/mg/ ∧ /math/ general

I got it from Concrete Mathematics on the 4th chapter so eat my dick

kek

bump

hey /math/
what are some good resources for getting into category theory and what are the prerequisites?
thanked

I found an RNG algorithm by randomly generating assembly basically

gonna use it to calculate random numbers in an OpenGL shader

top is a bitmap made by 1 bit per iteration bottom is what it looks like with sorted pixels

>MacLane, Categories for the working mathematician
>ncatlab
>Abstract and concrete categories

Although you pretty much don't need to know any prequesites except maybe some basic set theory I would argue that it is very useful to know

- basic linear algebra
- basic topology up to homotopies
- some basic algebra

so one can appreciate why one should even do category theory.

thank you. I'll look into them.
do these books cover some motivations and uses in maths of categories?
I haven't yet read something on them, but I never understood the underlying principle behind them.
could you care to explain to me, shortly ofc, what's the fuss regarding categories all about?
thanks

if you have enough time and interest, study also algebraic topology along the way. the best way to learn category theory is to use category theory.

A good read about that is ncatlab.org/nlab/show/category theory

some of it may be quite overwhelming for a complete novice. So I guess I'll try my own words:

Category theory is less an actual "theory" and more sort of a "language" or a "philosophy", which seems to inherently gives you the "right" intuition or point of view for many areas of mathematics, especially topology, algebra, algebraic geometry, etc.

The most interesting part of category theory are the definitions and less the actual theorems of category theory, because they serve to unify very different notions in different branches of mathematics back together, because from the viewpoint of category theory they behave very similarly. Thus it is makes it possible to quickly transfer knowledge in one branch to another branch. An example: Products

A product of sets or a product of topological spaces or of groups are defined quite differently, but from the viewpoint of category theory they all behave in the same way. If you know category theory and know how the product behaves, then you should be able to quickly determine what a product of top. spaces, or groups or... is, without having to memorize it for each seperate case.

that's truly interesting. so it's basically an abstraction on the form of some objects and how that abstraction behaves? sort of?

will do. just a small curiosity: does topology and algebraic geometry have any applications in theoretical CS ?