6 ms·

I've gone down this rabbit hole a few times, and I always return pissed off and a dozen hours poorer. Maybe someday I'll get it.

by jmugan 2y ago

analog31 2y ago
I was a college math major. Category theory wasn't one of the offered courses at my college, so I didn't study it specifically. But I didn't get through any of my math classes without working the problems and proofs, and without having a teacher to help guide me through the material. It can't be read like a book. At least that's my experience. And as I get older, being interested in the topic helps more and more.
- epgui 2y ago
  This is the only right attitude. Thank you for saying it.
- kqr 2y ago
  As a counterexample, I have self-studied queuing theory, extreme value analysis, combinatorics, generalised linear regression, etc. and had no problem with it. Category theory I just can't get through. Either it does not fit with my brain or I fail to see the practical implications, but something makes it not stick. (Curiously, differential equations (beyond the basics) are in a similar spot for me, even though they are obviously immediately practical in a huge number of areas!)
  - l__l 2y ago
    This oughtn't be super surprising, even the DE comment at the end - people do just have bits of maths they gel with more than others! Even so, CT is not easy to motivate without a lot of experience in a few specific areas of maths - it's definitely a very "meta" subject (even though a lot of these blogs pretend it's super applicable to everyday engineering) and is a very different lens from the maths taught up to that point.
ferfumarma 2y ago
That's such an amazing description of my experience as well. I find the topic inscrutable.
puzzledobserver 2y ago
I share this experience. Perhaps another way of asking the question is: Are there any results, either about individual programs or in PL theory as a whole, that were made simpler / clarified / generalized because of category theoretic insights?
- throwaway81523 2y ago
  Sure, Haskell's type system (and type systems in general) are informed by categories: https://en.wikibooks.org/wiki/Haskell/Category_theory https://en.wikibooks.org/wiki/Haskell/Category_theory This article is also nice: https://www.haskellforall.com/2012/08/the-category-design-pattern.html https://www.haskellforall.com/2012/08/the-category-design-pa... It explins how Haskell's monad laws follow directly from how categories work.
  - Koshkin 2y ago
    Indeed; Haskell is purely functional, and Category Theory is nothing but a purely functional language of mathematics.
    - epgui 2y ago
      Category theory is not “purely functional”, it is about morphisms, and morphisms are more abstract than functions. Category theory envelopes relations as well, as well as arguably anything else that can be formalized.
  - bmitc 2y ago
    But what does that buy you?
  - BoiledCabbage 2y ago
    Yes, but it's much, muvh faster and more productivr to just learn Haskell's type system (mainly Functors, Monads and Applicatives) as 3 individual "design patterns" than it is to figure it how you can even begin to apply the Yoneda Lemma to whatever programing problem you have in front of you. Category Theory has birthed some useful abstraction, but you don't really need any of CT to learn and use the abstractions. The basics of Abstract Algebra on the otherhand are absolutely worth the bit of time it takes to learn them. Groups, semi-groups, rings, fields, monoids - distribution, identity, zeros, associstivity, communitavity are pretty trivia to learn - most people already know the underlying concepts and they pop up all the time in programing. Monoids are incredibly useful - most people already know them, and intuitively use them, but it's helpful naming and understanding the pattern. Category Therory just doesn't have the same return on investment for software development.
sega_sai 2y ago
As a math course, I felt category theory was interesting as a way of unifying ideas across different areas of mathematics. But I never quite seen a value of it for programming (but maybe it's just me)
- ants_everywhere 2y ago
  It's IMO the right setting to talk about logic. That's one of the reasons it unifies ideas in math. Computer science is mostly an application of logic which is why category theory has become a useful tool in theoretical computer science.
  - CarpaDorada 2y ago
    If you're talking about toposes, many logics do not correspond to them. It's the other way around: many category theorists/logicians needed jobs and found computer jobs and hence the category theoretic perspective in CS.
    - ants_everywhere 2y ago
      You don't know what you're talking about. Applications of category theory to computer science predate the first US computer science department. There weren't any computer science jobs to speak of. Categorical logic is larger than elementary topoi. I would wager that you can't name a logic not expressible in category theory.
      - CarpaDorada 2y ago
