Thanks for this illuminating Work!
Thanks for taking the time haha, let me know if I can improve my exposition!
Getting Started with Category Theory
31–36 of 36 posts
Re: Getting Started with Category Theory
#32Isn'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?
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.
Re: Getting Started with Category Theory
#33Isn'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?
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…
Also, morphisms from A to B form a set.
Re: Getting Started with Category Theory
#34Earlier quoted context omitted.
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…
Also, morphisms from A to B form a set.
Only in locally-small categories. But yes, category theory often makes use of sets.
Re: Getting Started with Category Theory
#35Venting: 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.
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…
> I don't think I mentioned a monoid of endofunctors or flatMap a single time in the post
I think GP was just quoting a meme there. See also [0], where the meme is said [1] to originate.
[0]: https://james-iry.blogspot.com/2009/05/brief-incomplete-and-...
Re: Getting Started with Category Theory
#36Earlier quoted context omitted.
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…
> I don't think I mentioned a monoid of endofunctors or flatMap a single time in the post I think GP was just quoting a meme there. See also [0], where the meme is said [1] to originate. [0]: https://james-iry.blogspot.com/2009/05/brief-incomplete-and-... [1]: https://news.ycombinator.com/item?id=33438586
Oh yeah I'm well aware of the meme haha. I just wanted to show that I'm conscious of these things in my writing. My dedicated entry on monads (https://ryanbrewer.dev/wiki/monad) alludes to the meme in the first sentence :)