Getting Started with Category Theory (opens in new tab)

I wouldn't have described graph theory that way. But category theory seeks to formalise and generalise mathematics itself. Another popular branch of mathematics that does this is set theory, which you may have been thinking of rather than graph theory.

Set theory is generally taught before category theory at universities. "Simpler" is very subjective, but set theory is often seen as more intuitive because some of the concepts start getting taught much earlier in school.

You probably mean set theory instead of graph theory, since set theory and category theory are kind of seen as two foundations for math.

Both category theory and set theory use sets. But set theory tries to make absolutely everything into a set. It takes on a little complexity in this quest, because of Russel's paradox. Category theory can be seen as studying set theory, among other things, so it is "bigger" or more all-encompassing than set theory. Many things studied in category theory aren't possibly sets.

Set theory is more immediately intuitive, but category theory organizes things in a way that are ultimately more insightful, I think. Meaning that once you can get into the category theory headspace and learn to navigate it, it becomes a much better environment for thinking without mistakes. In my personal opinion.

Thanks for taking the time haha, let me know if I can improve my exposition!

I work with a bunch of functional programmers. We went through most of “category theory for programmers.” We had support from a math PhD.

Broad consensus was it was a waste of time. Functional programming has taken the useful bits, and some of the less useful bits. The rest is arcanum, and as useful to programming as astronomy

I'm a PhD in math. I love category theory and it's very useful for studying abstract algebra at the research mathematics level because it clarifies concepts and even provides algorithmic ways for computation at that level (e.g. adjoint functors and cotriples to compute homology). But to be honest, except for computer science researchers, I would not recommend it to programmers. I am also a programmer (at least a part-time one sometimes, and previously full-time), and I can say with absolute confidence that a deep understanding of category theory is 100% useless for programming.

Again, with a few exceptions, but if you are one of these exceptions, you will already know it.

I love category theory, but I think there's a secret category of "high effort programming things" that programmers who have done them love to say that "Everyone should do x because it will make them a better programmer".

Here's the kind of things I'm thinking of:

- Learn category theory

- Build an interpretter/compiler

- Develop your own programming language

- Learn about and built distributed systems

- Learn to write code for the GPU

- Understand assembly code

- Learn about CPU architecture

I think, especially since it's the holiday season, maybe lets take a step back and just accept these things probably will make you a better programmer, but there are lots of them. If you do all of them, you'll maybe become a very good programmer, but you'll definitely become a very tired human being.

If you have an interest in the mathematical underpinnings behind some of the ideas in Haskell et al, you might love category theory, but if you just want to do effective functional programming effectively, you're fine just doing that

I read a book on category theory that described how to model databases using category theory.

My conclusion was that the goal was not to provide insight into databases but rather into category theory, which seemed backwards to me.

Instead I picked up some books on the relational algebra/logic for databases, and those books were actually useful — you could show that some set of transformations would be mathematically identical.

At some point, too high level of abstraction is not useful. For category theory, it seemed that the point was to show how all these different things were “similar” but in a way that didn’t allow you to do anything with it.

You are not alone. Composition and the general idea of type is enough for most of us. You do not need Schopenhauer to discover that life is hard, or Hegel to know that opposites exist and sometimes their relation creates something different “not in the middle”.

Hey there! I'm the author, so I suppose I ought to address this :)

First I'll say that I absolutely get this head-banging-on-desk feeling of no progress. Monads got me like that for a while but F-Algebras/recursion schemes got me like that much more, so make sure you keep your distance from them haha. I'm sorry to have contributed to your frustration.

It actually sounds like you've grasped monads quite well. flatMap is the essence. I won't try to explain it though, because I know that's not what you're looking for, and I don't want to contribute to your frustration even more!

I will say that my usual readership includes a lot of people who like designing type systems for programming languages. Category theory helps make sure you don't make mistakes in this process, though there are other techniques of course. I also find it helps my ability to think formally a lot, which has helped me a ton in studying and discussing philosophy, a separate interest of mine. Hopefully you can see from my post that I didn't really make an effort to justify or explain category theory for regular programmers much. Category theory is overhyped for that use case. I personally really hate reading overly mathematical Haskell code!! But if you just enjoy math or philosophy or learning or thinking, I hope you can have some fun with the beauty of these ideas. And since authoring the post I've added a wiki https://ryanbrewer.dev/wiki that can give more accessible background on things like monoids.

I could be wrong but I don't think I mentioned a monoid of endofunctors or flatMap a single time in the post. I did mention monads, as an example of natural transformations, but completely from the perspective of beautiful math, not from a programming perspective at all. And once you learn about adjunctions, monads get even more gorgeous! https://ryanbrewer.dev/wiki/adjunction

But all of this math takes a ton of patience. I'm someone who loves programming because the feeling of solving a hard bug is exhilarating and satisfying. The emotional payoff is bigger the longer it takes, and math is the same way for me. Don't beat yourself up about it, and don't feel bad if category theory just isn't helpful or enjoyable for you and your particular way of thinking! :)