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Comment by user-the-name | Hacker News Reader

Maybe for a value of "has applications" that doesn't necessarily include anyone actually applying it.

As a generalisation, I don't think anyone by people into category theory actually cares about or applies category theory.

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I was about to agree, but then I realized it's not immediate that Set Theory has practical applications either.

However, Set Theory is essential to build mathematics.

Taking points from: https://mathoverflow.net/questions/10334/what-practical-appl...

Analysis, Number theory, most of modern mathematics rely on set theory, even computer science in the definition of Turing machines and dealing with infinities there are implicit axioms of set theory.

Likewise, perhaps category theory may not yield immediate applications, but it can be useful as a language (like a programming language, natural or mathematical) to express mathematical ideas, and to build mathematical systems and foundations.

I'm not sure how closely it relates to Category theory, but Homotopy Type Theory has yielded the fantastic Univalent foundations, a seemingly more modern and simple foundation for mathematics. This line of work also yielded a solid basis for Proof assistants.

I don't know enough about functional programming to comment...

It CAN be useful, you say, but is it actually? Is anyone using it? Beyond a handful of exceptions, I would say no.

Set theory actually IS used as the foundation of other work. But category theory isn't, as far as I know.

Shouldn't it be easier to explain a general concept than a specific one? The only reason I can think of why this isn't happening is because you need to learn a large amount of information before any of the category theory stuff can be applied in real life. But honestly speaking, that can't be true because languages like Haskell exist and isn't that on the whole programming using category theory? (I am be completely wrong about this).

OTOH it can also be just a pedagogy issue. That nobody has figured out how to condense it into an undergraduate level so working engineers can grasp basics.

> languages like Haskell exist and isn't that on the whole programming using category theory?

It's not. However claims like that get thrown around a fair amount so the confusion is understandable.

That said, some important Haskell abstractions were designed using category theory. So it can be helpful to know some of the lingo (since it will show up in abstraction names and descriptions).

And if you're looking to design the next breakthrough Haskell abstraction it might be extremely helpful, but that's not 99% of programmers. However, the people who can do that are super cool, eg https://www.staff.ncl.ac.uk/andrey.mokhov/selective-functors....

> Shouldn't it be easier to explain a general concept than a specific one?

It depends. Are you an abstract or a concrete thinker? That's one axis of one the standard ways of describing personalities. (Yeah, I know, psychology... but it does seem to describe an actual difference in how people think.)

Now, people with one kind of personality can learn to think in the other way, but they won't find it as easy.

I'm applying it.

Getting to feel a bit sour about how I get downvoted for talking about hacking on Hacker News and upvoted when I write about politics rubbish.

Anyone wanna talk about my applied category theory paper at the fall AAAI symposium? https://arxiv.org/abs/2011.11063

It is not that the HN community is diminishing your credentials in applied category theory or in any other fields, more so the inherited snarkiness in your short comment provides no one a favor and surely doesn't add any value to the discussion.

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