Category Theory

[Anonymous No.15117297]

Is category theory a waste of time? I just finished my third year and going through Rotman's Algebra I was introduced to pushouts, pullbacks, exact sequences, etc. Seems interesting but is it worth it? Or is what Rotman covers when presenting Noetherian rings, free modules, etc. enough at the moment? I think it might help me with a bird's eye view of algebra, since similar constructions and results arise when for example studying rings and then groups, or abelian groups and then modules, etc. Or should I just embrace the chaos of seemingly random connections between different structures for the time being?

And if it's worth it, what it's the best book to learn the actually useful parts? I'm thinking about Mac Lane or Leinster

[Anonymous No.15117299]

>>15117297
category theory?
it's an absolute meme field and a waste of time
t. guy who knows nothing about it

[Anonymous No.15117601]

>>15117297
I would ignore it. Much of the "objects" studied with it are based upon faulty logic like the so-called "axiom" of choice or non-sense like the "axiom" of infinity. That's of course ignoring the intuitive objects found in it like these "infinite sets," and these other strange "constructs"; hierarchies of cardinalities, hierarchies of angels, and then the resulting paradoxes which have still never been resolved. Mathematicians have only hand-waved it away with a meaningless word games and just ignore it. It's common practice for mathematicians to recite the ZFC creed and say the primitive objects prayer whenever problems come up.

[Anonymous No.15117659]

Learn algebraic topology instead

[Anonymous No.15117663]

>>15117297
Category theory is useless. I’ve never seen categories show up in any place of interest or importance.

[Anonymous No.15118799]

>>15117601
What is the Chad move after accepting this fact?

[Anonymous No.15118803]

>>15117659
I will do that after taking topology this semester

[Anonymous No.15118806]

>>15118799
learn how to do math without reals

[Anonymous No.15118840]

>>15118806
That sounds pretty cool anon, recommend me a book. Or am I forced to watch his videos?

[Anonymous No.15118848]

>>15118840
You have the choice of both https://web.maths.unsw.edu.au/~norman/

[Anonymous No.15119128]

>>15117601
>>15118806
is this nigga fr fr no cap fr?
bussin?

[Anonymous No.15119157]

>>15117297
Category theory, in my humble opinion, isn't extremely interesting on its own. There is some interesting stuff on categorical logic, though. But if you don't want to go into logic or just theoretical computer science, I don't think it's necessary to study as a field on its own. I'd recommend studying fields that use it extensively instead, in that case.

[Anonymous No.15119201]

Not really.
Good example is trying to find the initial object in the category of rotary 2-oids. A 2-oid is a quadruple (A,+,*,1) such that (A,+,1) and (A,*,1) are monoids, 1 <- A is the identity element for both, and A is rotary if (a + b) * c = (a * c) + b for all a,b,c <- A.
Homomorphism of 2-oids is a map of the domain that turns into a homomorphism for both the + monoids and the * monoids, i.e. in parallel consider the domain and codomain to be + monoids and check for homomorphism then switch both domain and codomain to * monoids and check for homomorphism again
note that + is NOT necessarily commutative, it's just another associative binary operator on A with identity element 1
at this point, I think the initial object is essentially equivalence classes of floating scrabble tiles, so the demand to go into the 3rd dimension isn't immediately obvious; and it isn't obvious that we have to do tensor product-like shenanigans with equivalence classes either...
However, categories are a huge fuckin' meme, and I can't stand this whole
>muh Working Mathematician
attitude
I mean, fuck you
fuuuk yuuuuuu

[Anonymous No.15119214]

>>15119201
Sorry, equivalence classes of floating scrabble tiles linked by skybridges, equivalent up to changing tile height
So, Chrono Trigger/Avatar type deal

[Anonymous No.15119236]

>>15119201
>I can't stand this whole
>>muh Working Mathematician
>attitude
elaborate

[Anonymous No.15119269]

>>15117297