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It sounds like category theory likely has no direct impact on your life. So you can move on. But please do not let this bleed into a criticism of category theo

It sounds like category theory likely has no direct impact on your life. So you can move on. But please do not let this bleed into a criticism of category theory as used in mathematics. Category theory from the very beginning was developed to help manage the complexity of modern mathematical fields like algebraic topology. It was then famously used by Grothendieck in algebraic geometry where some of the basic notions (schemes) were defined in terms of category theoretic concepts (functors). It's been applied to many other fields, since, including yes computer science, and mainly for the same purpose: giving precise terminology to common patterns (monads functors etc) and giving us the right concepts to design new functional programming languages. As someone who is an expert on these topics I find some of the popular sentiments about programmers using category theory to be a bit silly, but I'll admit it's overall probably good for my field because it cultivates a lot of interest in students. It probably plays a similar role to pop science/math in other fields: not very deep but fun and can be a gateway to "the real thing". The popular perception of category theory is a bit bizarre to me though. It is a beautiful theory with many useful results. But you don't see the same excitement or resentment towards fields like order theory or abstract algebra, which are very closely related to, and just as abstract as, category theory and are used in similar ways.

travisjungroth 4y ago
Weirdly, I don’t love or hate category theory but I get very excited about order theory and abstract algebra in software. It feels lonely exploring them compared to other things, which is funny to say. It’s not fully explored or the new hotness.
- boris_m 3y ago
  Category theory is order theory and abstract algebra.
  - travisjungroth 3y ago
    It’s not like they’re synonyms. There’s overlap and maybe even category theory is a superset. But the experience of working with them is different.
dimitrios1 4y ago
What is your recommendation for learning? I've been recommended Bartosz Milewski enough times, and started to dive in. I am not interested in learning the totality of Category theory, just enough to be more effective in FP languages like Haskell.
- cfiggers 4y ago
  Have you been recommended his blog series/book only, or the playlists on YouTube as well? I really like his recorded lectures on YouTube and they cover similar ground in a similar order to the blog posts (from what I've read—I'm further into the YouTube series than I am his written material).
- deterministic 4y ago
  Category Theory will not make you more efficient in FP languages like Haskell. I studied it enough to realise that it doesn’t give me any insights or thinking tools I can actually use to write better software. However I highly recommend reading “Software Foundations”. It is almost guaranteed to make you better at writing software in any language. Including Haskell. That’s what happened to me.
- trenchgun 3y ago
  You don't need to learn category theory to be more effective in FP languages like Haskell. Category theory was used as inspiration for design of ML and Haskell, but it is not necessary for programming in them.
khazhoux 4y ago
> It sounds like category theory likely has no direct impact on your life. So you can move on. Very dismissive statement that misses the person's point. > It is a beautiful theory with many useful results. But what are those results? Besides Yoneda, are there insightful, surprising, delightful results? I personally gave up on my CT study after seeing that it was just chapter after chapter of definitions and nothing else. I always compare it to abstract algebra. AA can be studied without any connection whatsoever to the physical world or even to numbers -- as "abstract" as math can get. And yet from the first chapter you are hit with surprising theorems, and they continue non-stop, challenging your brain at every turn. I fail to see this in CT.
- Twisol 4y ago
  > Very dismissive statement that misses the person's point. I read it as acknowledging that you shouldn't feel like you have to spend time on things that provide you no value. That seems to directly acknowledge the point I took from the earlier comment, which is that they keep spending time on it and coming away with no idea what they even should be getting from it, much less getting anything specifically. (I like category theory, but it's a reasonable reaction for most people. I'd love for more people to engage with it on its merits, but also, people have finite time and may rather spend it on things they derive joy from.)
- jiggawatts 4y ago
  This is what turned me off also. Category theory is all promises of potential benefits, but none seem to have materialised. The closest example to something useful I’ve seen is a CT-based explanation for why Automatic Differentiation is formulated the way it is. However, AD was invented before CT, and the explanation didn’t add any value that I could see. It didn’t result in a “better” AD, it simply attached esoteric labels to existing things.
- sleepyams 4y ago
  One interesting result which you may find interesting: https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem I also highly recommend this survey paper by John Baez and Mike Stay: https://math.ucr.edu/home/baez/rosetta.pdf https://math.ucr.edu/home/baez/rosetta.pdf There are plenty of interesting results in category theory, in fact your comparison to abstract algebra is apt. There is only so much you can say about an arbitrary group in general, or an arbitrary topological space, just like there is only so much you can say about an arbitrary category.
fatneckbeard 4y ago
category theory has a very hard "k" sound at the front and a g sound which is also hard, which makes people react more strongly to the name than order theory or abstract algebra.
HervalFreire 4y ago
It's because the lack of practical applications. People can make broken abstractions without knowledge of the fundamentals like compositions or functors and still get their shit to work. That matters more to engineers then true understanding. So a lot of engineers end up trying to understand it and when they fail they easily move on to other things because it's not required knowledge for their job.