        >Applications of category theory to computer science predate the first US computer science department. This doesn't sound plausible: according to Wikipedia, Eilenberg and Mac Lane introduced concepts of CT in 1942, and CT was originally used mainly homological algebra, with applications in logic/semantics later. Certainly CT was given credence by Grothendieck and Serre, working on (and solving) Weil's conjecture in the 50s and 60s. Lawvere's 1963 thesis predated categorical logic (according to his own words, <http://www.tac.mta.ca/tac/reprints/articles/5/tr5abs.html http://www.tac.mta.ca/tac/reprints/articles/5/tr5abs.html> p. 12, "but the method here, and indeed in the whole ensuing categorical logic, is to exploit the uniqueness by using adjointness itself as an axiom"). The first computer science department in the US was started in 1962 in Purdue University. Meanwhile for contrast the proofs of Church and Turing were published in 1936. >I would wager that you can't name a logic not expressible in category theory. I prefaced my statement with an "if"; you're not talking about toposes apparently. The interpretability of one theory in another is a concern of logicians and I'm not familiar with any restrictions on category theory, indeed it can be used for logics. I do not know topos theory but I was basing my statement on what I heard Colin McLarty say in an interview of his <https://www.youtube.com/watch?v=81sPQGIWEfM https://www.youtube.com/watch?v=81sPQGIWEfM>, can't give timestamp; he definitely named logics that cannot be expressed by the topos of a space. I feel that you've used two straw men: 1) specifically naming US 2) ignoring my "if topos" and saying "expressible in CT".
agnishom 2y ago
I feel that the main thing that can change it is having a plethora of examples. Also, I think math has much better examples than programming.
Ericson2314 2y ago
It's hard to write something that is both accessible and well-motivated. The best uses of category theory is when the morphisms are far more exotic than "regular functions". E.g. it would be nice to describe a circuit of live queries (like https://materialize.com/ https://materialize.com/ stuff) with proper caching, joins, etc. Figuring this out is a bit of an open problem. Haskell's standard library's Monad and stuff are watered down to the point that they are barely category theory, but they are also quite useful and would not have been readily invented without category theory. See even if you have no taste for "abstract nonsense", maybe you can still accept the fact that its left a trail of more accessible "semi-abstract semi-nonsense" in its wake. This stuff takes time. If it's not your cup of tea, no need to make yourself an early adopter. See also things like Lean where fancy type systems are finally reaching "regular non-CS" mathematicians with great success.
- Ericson2314 2y ago
  On the pure math side, Locales (https://ncatlab.org/nlab/show/locale https://ncatlab.org/nlab/show/locale) are so much more beautiful an axiomatization scheme than regular topological spaces, even if one is just doing regular classical rather than constructive math. We would have not discovered them except for category theory.
  - Ericson2314 2y ago
    I would also check out https://en.wikipedia.org/wiki/Algebraic_logic#Algebras_as_models_of_logics https://en.wikipedia.org/wiki/Algebraic_logic#Algebras_as_mo... The basic (pre-category theory) idea is instead of making up new weird math just for logical purposes, start thinking more abstractly and using "regular" math concepts. The section says "models" but it should work for syntax too not just semantics (the syntax is the "initial" semantics). Category theory takes all that order/lattice stuff and generalizes it in the same way programming generalizes logic ("whether" true/false to "which" inhabitant of a type). So it is definitely useful for people trying to explore the space of programming language designs. The reason category theory might be useful to "regular programmers" not programming language designers, basically boils down to the belief that programming and language design are not so different after all. I can't really argue that explicitly, but think "where does designing a library interface end, and designing a domain-specific language being?". That's the basic idea.
liontwist 2y ago
Category theory is a great tool for thinking about programming language design (especially types in functional programming). In some sense that translates to better programming, but there’s a lot more math topics that are likely to be directly applicable day to day. Do you know how to evaluate a polynomial efficiently? Fit a curve to points? Solve a linear system? What the Fourier transform is for? If no, hold off on the categories.
- prakashrj 2y ago
  Is Bézier curves not enough to fit curve to points? Just checking as I am very curious about this problem.
  - epgui 2y ago
    The answer is obviously no, but I’m not the right person to explain (biochemist). For some reason you were downvoted down to oblivion, and I think that was unfair.
  - roenxi 2y ago
    Bézier curves parameterise a curve with points. When people talk about "fitting a curve" I would expect they mean fitting a model rather than that the curve is fully determined by the points. Typically people fit linear or low-order polynomials, it'd be a weird day where someone wanted to use a Bézier for their model - those curves weren't designed for being statistically tractable or interesting. See https://en.wikipedia.org/wiki/Curve_fitting https://en.wikipedia.org/wiki/Curve_fitting
  - HappMacDonald 2y ago
    To expand upon roenxi's answer: Bezier curves are an example of creating a cubic (degree 3) parametric polynomial curve by using four points to describe where you want it to go. Curve fitting is about starting with a cloud of points, and trying to decide how to draw a polynomial (of whatever degree you want) that does a good job of describing the trend line of those points. Then you can use that polynomial to approximately interpolate points between the samples, or extrapolate points beyond the samples as an example.
j2kun 2y ago
