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Applied Category Theory Course

math.ucr.edu

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Re: Applied Category Theory Course

#31

Post by k__ »

bmitc wrote: post #8
stathibus wrote: post #7

Why is everyone here so obsessed with category theory? It has basically no useful theorems.

I think it's mainly software folks who feel mathematical learning it. Mathematicians primarily use it as a linkage and general tool in some context. I feel category theory needs something to latch it on to. Most software based applications seem a little too contrived, unless I have missed something interesting.

If CT is used to connect different parts of math and software is basically math proofs, then it makes sense programmers find CT interesting.

It let's you connect your software to math concepts.

Re: Applied Category Theory Course

#33

Post by diordiderot »

My Excerpts for HN crowd

>I'm not a programmer. I apologize for this flaw.

> this is not a course on "categories in computer science". Nonetheless, because category theory is about understanding and organizing abstract data structures, everything I say will be relevant in some way to computing! Furthermore, several chapters in Seven Sketches explicitly discuss databases, and type systems, and other aspects of computer science.

Re: Applied Category Theory Course

#34

Post by mejutoco »

mjburgess wrote: post #28
mjan22640 wrote: post #22

Earlier quoted context omitted.

Programming is applied algebra, the choice is not using vs not using, but understanding what you are doing vs being ignorant about it. Relevance is in the eye of the beholder. In typical business the incentive is to have a good enough code ready "yesterday", and it will be thrown away tomorrow, as the code and whatever it does are only a means to generate profit and not a goal in itself, and spending time on making i…

Programming is also applied physics. But understanding the kinetic forces behind typing is no guide to improved programming. To say that learning a field is useful is to say that knowing these abstractions is useful. Much of Haskell's "category theory" is a reuse of terms. Replace Monoid by Appendable, Monad by Composable, Functor by Runnable, etc. and most programming languages are "category theory". This says littl…

> If its authors hadnt used their knowledge of category theory, but rather named the abstractions in more ordinary terms, the language would be more useful to more people.

The language would be just as useful, but it might _feel_ more approachable. Depending on the terms that replaced those it might be more confusing, or the opposite, than it is now.

Re: Applied Category Theory Course

#35

Post by nabla9 »

j2kun wrote: post #11

I'm writing a book [1] about "bona fide" applications of mathematics to practical programming problems, where bona fide is my own personal definition [2]. I've had my eye on claims of applications of category theory for many years, and none of them have quite fit the bill (sorry, John, if you're reading this). When they talk about applications to databases it seems quite unrealistic or lacking in sufficient detail to…

I mostly agree. Category theory is typically 1-2 steps separated from what programmers do.

Category theory is useful for thinking about X, X is super useful for modelling and designing Y.

X in {Petri net, relational algebra, feedback diagrams, type system, ... } and Y in {communication protocol, database, programming language, ... }

Re: Applied Category Theory Course

#36

Post by 3np »

behnamoh wrote: post #6

I’ve seen many “applied” category theory posts and books but it’s important to remember that pure mathematicians’ definition of “applied” is way different than and more boring than you’d think. I still have to see some insights that CT gave us about a real world application that wouldn’t have been discovered without CT. Most of CT to me seems like definitions on top of definitions.

> Most of CT to me seems like definitions on top of definitions.

More like definitions of definitions :)

Re: Applied Category Theory Course

#37

Post by deterministic »

j2kun wrote: post #11

I'm writing a book [1] about "bona fide" applications of mathematics to practical programming problems, where bona fide is my own personal definition [2]. I've had my eye on claims of applications of category theory for many years, and none of them have quite fit the bill (sorry, John, if you're reading this). When they talk about applications to databases it seems quite unrealistic or lacking in sufficient detail to…

I completely agree. I have been looking for a long while and I haven’t found any examples where using CT made sense. There seems to be a lot of “look at me I am a mathematician!” usage of CT to obfuscate what is really very simple ideas that could otherwise have been explained much simpler without requiring the reader to know an obscure subset of CT.

So your basic idea happens to be a Co-Variant Non-Infinitoid Subspace Category? Seriously who cares?

Re: Applied Category Theory Course

#38

Post by epgui »

helix278 wrote: post #25
epgui wrote: post #5

Earlier quoted context omitted.

If you’re spending more than a few months on a topic you might be doing it wrong. I find that following a slightly stressful fast-paced schedule is actually kind of important for effective learning.

I'm working through a similar course with friends. We take two hours a week, and ocasionally do homework. We're about halfway since we started early this year. I feel its fine, no need to rush. The upside of taking it slow is that it stays with you for longer, I think. If you rush it and find no immediate application afterwards, you risk forgetting everything.

Long term retention requires spaced repetition of course. But I think the stressful pace does help not get bogged down on a first pass of the material.

It's impossible to cover everything about a topic in a short amount of time, but when you try, you at least develop a map of the terrain.

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