(05/15/2021, 11:25 PM)tommy1729 Wrote: [...] Is there any other thing about this branch hype of Leo that I missed ?
Not trying to be mean, but not sure why so much interest in it.
I mean it is either rather not interesting or not new as far as I can see.
It is just riemann surfaces ?? [...]
Hi Tommy, I apologize if the goal of this pool was not clear to you, my fault. As far as I'm concerned there is no hype on branches here. This post is NOT about branches. Is about naming conventions for superfunctions. If there was some misleading bit in the opening post I'd like to help clarify.
Here we are talking about defining a new unified terminological standard to refer to the solutions of Abel's, Scrhoeder's, Böttcher's and superfunction equations. I'm sure you agree with me that Abel functions, Schreoder functions, and supefunctions are very similar objects if we analyze them from an algebraic point of view. That's what I'd like to capture and it is indeed very interesting for some purposes.
So...no branches involved. The only link to Leo's thread is that he was referring to the set [f,g] I defined some months ago but generalized to the mutivalued/branched case.
Quote:[...]
I do welcome and respect this new member though.
He clearly has insights and belongs here , no mistake.
Welcome Leo
regards
tommy1729
I join you, of course he is welcome. Maybe was this post of yours intended to be a reply to his thread?
best regards
MphLee
ps: I hope you can leave an opinion on the pool Tommy!
JmsNxn Wrote:And in what space it sits in which you can mod out. AT least, that's what I find so interesting about it. Mphlee is definitely more interested in the category aspect; where this relates very nicely to category theory.
Yes exactly! This is zero% formal or accurate: you can not mod out by those sets (because they are not disjoint) but from a philosophical point of view you would desperately want to mod out those sets obtaining an unique solution and you can certainly behave like your'e handling a modded out object.
on a note, maybe I'm repeating myself, but just by introducing those sets you are already doing category theory.
JmsNxn Wrote:Oh, Mphlee. I guess I misunderstood what equivariant means. I think this is the perfect term. I'll cast my vote for that. I thought it was reserved for,
\(
\chi(f(t,x)) = f(t,\chi(x))\\
\)
I didn't realize it could be null in the t variable.
OFC! If that equation is valid for all t then, as a corollary, also for t=1... which is our initial function. \( \chi(f(1,x)) = g(1,\chi(x))\\ \).
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)