Getting Started with Category Theory
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Getting Started with Category Theory
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Re: Getting Started with Category Theory
#2Venting: I'm so tired of this. I've countless times learned that something something monoid of endofunctors. And yet, I've never been able to make that knowlwdge more useful than "do a flatMap here".
Not looking for solutions. Ok with emotional support.
Re: Getting Started with Category Theory
#3I compiled a list of Category Theory resources that might be helpful for beginners to gain an overview of what's available in the field: https://github.com/madnight/awesome-category-theory
Re: Getting Started with Category Theory
#4Venting: I'm so tired of this. I've countless times learned that something something monoid of endofunctors. And yet, I've never been able to make that knowlwdge more useful than "do a flatMap here". Not looking for solutions. Ok with emotional support.
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”.
Re: Getting Started with Category Theory
#5Venting: I'm so tired of this. I've countless times learned that something something monoid of endofunctors. And yet, I've never been able to make that knowlwdge more useful than "do a flatMap here". Not looking for solutions. Ok with emotional support.
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
Re: Getting Started with Category Theory
#6Isn't that one of the basis of maths? Namely you choose graph theory or category theory and you can rebuilt the whole maths?
If yes, which one is the "simpler", category or graph?
Re: Getting Started with Category Theory
#7Isn't that one of the basis of maths? Namely you choose graph theory or category theory and you can rebuilt the whole maths? If yes, which one is the "simpler", category or graph?
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.
Re: Getting Started with Category Theory
#8Isn't that one of the basis of maths? Namely you choose graph theory or category theory and you can rebuilt the whole maths? If yes, which one is the "simpler", category or graph?
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…
I'm not an expert so I write this comment to ask for help. Do you know if there is any relationship between category theory or set theory? I mean is it like category theory is a more general concept and set theory emerges as a specific case of the more general category theory.
I know sets well because well that's what I was taught in school. I'm just trying to understand where set theory fits in category theory or if they are two totally different things.
Re: Getting Started with Category Theory
#9Venting: I'm so tired of this. I've countless times learned that something something monoid of endofunctors. And yet, I've never been able to make that knowlwdge more useful than "do a flatMap here". Not looking for solutions. Ok with emotional support.
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
Re: Getting Started with Category Theory
#10Earlier quoted context omitted.
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…
I'm not an expert so I write this comment to ask for help. Do you know if there is any relationship between category theory or set theory? I mean is it like category theory is a more general concept and set theory emerges as a specific case of the more general category theory. I know sets well because well that's what I was taught in school. I'm just trying to understand where set theory fits in category theory or if…
I would treat them as totally different things. There is a Category of Sets, but a Set of Categories would be a bit harder to define. So axomatic set theory could be a specific case of category theory, I suppose. But you can probably do a Class of all categories. (A Class is sort of a set-theoretic way to get around Russel's paradox, incidentally, you usually use a Class to define categories, so...) Though that's actually quite an irrelevant point. It's a completely different language for describing mathematics. I think describing category theory as an alternative foundation for mathematics (you really mean topos theory here) is a bit of an exaggeration. it's technically true, but most mathematicians I know are using it as a powerful device to prove things in algebraic topology or geometry, etc.