The main problem is that category theorists keep writing stuff claiming that, if only you get through the math, you'll eventually be able to apply the category theory to typical everyday programming problems. And by the time they get to the Yoneda lemma or whatever, they've forgotten they're supposed to show some applications. All they show is how to express category theoretical concepts in a program. And it is mostly because the demonstrated applications are few (I have spent a lot of time looking and have found little convincing evidence). Having learned the subject myself, I'm not convinced it's useful for programmers. Hell, it's not even useful for all areas of mathematics, and that is its raison d'etre.
- endgame 2y ago
  This two-part keynote might give you a good flavour: * https://www.youtube.com/watch?v=4WMfKhKKVN4 https://www.youtube.com/watch?v=4WMfKhKKVN4 * https://www.youtube.com/watch?v=zooYfk5-yPY https://www.youtube.com/watch?v=zooYfk5-yPY If you can stand up a Cartesian-closed category, it is a model of a lambda calculus. So you can make a compiler plugin that takes lambda terms (a large subset of Haskell) and compiles it into all sorts of exotic settings (dataflow diagrams, derivatives of the function, ...) KittyHawk used it to compile Haskell to C in https://github.com/sellout/compiling-anything-to-categories https://github.com/sellout/compiling-anything-to-categories and someone talks about their work here: https://www.youtube.com/watch?v=VUBj8NW7uMA https://www.youtube.com/watch?v=VUBj8NW7uMA
- wenc 2y ago
  I often go back to this post by John D Cook. Quote below: https://www.johndcook.com/blog/applied-category-theory/ https://www.johndcook.com/blog/applied-category-theory/ Category theory can be very useful, but you don’t use it the same way you use other kinds of math. You can apply optimization theory, for example, by noticing that a problem has a certain form, and therefore a certain algorithm will converge to a solution. Applications of category theory are usually more subtle. You’re not likely to quote some theorem from category theory that finishes off a problem the way the selecting an optimization algorithm does. I had been skeptical of applications of category theory, and to some extent I still am. Many reported applications of category theory aren’t that applied, and they’re not so much applications as post hoc glosses. At the same time, I’ve seen real applications of categories, such as the design of LINQ mentioned above. I’ve been a part of projects where we used category theory to guide mathematical modeling and software development. Category theory can spot inconsistencies and errors similar to the way dimensional analysis does in engineering, or type checking in software development. It can help you ask the right questions. It can guide you to including the right things, and leaving the right things out. Category theory in LINQ https://queue.acm.org/detail.cfm?id=2024658 https://queue.acm.org/detail.cfm?id=2024658
UltraSane 2y ago
Exactly. While Category Theory is interesting and the way it can abstract things like the Diagonal argument is very elegant every time I try to learn it I end up feeling I would have been better off learning almost anything else.
weitendorf 2y ago
Even though I went pretty deep in math/cs in college and worked as a SWE for five years, I never really "got" the connection between category theory and actual practical software problems until I started working on a new project with complex uses of types and functional programming. IMO most programmers are not working on projects like that where category theory is even relevant. And for me even though it was relevant, other than being to identify something by its category theory vocab term, it wasn't really helpful to actually know category theory. Also, you probably should study axiomatic set theory and abstract algebra before taking on category theory and even in materials like this where they try to bring you up to speed on them, you'll not have had the exposure time to those subjects (or perhaps higher math in general) to understand things well. You'll also skip over stuff like https://en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n#Group_axioms https://en.wikipedia.org/wiki/Multiplicative_group_of_intege... which aren't category theory per se but prime your brain into thinking about the properties of sets, relations within/between sets, and repeatable "structures" across sets. The other problem I ran into is that most programming languages do not have sophisticated enough type/functional systems to be able to properly implement a lot of fancy stuff where category theory is relevant. For example, even though typescript had all the information necessary to know that class A is abstract and B extends it, or that class C is templatized by types subject to some constraint, it can't at compile time implement a lot of checks that it technically should to handle Functors (https://en.wikipedia.org/wiki/Functor_(functional_programming) https://en.wikipedia.org/wiki/Functor_(functional_programmin...). The languages that do handle these things properly are typically lacking in other ways that made them not worth it (for me) to use - it was better to handle the problem inelegantly in the less sophisticated language.
deleted 2y ago
[deleted]
deterministic 2y ago
There is nothing to “get” that is worth getting unless you are interested in pure math. As a programmer we already know how to compose types/functions/applications/systems. No need for category theory to understand how to do that.

