Category Theory: Lecture Notes and Online Books • Hacker News Board

Re: Category Theory: Lecture Notes and Online Books

#21

Post by Epa095 » Thu, Dec 30, 2021, 9:07 PM UTC

alde wrote: post #4

elnatro wrote: post #2

I find this topic fascinating but hard to start with. Does anyone have any non-Haskell example of category theory? Something that shows why is useful with a use-case.

This might be an unpopular opinion, but category theory isn't very useful at low levels of abstraction. It is an elegant mental framework/model that can be used to generalize many concepts, but in my experience such generalizations rarely give additional insights about the concept it is generalizing.

Freeman Dyson said:

>Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. Mathematics needs both birds and frogs. Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details.

It is my impression that those loving category theory are predominantly birds. I am a frog, and never really got the love for category theory.

Re: Category Theory: Lecture Notes and Online Books

#22

Post by Koshkin » Thu, Dec 30, 2021, 9:09 PM UTC

euroderf wrote: post #20

N00b question here. Does the mathematical characterization of category theory relate in any way to the bridges that the Langlands program is building ?

Well, one of the well-known category theorists has said [0],

> I’ve never succeeded in understanding the slightest thing about it.

[0] https://golem.ph.utexas.edu/category/2010/08/what_is_the_lan...

Re: Category Theory: Lecture Notes and Online Books

#23

Post by mbrodersen » Fri, Dec 31, 2021, 1:59 AM UTC

I have read and understood enough Category Theory to realise that it is kinda fun/interesting if you enjoy abstract math. But it won’t make you a better software (or Haskell) developer. I would instead recommend learning Coq/Lean/Idris/Agda to move up the abstraction level from Haskell, while still learning things that are relevant to developing software.

Re: Category Theory: Lecture Notes and Online Books

#24

Post by mbrodersen » Fri, Dec 31, 2021, 2:01 AM UTC

DarylZero wrote: post #16

lapinot wrote: post #14

Earlier quoted context omitted.

This feels to me like "is there any non rubik's cube example of group?". Category theory is a mathematical tool used by mathematicians and built for mathematicians, so you'll have trouble understanding why it's concretely relevant anyway if you're not in the business of doing maths :D The main motivation is that it's a good language for describing some kinds of objects and writing proofs about them. I'm personaly usi…

Haskell is why it's relevant =D

Not at all. I am an experienced Haskell developer and have had zero usage for Category Theory in my work. I have read and understood Category Theory because it’s fun to learn new abstract math. But I learned a lot more from learning Coq/Lean/Idris.

Re: Category Theory: Lecture Notes and Online Books

#25

Post by OracB7 » Fri, Dec 31, 2021, 3:13 AM UTC

I have some interest in the topic (thanks to Arraycast and Conor Hoekstra) and bought to Mock a Mockingbird by Raymond Smullyan, however it is still a bit too involved for my small brain.

On the other hand, I am very much enjoying How to Bake Pi by Eugenia Cheng, which is a few levels down in difficulty.

Re: Category Theory: Lecture Notes and Online Books

#26

Post by bern4444 » Fri, Dec 31, 2021, 4:41 PM UTC

elnatro wrote: post #2

I find this topic fascinating but hard to start with. Does anyone have any non-Haskell example of category theory? Something that shows why is useful with a use-case.

I wrote this article[0] as part of my own journey to understand monads and category theory.

I think you may find it helpful. It has a practical use case that builds up an intuitive model to a new monad. It goes through a few solutions for a stated problem which solve increasing requirements and eventually coalesces into writing a new monad as a complete solution to resolve all the built up requirements.

[0] https://sambernheim.com/blog/building-a-monad

Re: Category Theory: Lecture Notes and Online Books

#27

Post by bob_coecke » Tue, Jan 04, 2022, 3:46 PM UTC

Within the applied category realm where seven sketches lives, there are low-level concrete industrial applications that are becoming increasingly dominant with key industry players in quantum tech. The most known one is ZX-calculus which is explicitly used in things like compiler optimisation, error-correction, translations between computational models etc. This might be the 1st time that CT is playing a central role in a new technology. The reason is the high-level connotation that has been pushed far too long concerning category theory, originating in its abstract mathematical origins.

Bob Coecke, Chief Scientist, Quantinuum.