/sci/ - Science & Math

[Anonymous No.12610143]

Yo does anybody here know category theory?
Can you please explain it in simple words for someone who has just a bachelor in comp sci wtf category theory is about?
Like what are we actually trying to archive with this? "We want to be more abstract" is a non-answer I want to know why this has to be done in the first place. "To prove stuff" ok yeah I get it but WHAT EXACTLY.

I've seen 5 introduction videos so far and they are purely abstract and nobody says what this shit is about.

"It's about functors and arrows and morphisms" ok yeah I get it.

This is like the piece of art where someone just taped a banana on a wall. I get it, it's criticism about what is art, but without this context the thing itself is meaningless. The whole topic is meaningless without any context, someone need to explain.

[Anonymous No.12610153]

>>12610143
Set theory is a non-answer so we added some structure and now we have the category of categories.

[Anonymous No.12610155]

>>12610143
Category theory is like set theory: it's a conceptual framework by which foundations of mathematics can be (ostensibly) laid down. The difference is that set theory emphasizes and studies the content and nature of mathematical objects, whereas category theory emphasizes and studies the connections between these objects, and considers those connections mathematical objects in their own right.

[Anonymous No.12610168]

>>12610153
do you have ONE SIMPLE example of what a structure and a category is?

Every stuff I've seen so far only uses uninteresing self containing or identity or empty set shit examples ffs

[Anonymous No.12610175]

>>12610155
so category theorie, uhm, compares axiom frameworks?

[Anonymous No.12610181]

>>12610143
Category theory was made to advance algebraic topology. It's math made for math.

[Anonymous No.12610197]

Just talk to me like im 5yo or smth I still don't get it

What we have so far:
>we added some structure and now we have the category of categories
>(...) studies the content and nature of mathematical objects, (...) and studies the connections between these objects, and considers those connections mathematical objects in their own right.
>to advance algebraic topology. It's math made for math.

[Anonymous No.12610201]

>>12610143
Maybe think of set theory vs category theory as similar to imperative vs functional programming. They solve the same tasks, but their languages are different.

[Anonymous No.12610209]

>>12610143
https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/
https://www.youtube.com/playlist?list=PLbgaMIhjbmEnaH_LTkxLI7FMa2HsnawM_
https://www.youtube.com/playlist?list=PLbgaMIhjbmElia1eCEZNvsVscFef9m0dm
https://www.youtube.com/playlist?list=PLbgaMIhjbmEn64WVX4B08B4h2rOtueWIL
knock yourself out

[Anonymous No.12610216]

>>12610209
>https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/

hm I'm gonna check that out ty

[Anonymous No.12610238]

>>12610143
You draw letters and draw some arrows connecting the letters. That's the entire theory.

[Anonymous No.12610246]

>>12610238
that's just a directed graph

[Anonymous No.12610270]

>>12610246
*in the category of directed graphs

[Anonymous No.12610618]

>>12610143
It's the 'bird eye view' of mathematics. A category is made up of objects and arrows between them(subject to certain rules). The point of category is not to to look 'into/inside' each objects. The point is to take the objects as primitive and recast all their properties as properties of the arrows/morph isms between them. That's the general dumbed down version.

[Anonymous No.12610632]

>>12610168
A basic example of a category is the category of sets, often denoted by SETS. Its objects are sets and the morphism between them are just normal functions between sets. It's obvious that each set has a function to itself, and that you can compose functions

[Anonymous No.12610642]

>Yo does anybody here know category theory?

Learn Object oriented programming (Java/C#) and it is all clear,