Ask HN: How to Get into Category Theory?

https://news.ycombinator.com/item?id=27642986

by worldeva • 5 years ago

5 3 5 years ago

news.ycombinator.com

I've always been interested in "Pure Maths" and Category Theory, because I'd like to understand the mathematics/logic behind programming more deeply and rigorously (also, just the concept itself is cool).

However, I don't have a very advanced mathematical background (The highest that I've learned is Calculus 2), so I don't know what the "pathway" towards Category Theory is-

What are the prerequisites and/or some resources to learn Category Theory?

cosmicocean2• 5 years ago

Learn to read and do math proofs. Then learn some abstract algebra and general topology so that you can understand examples you'll meet in category theory. Then, bam, you're ready for category theory.

The other way is to dive straight into category theory. Doable, but difficult. You'll be learning how to parse math arguments and argumentation style specific to category theory and examples from other branches of math along with the theory(from those branches AND category theory itself). Tough shyt if you ask me.

To get started with learning how mathematicians present and defend their arguments, there's free and really good Book of Proof by Richard Hammack[0].

[0] https://www.people.vcu.edu/~rhammack/BookOfProof/

elviejo• 5 years ago

I was in the same boat a year ago and went to a mathematics professor teacher and he suggested this book:

Conceptual Mathematics by Lawvere[1]

The book teaches category theory to, smart, highschool students.

It's a great start.

After that I went with:

Category Theory for Programmers by Bartosz Milewski [2]

Next I would go with anything by David Spivak.

Now I understand that: A monad is not scary, it's just a monoid in the category of endofuctors" ;)

[1] https://www.amazon.com/-/es/F-William-Lawvere/dp/052171916X

[2]https://www.blurb.com/b/9621951-category-theory-for-programm...

cosmicocean2• 5 years ago

IMO, David Spivak's book[0] is much less technical than anything coming from Bartosz Milewski. In fact, I think Spivak's book is simpler than that of Lawvere. If you know a little naive set theory, Spivak's book is a breeze.

[0] Talking about the one "for scientists".

Ask HN: How to Get into Category Theory?

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