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What Is Applied Category Theory? (2018)

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Re: What Is Applied Category Theory? (2018)

#21

Post by bmitc »

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…

You may like the books Conceptual Mathematics: A First Introduction to Categories, Creative Mathematics, Advanced Calculus: A Differential Forms Approach, and Geomtrical Vectors.

https://www.amazon.com/dp/052171916X/

https://www.amazon.com/dp/0883857502/

https://www.amazon.com/dp/0817637079/

https://www.amazon.com/dp/0226890481/

Re: What Is Applied Category Theory? (2018)

#22

Post by ectoplasmaboiii »

Ceezy wrote: post #20

If anybody interested the best book to learn the category theory: https://www.maths.ed.ac.uk/~v1ranick/papers/maclanecat.pdf

For anyone else interested, Tom Leinster (also of Edinburgh Uni) has also written a good short book for beginners:

https://www.maths.ed.ac.uk/~tl/bct/

I did his course at uni that used this book as a basis and it was great. Tough, but great.

Re: What Is Applied Category Theory? (2018)

#23

Post by jbotz »

Ceezy wrote: post #20

If anybody interested the best book to learn the category theory: https://www.maths.ed.ac.uk/~v1ranick/papers/maclanecat.pdf

Why do you think this is the best book? And would someone's background, or lack thereof, in other fields of mathematics not have a bearing on that assessment?

Re: What Is Applied Category Theory? (2018)

#24

Post by newswasboring »

Category Theory is one of those things which I know are important and has applications in many engineering fields. I also have an intuition that its obviously because things need to flow into each other and composability is how we achieve that. But man, whenever I try to get into this I feel like someone is hitting me on the head with equations.

Re: What Is Applied Category Theory? (2018)

#25

Post by dmch-1 »

Samuel Eilenberg, one of the founders of category theory, used to tell to his students "You should have you own category". Meaning, that when you work on category theory you should have in mind applications to something. One of his students used to say "my category is Cat". Cat means the category of categories.

Re: What Is Applied Category Theory? (2018)

#27

Post by spinningslate »

I'm not a natural mathematician (emphatically not!) and pretty much every attempt I've made to wrap my head around Category Theory has foundered on an onslaught of formalism by paragraph 2.

To be clear, I'm not knoocking that: for those who can and do grok things from that sort of treatment, all power to your elbow (and no small amount of admiration).

But it's not how my brain works. I need an intuitive understanding first: exemplars, informal pictures, whatever. I can only start unscrambling the formalism once I have the intuition.

The author's introductory blog post is a great example [0]. It's without doubt the best "bootstrap" I've come across - where "best" means "most understanable to me". I really admire people who can take abstract/complex subject matters and lay them out in a clear and accessible way for the layperson. Tai-Danae Bradley definitely fits in that Category (dubious pun intended!).

[0]: https://www.math3ma.com/blog/what-is-category-theory-anyway

EDIT: fixed typo

Re: What Is Applied Category Theory? (2018)

#29

Post by monktastic1 »

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 exactly what you asked for, but this explanation of the Yoneda Lemma is amazing: https://youtu.be/h64yZs8ThtQ

Re: What Is Applied Category Theory? (2018)

#30

Post by johndoe42377 »

Just a nice set of ideas to be used for social signalling.

In with type systems, a typeclass is all you need. The mantra is "to be an X (being substituted for an X) is to be able to perform (implement) such and such actions (or have this or that biochemical properties).

It is that general, that deep, it could be even seen in molecular biology.

Category theory, on the other hand, is just a few nested abstract concepts, of which only monoid has some connection to reality, which ends up empty, like most abstract pseudo- philosophical bullshit.

And yes, I have watched and read everything by Bartosz. It is empty.

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