/sci/ - Science & Math

It's literally just fucking arrows.

>>10185058
>Category Theory
not science or math

>>10185082
it's literally math. The fact that you don't understand it doesn't mean it doesn't belong here, brainlet.

>>10185129
>it's literally math.
How so?

>>10185134
How is it not?

>>10185058
Why did they draw a dick in math on the cover of their book? Is that really there or photoshopped in?

>>10185155
Oh my god

>>10185148
>How is it not?
The burden of proof is on you.

>>10185058
The Virgin Category Theory vs The Chad Combinatoric Erudition.
~~~~~~~~~~~~~~~~~~~~~~~~~~
>Needs no preschool "arrows"
>Doesn't even need a central reference point.
>Instantly understands the hyperspace it inhabbits by merely presenting a dualistic object to 'invade' it.
>Conquers it completely through definition by proofs before transforming it into succint axioms of mathematical perfection.
>Immediatly deduces relavant results and analysis from statistical discrepancies within the form functions of any inhabitted location.
>Groupings literally become fluid in its presence.
>Interdimensionally relavant.

Where were you when category theory got btfo?

>>10185192
WHY ARE YOU LIKE THIS. CAN'T YOU JUST FUCK OFF AND LEAVE OUR CATS ALONE?!

>>10185198
You see? Already in less than 5 minutes of my CHAD combinatorical presence, you have already turned into a pussy! Chadbinatorics wins again!

>>10185216
I FUCKING HATE YOU.

Finally someone else who's talking about category theory on /sci/. We need to push this so it becomes part of sci culture.
I'm currently reading pic related.
And before that I read algebra chapter 0 by Paolo Aluffi.

>>10185192
>Where were you when category theory got btfo?
Skulling on the river cam plotting to take the lucasian chair

>>10185082
Retard.

>>10185129
This.

>>10185081
Arrows and objects. It's actually quite simple but people always try to explain it from the top down by using special cases from some other area of math as analogies.

>>10185192
What the fuck are you talking about?

>>10185228
There's a lot of category theory threads on /sci/. Not as much Topos Theory.

>>10185082
Why is there always one person who's like "hurr durr not science or math"

There exists more math than just analysis and algebra. There exists more science out there that isn't pure. I"m an analysisfag but if you're telling me combinatorics, category theory, etc. are anything less than math (and in the case of combinatorics, anything less than black magic), then you have no idea what you're talking about. you're more than likely either an undergrad who wants attention or a grad who wants to aggressively validate their own research interests

>>10185397
it's probably the same person that is wasting his life trying to annoy people on an anonymous board

i believe it might even be the same person that makes those is there a scientific explanation for x stupid subject

>>10185397
I sometimes post "not science or math" but only in threads which don't belong on /sci/

>>10185413
>is there a scientific explanation for x stupid subject
Threads like that should be an autoban.

>>10185417
>>10185429
Same for “what’s the evolutionary reason for x” threads

>>10185058
>In fifty years I believe category theory will be as "applied" a field of mathematics as calculus, linear algebra or probability theory
No, maybe it will be the new language of math (it sort of already is to some extent), but the actual study of category theory will remain a fringe subject, just like the study of set theory is today.

>Category theory in many respects is even more appropriate as "the laws of thought" than logic.
What does that even mean ?

*ahem*
FUCK CATEGORY THEORY AND FUCK ALGEBRAISTS

>>10185525
You can like more math than just analysis, you know.

>>10185058
>)good

>>10185446
>the actual study of category theory will remain a fringe subject, just like the study of set theory is today.
Why are they niche subjects?

>>10186181
In the case of set theory, because a lot of set theory involves studying the combinatorial properties of very large cardinals whereas most mathematicians will rarely need cardinals larger than N, R or 2^R.
Now of course, I was caricaturing a bit for effect. There are nontrivial applications of set theory to analysis, dynamics, operator algebras etc. but I (and I am not alone) have this distinctive feeling that the problems that set theorists are interested in, even when they have to do with mainstream math, are somewhat orthogonal to the preoccupations of "normal" mathematicians.