I've gone down this rabbit hole a few times, and I always return pissed off and a dozen hours poorer. Maybe someday I'll get it.

by jmugan 2y ago

I've gone down this rabbit hole a few times, and I always return pissed off and a dozen hours poorer. Maybe someday I'll get it.

analog31 2y ago

I was a college math major. Category theory wasn't one of the offered courses at my college, so I didn't study it specifically. But I didn't get through any of my math classes without working the problems and proofs, and without having a teacher to help guide me through the material. It can't be read like a book. At least that's my experience. And as I get older, being interested in the topic helps more and more.

epgui 2y ago
This is the only right attitude. Thank you for saying it.
kqr 2y ago
As a counterexample, I have self-studied queuing theory, extreme value analysis, combinatorics, generalised linear regression, etc. and had no problem with it. Category theory I just can't get through. Either it does not fit with my brain or I fail to see the practical implications, but something makes it not stick. (Curiously, differential equations (beyond the basics) are in a similar spot for me, even though they are obviously immediately practical in a huge number of areas!)
- l__l 2y ago
  This oughtn't be super surprising, even the DE comment at the end - people do just have bits of maths they gel with more than others! Even so, CT is not easy to motivate without a lot of experience in a few specific areas of maths - it's definitely a very "meta" subject (even though a lot of these blogs pretend it's super applicable to everyday engineering) and is a very different lens from the maths taught up to that point.

ferfumarma 2y ago

That's such an amazing description of my experience as well. I find the topic inscrutable.

puzzledobserver 2y ago

I share this experience. Perhaps another way of asking the question is: Are there any results, either about individual programs or in PL theory as a whole, that were made simpler / clarified / generalized because of category theoretic insights?

