After reading that, will I be able to write a hello world in Haskell?
Basic Category Theory
71–80 of 92 posts
Re: Basic Category Theory
#72If I may ask, why is the HN community so interested in this particular topic? I studied Math and have basic understanding of Category Theory... could someone point me to a text relating Categories and... something related to computers? What am I missing?
Category Theory organizes mathematical concepts, and a lot of the concepts there are applicable to Computer Science. As an example, consider the theory of Containers [0]. A container is an abtract mathematical model of some kind of data structures (such as lists, trees etc.). Like most mathematical structures they form a category. Further more, each container gives rise to a endo-functor Type → Type. In fact they for…
I really enjoyed learning about the so-called "combinatorial species" [1]. It is another good example of what you are describing. And this idea of differentiation as putting a hole, it just blows my mind every time i think about it.
Re: Basic Category Theory
#73"for readers with relatively little mathematical background." A well put together guide, but note that 'relatively little' here means you're OK with some abstract algebra, at least, as the second example of the introduction begins: This example involves rings, which in this book are always taken to have a multiplicative identity, called 1. Similarly, homomorphisms of rings are understood to preserve multiplicative id…
I actually laughed out loud when I got to that part. It seemed like the first page and a half he really tried to explain it without jargon and then just gave up. To be fair, though, who is going to read an introduction to category theory that isn't familiar with abstract algebra? Someone should write 'an introduction to introductions to category theory'
Bob Coecke writes good introductions to category theory, you might find some of his stuff enjoyable. Although he is often also introducing quantum physics and linguistics at the same time.
This paper is fascinating:
Re: Basic Category Theory
#74If I may ask, why is the HN community so interested in this particular topic? I studied Math and have basic understanding of Category Theory... could someone point me to a text relating Categories and... something related to computers? What am I missing?
Re: Basic Category Theory
#75The best intro I've ever seen is Bartosz Milewski's video series (intended mostly for coders): https://www.youtube.com/playlist?list=PLbgaMIhjbmEnaH_LTkxLI... It assumes almost no prior math knowledge (okay, you should know what sets and functions are...).
Looks so promising. Haven't decided yet whether I'll view through these 15 whopping hours or study the written (massive-book-length) equivalent chapters on his blog.. Sizing this up, my real question now becomes: as an active day-to-day-life programmer, by how much exactly will this propel my work if I already know and use monads, basic function composition and Haskell? I'm sure there's some amount of skill/quality/p…
I loved his videos, personally. I had some familiarity with basic category theory and functional programming, but Bartosz does a really good job of explaining everything without prior math knowledge. Compared to all the introductory books people recommend, he's an excellent teacher.
On the subject of it improving your coding, not so sure how much you could measure that. I think it's usually preferable to have a strong understanding of the basis of what you're working with, however, as it gives you some confidence to think critically about things you would usually just accept as fact.
Re: Basic Category Theory
#76After reading that, will I be able to write a hello world in Haskell?
No. It's not a Haskell book.
Re: Basic Category Theory
#77I enjoy "Make Category Theory Intuitive!" (2007), by Jocelyn Ireson-Paine http://www.j-paine.org/make_category_theory_intuitive.html
Like so much of category theory writing, it lacks examples. Seriously, point me to examples where category theory is actually useful outside of specific parts of mathematics, and I'd be very happy. By useful, I mean that it allows you to prove or understand something that would otherwise not have been proved (or is much more difficult to prove).
The point isn't so much proving new results, as showing how different results (that you thought looked similar but were distinct from each other) are actually exactly the same result in different settings. One of the things category theory does is tell you whether a result is "deeply meaningful" or not.
For example, I still don't know how the Segre embedding of projective varieties is constructed (my algebraic geometry lecturer laboured hard to try and impart that knowledge, with the result that I thought it was difficult and abstruse); but I now know that it's a product in an appropriate category, so while the construction may be really nontrivial, the object itself is just the same old product which I already know and love. I now know that the difficulty lay in showing that this object exists and has the required properties, rather than the object itself being in some deep moral sense "hard to understand".
Re: Basic Category Theory
#78"for readers with relatively little mathematical background." A well put together guide, but note that 'relatively little' here means you're OK with some abstract algebra, at least, as the second example of the introduction begins: This example involves rings, which in this book are always taken to have a multiplicative identity, called 1. Similarly, homomorphisms of rings are understood to preserve multiplicative id…
jargon like "homoporhism, rings, multiplicative identity" are just scary sounding words for simple concepts. Especially this day and age with wikipedia.
Now, not to say that proving things about groups and rings is simple. but just because the word has 5 syllables doesn't mean the concept is hard. Whereas certain concepts in calculus - I think - are quite difficult to solve for even simple looking integrals.
Re: Basic Category Theory
#79I lost interest in math after calculus, when it stopped being about results and more about abstract and complicated squiggles on the page . Elliptic functions are interesting because it seems calculus-like (such as elliptic integrals and the theta series) but this weird set/category theory stuff just doesn't do it for me.
"Stopped being about results"? I think you're referring to the building-up of the vocabulary required to attain results. As an analogy, you learnt to count (1,2,3,4,…), but then when addition and multiplication were introduced, it "stopped being about numbers, and more about abstract and complicated operations on numbers". Yes, fine, but addition and multiplication open the gateway to the study of the primes, from wh…
I'd say addition and multiplication are more important than prime numbers, or number theory, for that matter.
Re: Basic Category Theory
#80[deleted]