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What Is Applied Category Theory? (2018)

arxiv.org

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Re: What Is Applied Category Theory? (2018)

#11

Post by konamicode »

kbr wrote: post #4

As a high schooler interested in things that are probably out of my league, I love reading this kind of stuff. The author mentions their unconventional style at the beginning: hyperlinks, color, italics, exclamations, parentheses, side notes, etc. They address your thoughts and craft their explanations around them instead of being terse and optimizing for length. The author's blog [1] has more of this style and has r…

If you’re interested in machine learning I can recommend Christopher Olah’s blog: https://colah.github.io/

Re: What Is Applied Category Theory? (2018)

#12

Post by mhh__ »

kbr wrote: post #4

As a high schooler interested in things that are probably out of my league, I love reading this kind of stuff. The author mentions their unconventional style at the beginning: hyperlinks, color, italics, exclamations, parentheses, side notes, etc. They address your thoughts and craft their explanations around them instead of being terse and optimizing for length. The author's blog [1] has more of this style and has r…

Although they might be very out of your league depending on what your interests are, Anthony Zee has a similar writing style (in print)

Re: What Is Applied Category Theory? (2018)

#13

Post by kbr »

enchiridion wrote: post #5
kbr wrote: post #4

As a high schooler interested in things that are probably out of my league, I love reading this kind of stuff. The author mentions their unconventional style at the beginning: hyperlinks, color, italics, exclamations, parentheses, side notes, etc. They address your thoughts and craft their explanations around them instead of being terse and optimizing for length. The author's blog [1] has more of this style and has r…

I don't have any resources to share on this, but I was also interested in this type of thing at your age (still am). If it interests you, never assume something is out of your league. You have time on your side. Sustained effort compounded over time is unreasonably powerful. Keep pushing!

> Sustained effort compounded over time is unreasonably powerful.

Thank you, this hits close to home and is great advice, I appreciate it.

Re: What Is Applied Category Theory? (2018)

#14

Post by xelxebar »

kbr wrote: post #4

As a high schooler interested in things that are probably out of my league, I love reading this kind of stuff. The author mentions their unconventional style at the beginning: hyperlinks, color, italics, exclamations, parentheses, side notes, etc. They address your thoughts and craft their explanations around them instead of being terse and optimizing for length. The author's blog [1] has more of this style and has r…

Not addressing your question, but the Yoneda Lemma is kind of a charlatan.

On first reading, it seems magical and deep, but once you grok the proof, it feels like a relatively trivial observation. The whole thing is just about arrow composition!

In a way, once you're on the other side, the Yoneda Lemma feels a bit like a checkpoint during the accimatization period where your brain gets used to thinking in categories and commutative diagrams.

Not quite sure it's exactly the style you're talking about, but Bartosz Milewski has a nice series of video lectures going all the way from nothing up to Coend stuff. IIRC the series gets to the Yoneda Lemma somewhere in the second series:

https://invidious.snopyta.org/channel/UC8BtBl8PNgd3vWKtm2yJ7...

Re: What Is Applied Category Theory? (2018)

#15

Post by Gormisdomai »

xelxebar wrote: post #14
kbr wrote: post #4

As a high schooler interested in things that are probably out of my league, I love reading this kind of stuff. The author mentions their unconventional style at the beginning: hyperlinks, color, italics, exclamations, parentheses, side notes, etc. They address your thoughts and craft their explanations around them instead of being terse and optimizing for length. The author's blog [1] has more of this style and has r…

Not addressing your question, but the Yoneda Lemma is kind of a charlatan. On first reading, it seems magical and deep, but once you grok the proof, it feels like a relatively trivial observation. The whole thing is just about arrow composition! In a way, once you're on the other side, the Yoneda Lemma feels a bit like a checkpoint during the accimatization period where your brain gets used to thinking in categories…

"On first reading, it seems magical and deep, but once you grok the proof, it feels like a relatively trivial observation. The whole thing is just about ____ composition!"

I think if you replace _____ with the right word almost every result I've seen in my (albeit somewhat limited) exposure to category theory can be described this way.

(not that that detracts from your answer!)

Re: What Is Applied Category Theory? (2018)

#16

Post by Garlef »

xelxebar wrote: post #14
kbr wrote: post #4

As a high schooler interested in things that are probably out of my league, I love reading this kind of stuff. The author mentions their unconventional style at the beginning: hyperlinks, color, italics, exclamations, parentheses, side notes, etc. They address your thoughts and craft their explanations around them instead of being terse and optimizing for length. The author's blog [1] has more of this style and has r…

Not addressing your question, but the Yoneda Lemma is kind of a charlatan. On first reading, it seems magical and deep, but once you grok the proof, it feels like a relatively trivial observation. The whole thing is just about arrow composition! In a way, once you're on the other side, the Yoneda Lemma feels a bit like a checkpoint during the accimatization period where your brain gets used to thinking in categories…

> The whole thing is just about arrow composition!

There's much much more to it.

For example, a version of the yoneda lemma also holds for metric spaces (instead of a set of arrows between to things, you simply have a number indicating a distance between two things).

Here's how I like to think about the yoneda lemma:

If you have some kind of objects you want to talk about, one way to do this is by relating these objects to each other. Once you have established such a "method of discourse" (i.e. a way to talk about how your objects relate to each other) the yoneda lemma tells you:

1. You can forget about the inner structure of your objects; Everything is already contained in your "method of discourse".

2. Inversely: The choice of a "method of discourse" severely limits what you can say about your objects.

3. There is no spoon: To understand how you can escape these limitations you need a "method of discourse" for "methods of discourse".

Re: What Is Applied Category Theory? (2018)

#17

Post by gugagore »

There is an applied category theory course that is currently in the process of wrapping up: https://applied-compositional-thinking.engineering/

The examples in the course offer a complementary entry point to category theory compared to an approach that leverages programmers' knowledge of functional programming.

Personally, the more examples the better. I'm grateful to be able to rely on the example of a category as a collection of objects corresponding to types, and arrows between types corresponding to functions with that type signature, and arrow composition corresponding to function composition (and functors, and natural transformations, and ... corresponding to familiar concepts like polymorphic types, and map, and polymorphic functions and ...). I believe that many programmers can [come to] understand this one specific example of category theory objects, even if the words are unfamiliar. And there are so many more examples! There is a great pleasure in formalizing the analogies across different aspects of math and engineering.

To get a flavor of and gentle introduction to the analogy-making power of category theory, I recommend this talk by Eugenia Cheng: https://www.youtube.com/watch?v=ho7oagHeqNc

Re: What Is Applied Category Theory? (2018)

#18

Post by wires »

gugagore wrote: post #17

There is an applied category theory course that is currently in the process of wrapping up: https://applied-compositional-thinking.engineering/ The examples in the course offer a complementary entry point to category theory compared to an approach that leverages programmers' knowledge of functional programming. Personally, the more examples the better. I'm grateful to be able to rely on the example of a category as a…

Worth mentioning that we are offering a high-quality (paid) course https://training.statebox.org

Re: What Is Applied Category Theory? (2018)

#19

Post by fredgrott »

To give you an idea of how we are using this pdf..

I am reapplying category theory to use functions in dart-Flutter to avoid using statefull widgets and instead use a reactive function approach to state management.

Side benefits is it's easier to explain to beg flutter devs than statefull widgets.

Thanks behnamoh for posting this link

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