4 ms·
The underlying idea is the idea of fixed points (aka spectra, diagonalizations, embedding, invariants, braids). By fixed point I mean something like the "Lawver
by adamnemecek 4y ago
The underlying idea is the idea of fixed points (aka spectra, diagonalizations, embedding, invariants, braids). By fixed point I mean something like the "Lawvere's fixed point theorem".
https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theorem https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theore...
I have a linkdump on this
https://github.com/adamnemecek/adjoint https://github.com/adamnemecek/adjoint
I also have a discord https://discord.gg/mr9TAhpyBW https://discord.gg/mr9TAhpyBW
- klysm 4y agoWhat's the discord for?
- adamnemecek 4y agoFurther discussion.
- klysm 4y agoAbout what specifically
- generationP 4y agoThe only two 1-dimensional representations of the symmetric group (i.e., what you can call fixed points if you squint a bit) are the ones that correspond to the partitions (n) and (1,1,...,1), which are the least interesting ones. Everything else is significantly more complicated. It's a block-diagonalization (Young seminormal form) with lots of nontrivial blocks. So no, you won't understand it in terms of fixed points (and certainly not of Lawvere's theorem, which I've never seen used in the entire subject).