throwaway81523 2y ago
Sure, Haskell's type system (and type systems in general) are informed by categories: https://en.wikibooks.org/wiki/Haskell/Category_theory https://en.wikibooks.org/wiki/Haskell/Category_theory This article is also nice: https://www.haskellforall.com/2012/08/the-category-design-pattern.html https://www.haskellforall.com/2012/08/the-category-design-pa... It explins how Haskell's monad laws follow directly from how categories work.
- Koshkin 2y ago
  Indeed; Haskell is purely functional, and Category Theory is nothing but a purely functional language of mathematics.
  - epgui 2y ago
    Category theory is not “purely functional”, it is about morphisms, and morphisms are more abstract than functions. Category theory envelopes relations as well, as well as arguably anything else that can be formalized.
- bmitc 2y ago
  But what does that buy you?
- BoiledCabbage 2y ago
  Yes, but it's much, muvh faster and more productivr to just learn Haskell's type system (mainly Functors, Monads and Applicatives) as 3 individual "design patterns" than it is to figure it how you can even begin to apply the Yoneda Lemma to whatever programing problem you have in front of you. Category Theory has birthed some useful abstraction, but you don't really need any of CT to learn and use the abstractions. The basics of Abstract Algebra on the otherhand are absolutely worth the bit of time it takes to learn them. Groups, semi-groups, rings, fields, monoids - distribution, identity, zeros, associstivity, communitavity are pretty trivia to learn - most people already know the underlying concepts and they pop up all the time in programing. Monoids are incredibly useful - most people already know them, and intuitively use them, but it's helpful naming and understanding the pattern. Category Therory just doesn't have the same return on investment for software development.

sega_sai 2y ago

As a math course, I felt category theory was interesting as a way of unifying ideas across different areas of mathematics. But I never quite seen a value of it for programming (but maybe it's just me)

ants_everywhere 2y ago
It's IMO the right setting to talk about logic. That's one of the reasons it unifies ideas in math. Computer science is mostly an application of logic which is why category theory has become a useful tool in theoretical computer science.
- CarpaDorada 2y ago
  If you're talking about toposes, many logics do not correspond to them. It's the other way around: many category theorists/logicians needed jobs and found computer jobs and hence the category theoretic perspective in CS.
  - ants_everywhere 2y ago
    You don't know what you're talking about. Applications of category theory to computer science predate the first US computer science department. There weren't any computer science jobs to speak of. Categorical logic is larger than elementary topoi. I would wager that you can't name a logic not expressible in category theory.
    - CarpaDorada 2y ago
      >Applications of category theory to computer science predate the first US computer science department. This doesn't sound plausible: according to Wikipedia, Eilenberg and Mac Lane introduced concepts of CT in 1942, and CT was originally used mainly homological algebra, with applications in logic/semantics later. Certainly CT was given credence by Grothendieck and Serre, working on (and solving) Weil's conjecture in the 50s and 60s. Lawvere's 1963 thesis predated categorical logic (according to his own words, <http://www.tac.mta.ca/tac/reprints/articles/5/tr5abs.html http://www.tac.mta.ca/tac/reprints/articles/5/tr5abs.html> p. 12, "but the method here, and indeed in the whole ensuing categorical logic, is to exploit the uniqueness by using adjointness itself as an axiom"). The first computer science department in the US was started in 1962 in Purdue University. Meanwhile for contrast the proofs of Church and Turing were published in 1936. >I would wager that you can't name a logic not expressible in category theory. I prefaced my statement with an "if"; you're not talking about toposes apparently. The interpretability of one theory in another is a concern of logicians and I'm not familiar with any restrictions on category theory, indeed it can be used for logics. I do not know topos theory but I was basing my statement on what I heard Colin McLarty say in an interview of his <https://www.youtube.com/watch?v=81sPQGIWEfM https://www.youtube.com/watch?v=81sPQGIWEfM>, can't give timestamp; he definitely named logics that cannot be expressed by the topos of a space. I feel that you've used two straw men: 1) specifically naming US 2) ignoring my "if topos" and saying "expressible in CT".

agnishom 2y ago

I feel that the main thing that can change it is having a plethora of examples. Also, I think math has much better examples than programming.

