adjoint VS milewski-ctfp-pdf

This idea shows up in essentially all scientific fields. It’s the idea of adjointness. Together with norm, they give you the idea of fixed points, (invariants, spectra, embeddings, braids etc).I'm

Lawvere's fixed point theorem is I think the best formulation of the idea

https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theore...

I've been putting together a brain dump on the topic

https://github.com/adamnemecek/adjoint/

Join the discord https://discord.gg/mr9TAhpyBW

I’ve always thought that the completeness theorem was more interesting.

Also I really like approaching this from Lawvere’s fixed point theorem. https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem

I have been thinking about some of this stuff

https://github.com/adamnemecek/adjoint

Yeah I have been realizing this lately as well. I have written up a bit on this

https://github.com/adamnemecek/adjoint/

Check the raw source there’s a bunch of links.

Fixed points, diagonalizations and eigenshit are all the same thing.

I think that there are like three concepts in math or the world, the concepts being the adjoint, norm and fixed point.

https://github.com/adamnemecek/adjoint

The concept of a fixed point is so ubiquitous.

Game theory, just liek essentially everything in math, physics and probability, and cs is about adjoints, norms, and fixed points https://github.com/adamnemecek/adjoint/

Nash equilibrium is a fixed point.

For me it was the idea of adjoint functors which is the central idea of category theory.

I wrote up a bit on it here https://github.com/adamnemecek/adjoint

Category Theory for Programmers by Bartosz Milewski (https://github.com/hmemcpy/milewski-ctfp-pdf/releases)

Strangely similar name to the well-known 'Category Theory for Programmers'

https://github.com/hmemcpy/milewski-ctfp-pdf

There's this, but the programmer doesn't have to be working:

https://bartoszmilewski.com/2014/10/28/category-theory-for-p...

Milewski's "Category Theory for Programmers".

(3) category theory. I was never advised to read any, but found that bartosz's introduction really good. https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/. Helps to rewire the brain.

It's also possible to model programming languages using category theory, but I know less about that. If you're interested in following this up, then Benjamin Pierce has what I'm told is a good introduction to category theory for computer scientists, and Bartosz Milweski has an online book (it might be available in hard copy as well, I'm not sure) called Category Theory for Programmers. I believe simple programming languages like the simply typed lambda calculus end up being modelled as Cartesian closed categories.