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Just a fing on the stringer so I don't forget about the -biscuits that Urs served up in the Cafe about hyperstructures — and the links to triadicity that I thought I saw for a moment there before they were disapparated.
It's a perennial issue so I'm sure it will come up again.
Maybe not 2-day, maybe not 2-morrow …
Is there any way I could get the Cafe hosts to copy the Forum with the posts that were deleted from the Borisov thread?
There's a kind of refractory period in my brain where I tend to forget things that I've just written down, and it's making it nearly impossible for me to remember what it was I thought — for a second — I saw there.
It would be much appreciated …
You would have to ask John Baez, he must have deleted it.
Did he contact you about it?
If and when you get back either the material or your memory about it, I would like to ask you to explain more what it is all about. When I saw it on the blog, I couldn't make heads or tails of it and came away with no good idea of what you actually meant to say. I am guessing that this is also the reason why John removed the material.
At one point you said something about an "exercise for the reader". You should maybe know that there might be a huge gap between what you expect the rest of us known about your material, and what we actually do know.
Because, to be frank again, I have no idea whatsoever yet what "triadicity" is or has to do with higher categories or hyperstructures. In fact, I can't make much of the comments further above in this thread here either. I keep having the feeling that you are assuming some private internal language has been well accepted here, where in fact it has not yet, not among the rest of us, at least.
Yes, I can understand how the exchange that occurred there might have been judged off-topic for a thread dedicated to the specifics of Borisov's paper, but I think it was the link you gave to hyperstructures and especially the allusion to those remarks of Nils Baas that resonated with longtime questions in my own studies.
"Triadicity" is just a reference to triadic or ternary relations — their prevalence in logic and math and physics.
Aside from the fact that many phyla of important objects in mathematics are 3-adic relations — groups to name just one — category theorists are known to remark on the fact that arrow composition is a 3-place relation and that a reliance on this operation is one of the differences that make a difference between category theory and set theory, at least, in practice — as working media of research and communication.
But there is another place where 3-adic relations are pivotal, and that is in the definition of a natural transformation.
Have to run off to lunch …
Well, if you're going to be frank, I guess I must be earnest …
I wasn't trying to be cryptic … this time … I think I was just assuming — partly from all the references I've seen to the Kauffman, Spencer-Brown, Peirce Gedankenkreis — that folks hereabouts would've run across these themes before.
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