Ericson2314 2y ago

It's hard to write something that is both accessible and well-motivated. The best uses of category theory is when the morphisms are far more exotic than "regular functions". E.g. it would be nice to describe a circuit of live queries (like https://materialize.com/ https://materialize.com/ stuff) with proper caching, joins, etc. Figuring this out is a bit of an open problem. Haskell's standard library's Monad and stuff are watered down to the point that they are barely category theory, but they are also quite useful and would not have been readily invented without category theory. See even if you have no taste for "abstract nonsense", maybe you can still accept the fact that its left a trail of more accessible "semi-abstract semi-nonsense" in its wake. This stuff takes time. If it's not your cup of tea, no need to make yourself an early adopter. See also things like Lean where fancy type systems are finally reaching "regular non-CS" mathematicians with great success.

Ericson2314 2y ago
On the pure math side, Locales (https://ncatlab.org/nlab/show/locale https://ncatlab.org/nlab/show/locale) are so much more beautiful an axiomatization scheme than regular topological spaces, even if one is just doing regular classical rather than constructive math. We would have not discovered them except for category theory.
- Ericson2314 2y ago
  I would also check out https://en.wikipedia.org/wiki/Algebraic_logic#Algebras_as_models_of_logics https://en.wikipedia.org/wiki/Algebraic_logic#Algebras_as_mo... The basic (pre-category theory) idea is instead of making up new weird math just for logical purposes, start thinking more abstractly and using "regular" math concepts. The section says "models" but it should work for syntax too not just semantics (the syntax is the "initial" semantics). Category theory takes all that order/lattice stuff and generalizes it in the same way programming generalizes logic ("whether" true/false to "which" inhabitant of a type). So it is definitely useful for people trying to explore the space of programming language designs. The reason category theory might be useful to "regular programmers" not programming language designers, basically boils down to the belief that programming and language design are not so different after all. I can't really argue that explicitly, but think "where does designing a library interface end, and designing a domain-specific language being?". That's the basic idea.

liontwist 2y ago

Category theory is a great tool for thinking about programming language design (especially types in functional programming). In some sense that translates to better programming, but there’s a lot more math topics that are likely to be directly applicable day to day. Do you know how to evaluate a polynomial efficiently? Fit a curve to points? Solve a linear system? What the Fourier transform is for? If no, hold off on the categories.

prakashrj 2y ago
Is Bézier curves not enough to fit curve to points? Just checking as I am very curious about this problem.
- epgui 2y ago
  The answer is obviously no, but I’m not the right person to explain (biochemist). For some reason you were downvoted down to oblivion, and I think that was unfair.
- roenxi 2y ago
  Bézier curves parameterise a curve with points. When people talk about "fitting a curve" I would expect they mean fitting a model rather than that the curve is fully determined by the points. Typically people fit linear or low-order polynomials, it'd be a weird day where someone wanted to use a Bézier for their model - those curves weren't designed for being statistically tractable or interesting. See https://en.wikipedia.org/wiki/Curve_fitting https://en.wikipedia.org/wiki/Curve_fitting
- HappMacDonald 2y ago
  To expand upon roenxi's answer: Bezier curves are an example of creating a cubic (degree 3) parametric polynomial curve by using four points to describe where you want it to go. Curve fitting is about starting with a cloud of points, and trying to decide how to draw a polynomial (of whatever degree you want) that does a good job of describing the trend line of those points. Then you can use that polynomial to approximately interpolate points between the samples, or extrapolate points beyond the samples as an example.

j2kun 2y ago

The main problem is that category theorists keep writing stuff claiming that, if only you get through the math, you'll eventually be able to apply the category theory to typical everyday programming problems. And by the time they get to the Yoneda lemma or whatever, they've forgotten they're supposed to show some applications. All they show is how to express category theoretical concepts in a program. And it is mostly because the demonstrated applications are few (I have spent a lot of time looking and have found little convincing evidence). Having learned the subject myself, I'm not convinced it's useful for programmers. Hell, it's not even useful for all areas of mathematics, and that is its raison d'etre.

