Category Theory

>>8562159
What is category theory though?

basic category theory - leinster
simmons - an introduction to category theory

>>8562162
I used to wonder the same thing. Here you go.
http://rs.io/why-category-theory-matters/

File: category theory for mathfags.jpg (127KB, 1200x1850px) Image search: [Google]

127KB, 1200x1850px

>>8562159

damn i love when girls wear thin sandals like this. makes the feet look so hot

>>8563315
Kill yourself.

>>8563318
>literally autistic

kek

Categories for the working mathematician - Mac Lane
Algebra, Chapter 0 - Aluffi

>>8563419
aluffi is not an intro to category theory in any sense of the word

>>8563315
it's clearly a trap you faggot

>>8562159
It hardly makes any sense to start learning CT on its own. Do Algebraic Topology/Algebraict Geometry/Representation Theory instead.

>>8562176
Pasting because the site fucked up the latex
[math]\( P \xrightarrow{\quad f \quad} \mathbb{R}^{2} \)[/math]

>>8562176
oh my god that's disgusting

category theory is not an alternative to set theory. there is no foundations of math in pure category theory. you're confusing that with HoTT or at best topoi.

category theory is a language for organization. the differential geometers invented it when they started drowning in the number of levels of generality they were operating on.
what it does is give you a pictorial language to better understand what it is requures proving, and for mechanising those proofs to a remarkable degree (viz. "diagram chasing")

this fucker on the other claims not only that *graduate level mathematics* is beyond him, but also that he's a fucking authority on whaye category theory is
even if this bs he wrote is written for the layperson or j random hacker who's stupid and can't come up with a monad-burrito analogy, spreading disinformation as though you are an expert is morally corrupt and basically a cardinal fucking sin

t. "graduate level mathematician"

>>8562159
just fucking read maclane if you're such a big pmath boy
if you can't handle it, flog yourself 20 times for thinking category theory is an approproate topic to learn at this level of mathematical maturity and then pick up awodey or something
because you're sure as shit not gonna go learn something useful like modern geometry which naturally motivates the use of categories by virtue of being incomprehensible otherwise

>>8563422
It's the study of algebra from the point of view of categories. I dont know what level OP is in, but I found it a great book introducing categories and making it intuitive by relearning algebra.

>>8562159
>Pure math fag
more like pure beta

>>8563576
aluffi literally doesn't even define a natural transformation for 500 pages

just because he uses the most basic of categorical language while talking about algebra doesn't make it an introduction to category theory

>>8562159
vicky wu is a freaking insane schizo sociopath, you can see it in her eyes

2/10 literally actually has an untreated mental condition and her feet arent great either

also awful cantonese accent

>>8563577
Don't knock foot fetish till you try it desu

Ive been hearing about category theory for so long, what are the minimal prerequisites for the books mentioned?

>>8563566
Sometimes I wonder why people with so much knowledge of upper level mathematics get on 4chan?

Maclane is still the best source for basic category theory. Some of the layer chapters should be supplemented with other material. The best way to learn category is to use it in other areas, I only really became comfortable with the basic machinery years after I became fluent in it, while picking up some simplicial homotopy theory. Homotopy theory in general is a good place to find examples of category theory. For example, coends play a crucial (sometimes left implicit) role in setting up smash products of spectra, or in "calculating" kan extensions, for instance in singularization/realization contexts.

>>8566124
most of us grew up here

i've been here from age 13 to now doing graduate studies in math

you never really leave

>>8566142
>you never really leave
Save for you know the original bunch of tards that hang around here with us. Sites gone from a treehouse for retards with a specific sense of humour to a catch-all shithole.

>>8566160
How depressing :/

>>8566160
hung*

>>8566161
Are you the dude I replied to?

>>8566163
>Are you the dude I replied to?
no

>>8563566
>there is no foundations of math in pure category theory.
of course there is, for example
https://ncatlab.org/nlab/show/fully+formal+ETCS
to name one.
Of course, just as people don't really need set theory for decades, nobody is really interested in those alternatives.

>>8566200
ETCS doesn't depend on category theory, people just express it in categorical language because it makes them happier.