travisjungroth 4y ago

Weirdly, I don’t love or hate category theory but I get very excited about order theory and abstract algebra in software. It feels lonely exploring them compared to other things, which is funny to say. It’s not fully explored or the new hotness.

boris_m 3y ago
Category theory is order theory and abstract algebra.
- travisjungroth 3y ago
  It’s not like they’re synonyms. There’s overlap and maybe even category theory is a superset. But the experience of working with them is different.

dimitrios1 4y ago

What is your recommendation for learning? I've been recommended Bartosz Milewski enough times, and started to dive in. I am not interested in learning the totality of Category theory, just enough to be more effective in FP languages like Haskell.

cfiggers 4y ago
Have you been recommended his blog series/book only, or the playlists on YouTube as well? I really like his recorded lectures on YouTube and they cover similar ground in a similar order to the blog posts (from what I've read—I'm further into the YouTube series than I am his written material).
deterministic 4y ago
Category Theory will not make you more efficient in FP languages like Haskell. I studied it enough to realise that it doesn’t give me any insights or thinking tools I can actually use to write better software. However I highly recommend reading “Software Foundations”. It is almost guaranteed to make you better at writing software in any language. Including Haskell. That’s what happened to me.
trenchgun 3y ago
You don't need to learn category theory to be more effective in FP languages like Haskell. Category theory was used as inspiration for design of ML and Haskell, but it is not necessary for programming in them.

khazhoux 4y ago

> It sounds like category theory likely has no direct impact on your life. So you can move on. Very dismissive statement that misses the person's point. > It is a beautiful theory with many useful results. But what are those results? Besides Yoneda, are there insightful, surprising, delightful results? I personally gave up on my CT study after seeing that it was just chapter after chapter of definitions and nothing else. I always compare it to abstract algebra. AA can be studied without any connection whatsoever to the physical world or even to numbers -- as "abstract" as math can get. And yet from the first chapter you are hit with surprising theorems, and they continue non-stop, challenging your brain at every turn. I fail to see this in CT.

Twisol 4y ago
> Very dismissive statement that misses the person's point. I read it as acknowledging that you shouldn't feel like you have to spend time on things that provide you no value. That seems to directly acknowledge the point I took from the earlier comment, which is that they keep spending time on it and coming away with no idea what they even should be getting from it, much less getting anything specifically. (I like category theory, but it's a reasonable reaction for most people. I'd love for more people to engage with it on its merits, but also, people have finite time and may rather spend it on things they derive joy from.)
jiggawatts 4y ago
This is what turned me off also. Category theory is all promises of potential benefits, but none seem to have materialised. The closest example to something useful I’ve seen is a CT-based explanation for why Automatic Differentiation is formulated the way it is. However, AD was invented before CT, and the explanation didn’t add any value that I could see. It didn’t result in a “better” AD, it simply attached esoteric labels to existing things.
sleepyams 4y ago
One interesting result which you may find interesting: https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem I also highly recommend this survey paper by John Baez and Mike Stay: https://math.ucr.edu/home/baez/rosetta.pdf https://math.ucr.edu/home/baez/rosetta.pdf There are plenty of interesting results in category theory, in fact your comparison to abstract algebra is apt. There is only so much you can say about an arbitrary group in general, or an arbitrary topological space, just like there is only so much you can say about an arbitrary category.

fatneckbeard 4y ago

category theory has a very hard "k" sound at the front and a g sound which is also hard, which makes people react more strongly to the name than order theory or abstract algebra.

HervalFreire 4y ago

It's because the lack of practical applications. People can make broken abstractions without knowledge of the fundamentals like compositions or functors and still get their shit to work. That matters more to engineers then true understanding. So a lot of engineers end up trying to understand it and when they fail they easily move on to other things because it's not required knowledge for their job.