endgame 2y ago
This two-part keynote might give you a good flavour: * https://www.youtube.com/watch?v=4WMfKhKKVN4 https://www.youtube.com/watch?v=4WMfKhKKVN4 * https://www.youtube.com/watch?v=zooYfk5-yPY https://www.youtube.com/watch?v=zooYfk5-yPY If you can stand up a Cartesian-closed category, it is a model of a lambda calculus. So you can make a compiler plugin that takes lambda terms (a large subset of Haskell) and compiles it into all sorts of exotic settings (dataflow diagrams, derivatives of the function, ...) KittyHawk used it to compile Haskell to C in https://github.com/sellout/compiling-anything-to-categories https://github.com/sellout/compiling-anything-to-categories and someone talks about their work here: https://www.youtube.com/watch?v=VUBj8NW7uMA https://www.youtube.com/watch?v=VUBj8NW7uMA
wenc 2y ago
I often go back to this post by John D Cook. Quote below: https://www.johndcook.com/blog/applied-category-theory/ https://www.johndcook.com/blog/applied-category-theory/ Category theory can be very useful, but you don’t use it the same way you use other kinds of math. You can apply optimization theory, for example, by noticing that a problem has a certain form, and therefore a certain algorithm will converge to a solution. Applications of category theory are usually more subtle. You’re not likely to quote some theorem from category theory that finishes off a problem the way the selecting an optimization algorithm does. I had been skeptical of applications of category theory, and to some extent I still am. Many reported applications of category theory aren’t that applied, and they’re not so much applications as post hoc glosses. At the same time, I’ve seen real applications of categories, such as the design of LINQ mentioned above. I’ve been a part of projects where we used category theory to guide mathematical modeling and software development. Category theory can spot inconsistencies and errors similar to the way dimensional analysis does in engineering, or type checking in software development. It can help you ask the right questions. It can guide you to including the right things, and leaving the right things out. Category theory in LINQ https://queue.acm.org/detail.cfm?id=2024658 https://queue.acm.org/detail.cfm?id=2024658

UltraSane 2y ago

Exactly. While Category Theory is interesting and the way it can abstract things like the Diagonal argument is very elegant every time I try to learn it I end up feeling I would have been better off learning almost anything else.

weitendorf 2y ago

Even though I went pretty deep in math/cs in college and worked as a SWE for five years, I never really "got" the connection between category theory and actual practical software problems until I started working on a new project with complex uses of types and functional programming. IMO most programmers are not working on projects like that where category theory is even relevant. And for me even though it was relevant, other than being to identify something by its category theory vocab term, it wasn't really helpful to actually know category theory. Also, you probably should study axiomatic set theory and abstract algebra before taking on category theory and even in materials like this where they try to bring you up to speed on them, you'll not have had the exposure time to those subjects (or perhaps higher math in general) to understand things well. You'll also skip over stuff like https://en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n#Group_axioms https://en.wikipedia.org/wiki/Multiplicative_group_of_intege... which aren't category theory per se but prime your brain into thinking about the properties of sets, relations within/between sets, and repeatable "structures" across sets. The other problem I ran into is that most programming languages do not have sophisticated enough type/functional systems to be able to properly implement a lot of fancy stuff where category theory is relevant. For example, even though typescript had all the information necessary to know that class A is abstract and B extends it, or that class C is templatized by types subject to some constraint, it can't at compile time implement a lot of checks that it technically should to handle Functors (https://en.wikipedia.org/wiki/Functor_(functional_programming) https://en.wikipedia.org/wiki/Functor_(functional_programmin...). The languages that do handle these things properly are typically lacking in other ways that made them not worth it (for me) to use - it was better to handle the problem inelegantly in the less sophisticated language.

deleted 2y ago

[deleted]

deterministic 2y ago

There is nothing to “get” that is worth getting unless you are interested in pure math. As a programmer we already know how to compose types/functions/applications/systems. No need for category theory to understand how to do that.