Category Theory

it's clearly a trap you faggot

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

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

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"

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

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.

>Pure math fag
more like pure beta

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

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

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?

Sometimes I wonder why people with so much knowledge of upper level mathematics get on Veeky Forums?

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.

most of us grew up here

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

you never really leave

>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.

How depressing :/

hung*

Are you the dude I replied to?

>Are you the dude I replied to?
no

>there is no foundations of math in pure category theory.
of course there is, for example
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.

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