3 ms·

I'm trying to learn category theory. It's not the kind of thing you can learn the way this article suggests. I find learning new abstractions rather difficult e

by xupybd 4y ago

I'm trying to learn category theory. It's not the kind of thing you can learn the way this article suggests. I find learning new abstractions rather difficult especially at the level of category theory. If anyone has any tips I'd love to hear them.

Jensson 4y ago
Have you studied abstract algebra first? Category theory is an abstraction level above abstract algebra, so the normal way to learn it is to first get a solid foundation in abstract algebra.
- xupybd 4y ago
  I have not. Thank you I'll start learning that first.
- quickthrower2 4y ago
  In the same way that being an athlete is a step up from using a PT the gym: It is a very big step up. Probably this would be your career.
363849473754 4y ago
As Jensson recommended I would learn abstract algebra first to understand concrete examples in category theory. If abstracts algebra is too difficult then learn introduction to proofs before continuing with abstract algebra. Try doing problems and posting them online to have them checked. Currently you can use discord, reddit, math stack exchange etc Don’t worry about rushing it. Everything builds on itself. For instance once you rigorously study introduction to proofs you’ll see the same sort of proofs again when you begin studying abstract algebra and will already be familiar with the concepts.
- anonymousDan 4y ago
  Any good resources for proofs and/or abstract algebra?
  - 363849473754 4y ago
    for proofs i really liked two sources: susanna epps’s discrete math book and also rosen’s discrete math text (though epp’s is friendlier for the beginner) supplement those books with these lecture videos: https://youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz https://youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNo... they appear to follow rosen but they’re the same topics you’d see in epp if you’re the complete beginner go with epp and then use rosen as a supplement. if you are an advanced undergraduate in math but don’t know category theory then: https://math.jhu.edu/~eriehl/context.pdf https://math.jhu.edu/~eriehl/context.pdf or Basic Category Theory by Tom Leinster (even though i’ll list a bunch more resources below i’d probably start with leinster and work up enough math maturity to push through it.) i also liked this: https://arxiv.org/pdf/1912.10642.pdf https://arxiv.org/pdf/1912.10642.pdf if you don’t know advanced math then there is an upcoming (not yet released book) called “the joy of abstraction” i cannot attest for the book as i haven’t read it but may be good for true beginners: https://www.cambridge.org/us/academic/subjects/mathematics/logic-categories-and-sets/joy-abstraction-exploration-math-category-theory-and-life?format=HB https://www.cambridge.org/us/academic/subjects/mathematics/l... (click “look inside”) they say “no formal mathematical background needed” you can read the description and see if that is something that would be of interest to you. this guy has videos + a book https://youtu.be/fY02LIW8fvk https://youtu.be/fY02LIW8fvk there are a lot of books like “category theory for programmers”, “programming in categories” and the “seven sketches” books along with lecture recordings and videos that you may find helpful. category theory for programmers might be the easiest of those three books. i worked a bit out of the programming with categories (http://brendanfong.com/programmingcats_files/cats4progs-DRAFT.pdf http://brendanfong.com/programmingcats_files/cats4progs-DRAF...) book and ignored all the haskell sections and just focused on the math parts (this is a distinct book from “category theory for programmers”. people confuse the two due to the names and the fact they both use haskell). if you know category theory and want to learn topology then there is “ Topology A Categorical Approach” by bradley et al.
    - xupybd 4y ago
      This is what makes HN amazing. I now have a much better path to learning something that I've been struggling with for some time.
OracB7 4y ago
Eugenia Cheng has some interesting and accessible videos, e.g.: https://www.youtube.com/watch?v=ho7oagHeqNc https://www.youtube.com/watch?v=ho7oagHeqNc and in a similar vein I am enjoying her book: "How to Bake Pi". Getting more into the technical side of things, Bartosz Milewski has good lessons in this playlist: https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbmEnaH_LTkxLI7FMa2HsnawM_ https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbm...

by xupybd 4y ago

Jensson 4y ago

Have you studied abstract algebra first? Category theory is an abstraction level above abstract algebra, so the normal way to learn it is to first get a solid foundation in abstract algebra.

xupybd 4y ago
I have not. Thank you I'll start learning that first.
quickthrower2 4y ago
In the same way that being an athlete is a step up from using a PT the gym: It is a very big step up. Probably this would be your career.

363849473754 4y ago

As Jensson recommended I would learn abstract algebra first to understand concrete examples in category theory. If abstracts algebra is too difficult then learn introduction to proofs before continuing with abstract algebra. Try doing problems and posting them online to have them checked. Currently you can use discord, reddit, math stack exchange etc Don’t worry about rushing it. Everything builds on itself. For instance once you rigorously study introduction to proofs you’ll see the same sort of proofs again when you begin studying abstract algebra and will already be familiar with the concepts.

anonymousDan 4y ago
Any good resources for proofs and/or abstract algebra?
- 363849473754 4y ago
  for proofs i really liked two sources: susanna epps’s discrete math book and also rosen’s discrete math text (though epp’s is friendlier for the beginner) supplement those books with these lecture videos: https://youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz https://youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNo... they appear to follow rosen but they’re the same topics you’d see in epp if you’re the complete beginner go with epp and then use rosen as a supplement. if you are an advanced undergraduate in math but don’t know category theory then: https://math.jhu.edu/~eriehl/context.pdf https://math.jhu.edu/~eriehl/context.pdf or Basic Category Theory by Tom Leinster (even though i’ll list a bunch more resources below i’d probably start with leinster and work up enough math maturity to push through it.) i also liked this: https://arxiv.org/pdf/1912.10642.pdf https://arxiv.org/pdf/1912.10642.pdf if you don’t know advanced math then there is an upcoming (not yet released book) called “the joy of abstraction” i cannot attest for the book as i haven’t read it but may be good for true beginners: https://www.cambridge.org/us/academic/subjects/mathematics/logic-categories-and-sets/joy-abstraction-exploration-math-category-theory-and-life?format=HB https://www.cambridge.org/us/academic/subjects/mathematics/l... (click “look inside”) they say “no formal mathematical background needed” you can read the description and see if that is something that would be of interest to you. this guy has videos + a book https://youtu.be/fY02LIW8fvk https://youtu.be/fY02LIW8fvk there are a lot of books like “category theory for programmers”, “programming in categories” and the “seven sketches” books along with lecture recordings and videos that you may find helpful. category theory for programmers might be the easiest of those three books. i worked a bit out of the programming with categories (http://brendanfong.com/programmingcats_files/cats4progs-DRAFT.pdf http://brendanfong.com/programmingcats_files/cats4progs-DRAF...) book and ignored all the haskell sections and just focused on the math parts (this is a distinct book from “category theory for programmers”. people confuse the two due to the names and the fact they both use haskell). if you know category theory and want to learn topology then there is “ Topology A Categorical Approach” by bradley et al.
  - xupybd 4y ago
    This is what makes HN amazing. I now have a much better path to learning something that I've been struggling with for some time.

OracB7 4y ago

Eugenia Cheng has some interesting and accessible videos, e.g.: https://www.youtube.com/watch?v=ho7oagHeqNc https://www.youtube.com/watch?v=ho7oagHeqNc and in a similar vein I am enjoying her book: "How to Bake Pi". Getting more into the technical side of things, Bartosz Milewski has good lessons in this playlist: https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbmEnaH_LTkxLI7FMa2HsnawM_ https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbm...