Generalized Kneser superfunction trick (the iterated limit definition)

[MphLee]

Hey James, you are touching many topics.
I'm in the middle of a huge effort of tackling all the points you raise.
The answer is growing longer and longer so I guess I'll cut it into little pieces.

In order:

1. Very soon I'll make a brief comment on a detail on notation and the bullet: this is self contained and short so will be the first;
   
   Composition, bullet notation and the general role of categories, (February 2, 2021)
2. Then I'll go on with those superfunction-complete spaces. This is more self-contained and the categorical treatment is much more clean than the one needed for the "compositorial" and for the various multi-valued superfunctions trick. I'll post a new thread for this since you seems very interested in it.
   I'll make you wait longer for this, since I want to gain more understanding on your paper first and solving some unsolved mysteries in this thread;
   
3. I need some clarifications on the convergence issues;
   
4. I'm beginning to translate the example you represented in this thread and coming up with a proof sketch of the general mutivalued superfunction trick. This part is longer and more involved and it has my priority now.
   

Oh btw, I'm very glad you find something worth thinking in my "paper." I, instead, love to finally see some concrete stuff that seems to fill the empty abstractions that I play with.

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EDIT 1 (Jan 30, 2021): First point is completed. Here's my preliminary thoughts on the bullet notation: I'll make a new thread about this once ive  [tex]-ed it very  soon, so that we can talk about this there if you want.

  (2021 01 30) Composition bullet notation and the general role of categories.pdf (Size: 544.4 KB / Downloads: 924)
EDIT 2 (Feb 02, 2021): Updated, corrected and polished the draft, made some paragraphs more clear. Created a new thread about the role of categories and composition.

  (2021 02 02) Composition bullet notation and the general role of categories - the softest introduction ever made.pdf (Size: 585.27 KB / Downloads: 896)