adjoint
milewski-ctfp-pdf
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adjoint
- The Mathematical Hacker
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Why Is Symmetry So Important in Particle Physics?
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
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Gödel’s first incompleteness theorem – an interactive tutorial
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
- Young Diagrams and Classical Groups [pdf]
- Gödel, Escher, Bach: an in-depth explainer
- Transformers Seem to Mimic Parts of the Brain
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A software engineer's circuitous journey to calculate eigenvalues
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.
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Tools for Better Thinking
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.
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Interactive introduction to game theory and trust
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.
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Emily Riehl is rewriting the foundations of higher category theory
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
milewski-ctfp-pdf
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reflect-cpp - Now with compile time extraction of field names from structs and enums using C++-20.
Category Theory for Programmers by Bartosz Milewski (https://github.com/hmemcpy/milewski-ctfp-pdf/releases)
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Category Theory for Programming
Strangely similar name to the well-known 'Category Theory for Programmers'
https://github.com/hmemcpy/milewski-ctfp-pdf
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Polynomial Functors: A Mathematical Theory of Interaction [pdf]
There's this, but the programmer doesn't have to be working:
https://bartoszmilewski.com/2014/10/28/category-theory-for-p...
- Monads vs Classes
- 今天看到的,是真的离谱。
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Reading recomendations on Category Theory
Milewski's "Category Theory for Programmers".
- Ask HN: Math for Programmers?
- [Math] Category Theory for Programmers
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Some math topics get mentioned a bunch in functional programming articles and forums. Which ones have ever actually helped you in writing your programs?
(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.
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what is the relation of a class in programming and category theory?
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.
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