(01/13/2021, 12:22 AM)MphLee Wrote: I'm glad to see you are completing a circle. I followed you during this time at ArXiv, reading your stuff. The turn on Iterated composition was a pleasure, and I'd expected it in some way.
I'm doing well, finally I could start university, but I was not very lucky, covid came... so I'm sure that on the math side you did for sure better than me.
I did indeed find cool things. My attack on the subject went way more algebraic-abstract than ever, and far than ever I hope (Spoiler alert: yep, recursions are functors, h.ops are functors and flows are probably Kan-extensions). I like to excuse myself saying that I'm more of a theory-builder than a Problem-cracker mathematician. At the end I'm not even a mathematician... so idc...
That's also an excuse for not being that good at analysis (or the cause?)... but said that, I find very interesting what I can understand of your paper... If I ever come up with some doubt I might write here!
Good luck with life and wish you the best.
Oh I totally missed your reply MphLee!
Thanks for following me on arxiv! I've been doing tons of stuff there (occasionally uploading incorrect drafts...)! I'm glad you liked the infinite compositions; full circle back to tetration, lol.
Honestly, your discussions of hyper operators were always category theory (iterations within iterations within iterations), rather than \( \epsilon,\delta \). I'm happy to hear that's where you've gravitated towards; kinda always felt you were writing Godel code, lol. Happy to hear you're still working on tetration. Honestly, I'd like to read some of your cool ideas. As far as Kan extensions go, I'm clueless. Frankly, all I know from category theory is from group theory; don't know how much help I'd be. But I'd be happy to talk.
Regards, James