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If anyone is looking to get into Category Theory as a programmer, I would recommend giving Bartosz Milewski's Category Theory for Programmers a shot[0]. Quite g

If anyone is looking to get into Category Theory as a programmer, I would recommend giving Bartosz Milewski's Category Theory for Programmers a shot[0]. Quite good, and you can read it as a blog post on that site or get the ebook/physical book to leaf through. For a more theoretical/less applied approach that's still relevant to computer science/programming, check out Benjamin Pierce's Basic Category Theory for Computer Scientists[1]. It's a very good introduction to the parts of Category Theory that are useful for [theoretical] CS, and delves into semantics of programming languages, types, and concurrency a fair amount. [0] https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/ https://bartoszmilewski.com/2014/10/28/category-theory-for-p... [1] https://mitpress.mit.edu/books/basic-category-theory-computer-scientists https://mitpress.mit.edu/books/basic-category-theory-compute...

mathgenius 8y ago
For a first introduction to category theory, from the masters thereof, I would highly recommend the book by Lawvere and Shanual "Conceptual Mathematics: A First Introduction to Categories". It almost doesn't look like a mathematics book, but believe me, these guys know what they are talking about. They distill some very high-brow ideas down to something us mere mortals can grok.
armitron 8y ago
I watched a little less than the first half of Bartosz video lectures and I still don't see what the fuss is about from the perspective of an engineer that is looking to get better at engineering. I can't find something there that would help me implement better systems. What I do see is an attempt to shoehorn a mathematical model onto certain programming paradigms in order to be able to say that these paradigms are instances of the model. In short, a lot of talk about abstractions (or "abstract nonsense") but very little of engineering significance. Please let me know if I'm missing something by listing concrete examples of how category theory can help me with engineering problems. Disclaimer: I'm not a mathematician.
- eindiran 8y ago
  I think that the most plausible way that Category Theory is going to improve your life as an engineer is that it will sneak into the way your tools are designed. You don't personally need to know about the Yoneda lemma to benefit from a better designed programming language whose type system was informed by algebras of types, allowing it to leverage exhaustive pattern matching. With that said, learning about techniques used in functional programming that have their origin in category theory (maps, folds, algebraic data types, monads, monoids, etc) can allow you to think about how to solve problems (even in non-functional languages) in ways that can be more "natural" to the problem, in that the abstractions used resemble the problem description more closely. That ability to decompose difficult problems in new ways can definitely make you a better engineer.
- gizmo686 8y ago
  Catagory theory is a fantastic tool for understanding programming language design. As a user, you don't need to understand catagory theory, but you benifit when the language designers do. As a software engineer, category theory is sometimes useful in API design as well; although more often than not, your API is constrained by the existing ecosystem too much for category theory to give you much benefit (and, frankly, simple enough that category theory is overkill).
- maxander 8y ago
  A very abstract idea of its relevance, insofar as I understand it; engineering generally boils down to putting together available things to create some whole, and category theory gives a vocabulary for describing how things (considered very abstractly) can be put together. So for instance, one of the big applications to CS is in type systems, which describe what kinds of expressions/values can be put together, and in what ways, to create valid programs.
- Retra 8y ago
  Most engineering is based on mathematics because proofs are a powerful support for any idea you plan to implement. It's one thing to throw something together and have it work, and a totally different thing to prove it is optimal in some way.

mathgenius 8y ago

For a first introduction to category theory, from the masters thereof, I would highly recommend the book by Lawvere and Shanual "Conceptual Mathematics: A First Introduction to Categories". It almost doesn't look like a mathematics book, but believe me, these guys know what they are talking about. They distill some very high-brow ideas down to something us mere mortals can grok.

armitron 8y ago

I watched a little less than the first half of Bartosz video lectures and I still don't see what the fuss is about from the perspective of an engineer that is looking to get better at engineering. I can't find something there that would help me implement better systems. What I do see is an attempt to shoehorn a mathematical model onto certain programming paradigms in order to be able to say that these paradigms are instances of the model. In short, a lot of talk about abstractions (or "abstract nonsense") but very little of engineering significance. Please let me know if I'm missing something by listing concrete examples of how category theory can help me with engineering problems. Disclaimer: I'm not a mathematician.

eindiran 8y ago
I think that the most plausible way that Category Theory is going to improve your life as an engineer is that it will sneak into the way your tools are designed. You don't personally need to know about the Yoneda lemma to benefit from a better designed programming language whose type system was informed by algebras of types, allowing it to leverage exhaustive pattern matching. With that said, learning about techniques used in functional programming that have their origin in category theory (maps, folds, algebraic data types, monads, monoids, etc) can allow you to think about how to solve problems (even in non-functional languages) in ways that can be more "natural" to the problem, in that the abstractions used resemble the problem description more closely. That ability to decompose difficult problems in new ways can definitely make you a better engineer.
gizmo686 8y ago
Catagory theory is a fantastic tool for understanding programming language design. As a user, you don't need to understand catagory theory, but you benifit when the language designers do. As a software engineer, category theory is sometimes useful in API design as well; although more often than not, your API is constrained by the existing ecosystem too much for category theory to give you much benefit (and, frankly, simple enough that category theory is overkill).
maxander 8y ago
A very abstract idea of its relevance, insofar as I understand it; engineering generally boils down to putting together available things to create some whole, and category theory gives a vocabulary for describing how things (considered very abstractly) can be put together. So for instance, one of the big applications to CS is in type systems, which describe what kinds of expressions/values can be put together, and in what ways, to create valid programs.
Retra 8y ago
Most engineering is based on mathematics because proofs are a powerful support for any idea you plan to implement. It's one thing to throw something together and have it work, and a totally different thing to prove it is optimal in some way.