it, and not planning to, so I cannot help you summarize it. Nor have I claimed that she is transphobe, so I don’t feel the need to justify that stand.
If you choose to ignore everything else and focus on this one issue, then I have to admit I don’t know much about it.







I believe they are higher dimensional string diagrams. Maybe called n-diagrams? They are used in higher homotopy and higher category theory, I believe. But not entirely sure.
https://arxiv.org/pdf/2305.06938
EDIT: Found it! they are called surface diagram, which are generalization of string diagram to 3-categories https://golem.ph.utexas.edu/category/2010/03/modeling_surface_diagrams.html https://ncatlab.org/nlab/show/surface+diagram
Still not sure what the proof is talking about though :(
But from the conclusion it looks like some sort of natruality condition, where the morphisms are slided around except beta.
EDIT AGAIN: got in touch with my string diagram contact. Here is the paper https://arxiv.org/pdf/0807.0658
Note the conclusion at the bottom, the proof on the right and the axiom on the left doesn’t seem to be related.
The proof on the right is Theorem 6; the equality at bottom is in section 3.4, where the proof is omitted because “follows from definition”; the axiom on the left is HM1 and HM2 on page 19.