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Comment by ogogmad | Hacker News Reader

I think category theory is useful, but not yet in computing.

I suspect it's hard if you don't really need it for anything. Do you really need to understand universal properties and adjoint functors and the Yoneda lemma? If you don't, you'll struggle to learn what those are.

Interestingly, experience in functional programming can help you understand category theory, but not so much the other way round. For instance: Parametric polymorphism gives you intuition for natural transformations. And natural transformations are central to every application of category theory.

The convincing applications of category theory are very mathematical. You'll find them in algebraic topology, representation theory, algebraic geometry, and non-classical logic.

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It is useful here:

https://en.m.wikipedia.org/wiki/ZX-calculus

https://zxcalculus.com/

https://www.reddit.com/r/quantum/s/2NzsJaDYwm

Quantum computing is still a bit niche, no? And graphical notations already existed in physics and quantum computing, I believe. What does the category theory do here, except reformulate things that experts already understood, but in category theory language?

I think a convincing application of category theory should involve doing calculations with category theory concepts and definitions, which involve things like: commutative diagrams, representable functors, universal properties, adjoint functors. If a whole heap of these concepts doesn't get used - and you don't perform calculations with them - then you're just reformulating something using different terminology.

Thanks anyway for the link. Very pretty.

I wouldn't call "niche" something some big companies have been spending billions of dollars on.

In module theory, which is a bit close to ZX, category theory gets used in a big way to calculate things: See left/right exact functors, co/contravariant functors, derived functors, the hom-tensor adjunction, etc.

But!! I'm not seeing ANY of that in ZX.

would you say that 3 reformulates 1+1+1 in another language? because if yes, such reformulations shouldn’t be disregarded just because they’re “reformulations”. so we can say there are kinds of reformulations which make things incredibly easier, and category theory is one of them

Why do you think category theory makes it easier? That's one thing category theory does not do. How well do you understand the subject?

There is a category theory "school of thought" in many subjects, which believes without solid evidence that category theory must be immensely useful to their subject. But it's often just that: a school of thought. This is the situation of category theory in CS. My concern is that people aren't being honest about this.

you’re right, and I’m in that school of thought, but mainly for math. In essence, I know people who use it in their reaearch and I trust them (and there’s a lot of good people doing good stuff with CT—it’s ubiquitous, so I’m fine with trusting them). I have a beginner understanding of CT, actually I finally started studying it seriously a month ago, after being exposed to it sporadically for some time. I’m not claiming anything about CT in CS, but I’m optimistic about that it can have a more widespread positive effect in it

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