Logicians are always a little off, they are to normal mathematicians what mathematicians studying mathematical physics are to physicists.

>>10185148
>How is it not?
Categories are not mathematical objects.

>>10186813
Categories are both homes to mathematical objects, and mathematical objects themselves :)

>>10185651
All math that isn't analysis is either philosophy (logic, so still respectable) or fucking shit alg*bra playing with silly little toys and making unstable towers out of children's building blocks or le ebic meme number theory autism reddit math
analysis, on the other hand... BASED and REDPILLED!

>>10185525
Baked and gaypilled

>>10186840
> What is analytic number theory?
> What is arithmetic combinatorics?
> Who is Terence Tao?

>>10185198
>>10185216
Cats are most powerful among all wizards of the tools of mathematics! :D

Haha I can make the shape of a peepee with arrows and get away with it

>>10187505
analytic number theory is ok (even if it's a bastardization of analysis for a discr*te object of study)
arithmetic combinatorics, like all other number theory, is a meme and the people who study it belong on reddit

>>10185386
>Objects
If you are doing cat theory with objects you are missing the point. All you need is a collection of arrows, and a collection of triplets of these arrows which satisfies some conditions to represent composition (3rd arrow is the composition of the first 2), and a subcollection of the collection of arrows to represent identity arrows.

>>10185058
Ok

>>10188089
There are lots of semantics you can apply to a category. Only a pretentious undergrad would argue that objects have no use. It's like arguing for a logic without predicates (actually though, google categorical logic).

>>10188094
It has a use, as a derived thing, not as a fundamental thing like arrows are.

>>10188104
Whatever, enjoy having fucked up convoluted definitions for basic category theory concepts. retard.

>>10188105
O no, I have to define objects in terms of arrows before continuing with them, once.

>>10187529
STFU THERE IS NO CORRELATION BETWEEN SCIENCE AND ILLIUSION.

(We only say this to demoralize you so you'll never try and make this association again, thus ensuring we have market monopoly)

What practical applications does category theory have? None? Disregarded.

>>10185081
underrated

>>10188221
>PrAcTiCaL aPpLiCaTiOnS
kys brainlet engineer

>>10188221
One application is monads in programming that makes software safer and easier to reason about.

>>10185058
>Category Theory is a mathematical formalism that is an alternative to set theory
Yikes

>>10188108
hurp durp ur missing da point

>>10185058
Category theory = autism
autistic people put things in category

>>10188221
There's a lot in mathematics, physics, computer science, and logic. The biggest practical applications are probably in programming language theory and quantum mechanics.

That said, it isn't as big or complicated as people make it seem. Learning the basics is about as difficult as learning graph theory and learning the more complicated stuff isn't all that much harder. It's only so polarizing because for some reason it's become a thing that stronger undergrads use to be pretentious and hold over weaker undergrads despite the fact that either could learn it trivially if it's explained clearly.

>>10185228
>And before that I read algebra chapter 0 by Paolo Aluffi.
Kind of a shitty book for learning category theory imo. Instead of first teaching you category theory and then using it to teach you algebra it tries to teach you both at the same time in a way that can only hurt your understanding of both subjects.

>>10190210
Monads are pretty cool but they're just one tiny way in which category theory can be applied to programming languages.
More generally there is a family of correspondences between type theory, category theory, and logic. The most famous example is the Curry-Howard correspondence where the typed lambda calculus is equivalent to intuitionistic logic which is the internal logic to cartesian closed categories.
The idea here is that if you're developing a programming language then you can choose a type system (i.e. type theory) and use the corresponding category to reason about it's algebraic structures and corresponding logic to reason about what it's "really" doing (the semantics of the programming language).

>>10190502
That's not how it works, category is kind of a misnomer.