I am squirtle from Super Smash Bros. Brawl (Wii 2008) with photoshopped sunglasses
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@עמיתלרמן
6 күн бұрын
Abstract nonsense is a real defined (not mathematically) thing that mathematicians use in language. It means a long proofy piece that the communicator should be familiar with. There is even a wiki page for "abstract nonsense"
@twokit
23 күн бұрын
Ah, but being a proof by contradiction this requires classical logic. Now make it constructive.
@user-pr6ed3ri2k
26 күн бұрын
coker
@jonasehrhard7762
Ай бұрын
I might not be the first person to note this, but to define $g$ you should really reverse the direction of the ray, i.e. start in $f(x)$ and go through $x$. This way you get automatically $g(x) = x$ if $x$ is on the boundary. Otherwise your map $g$ will not be continuous.
@jakeaustria5445
Ай бұрын
Thank you
@lwmarti
3 ай бұрын
Q: What do you call someone reading a category theory paper? A: A co-author.
@quantumgaming9180
10 күн бұрын
Bro... that sad 😢 And funny 😂
@df-163
3 ай бұрын
Why is the function g surjective on the unit circle? I didn't quite understand the reasoning for this
@fouche_ehcuof
4 ай бұрын
Jacob Lurie is one of the most clever mathematicians of this generation, but the idea that he invented higher category theory is just laughable. Higher category theory existed before Lurie was even born.
@Sara-cy3wo
4 ай бұрын
Wow I am surprised this made so much more sense than a course I took on algebraic topology 😊
@2394098234509
4 ай бұрын
Oh boy this will come in handy next time I'm holding a 2-dimensional disc in one hand and another 2-dimensional disc in my other hand and I need to know whether there's a fixed point on the two discs wrt a map.
@newwaveinfantry8362
5 ай бұрын
Brower's fixed point theorem doesn't necessitate the concept of a category and predates it.
@citricdemon
5 ай бұрын
Isn't there an obvious application of category theory in quantum mechanics?
@chapol8573
5 ай бұрын
I understood nothing.
@trymbruset3868
5 ай бұрын
I never realised that "figuring out the fundamental group" is a functor. Colour me impressed I learned something!
@peterchindove7146
5 ай бұрын
Absolutely fantastic concise video. Thank you.
@peterchindove7146
5 ай бұрын
You could have actually mentioned that the vector gauge field can be understood as an element of bhTop and that this element explains phase changes in charged in particles in the absence of a magnetic field...but hey, what does an applied mathematician know?
@ratfuk9340
6 ай бұрын
more
@broccoloodle
6 ай бұрын
this is 100% real world application of category theory 😂
@sunnytokas3339
8 ай бұрын
There is a a way simpler way to solve this
@jangronwald40
8 ай бұрын
Get a gf
@jangronwald40
8 ай бұрын
And i dont mean the class of general frames
@SystemsMedicine
8 ай бұрын
Maybe I’m simply misremembering here, but I thought the (old) standard proof for fixed point mappings of a disc involves Schlicht maps, and predates category theory. [I appreciate that the category theory version may be more abstract, but mentally rolling around in more ‘earthy’ geometry has its pleasures.]
@mappingtheshit
8 ай бұрын
2:34 I spotted a man not so bright
@TensorLiquidExp
8 ай бұрын
Usually people who can appreciate CT at least have basic understanding of some algebraic or topological structures and their standard constructions, because the theory is about structures and relations. Jonathan Blow barely understands root formula of quadratic equations, why would he expect to be "impressed" by category theory? This is like a three year old who can barely speak human language and never touched a computer before but want to be "impressed" by C++ code so he looks at its syntax then throw a tantrum when it doesn't make sense.
@cube2fox
9 ай бұрын
Timestamp to "The First Real Application of Category Theory"?
@Assault_Butter_Knife
9 ай бұрын
Real world applications to abstract nonsense I've been studying for years? Dude I'm soying out
@TensorLiquidExp
8 ай бұрын
this comment and the video pretty much summarize the soy math students (bro learned some undergrad math not fully understanding it yet want to explain it to people by cramming memes into the exposition and namedropping some famous mathematicians) The only way you can claim CT doesnt have 'applications' is by insisting on avoiding Categorical language entirely which is a very contrived and stupid gymnastic way to look at structures I dont know who still do it. People who do modern algebra and geometry but insist on avoiding CT at all cost are just stupid, I cant take them seriously. Any attempt to get rid of category theory in one's thinking about structures is almost as stupid as attempt to get rid of set theoretic language in elementary math, sure it might be possible, but why would someone gimp themselves that way? (btw why dont these people ask about "real world applications" of set theory? it just shows basic misunderstanding about languages and structures in math)
@BLVGamingY
9 ай бұрын
at 9:30 I'm confused as to how g is an isomorphism so this whole entire video has gone over my head
@Milan_Openfeint
9 ай бұрын
I don't know how anyone could understand anything from this video. Flashing text, distracting typos, everything going too fast with no direction, introducing a gazilion new terms every minute, and the result isn't even there. Maybe the subsribers of this channel are used to this style, but as a standalone video, it's a waste of time to watch.
@Custodian123
9 ай бұрын
Yes.
@BenfanichAbderrahmane
10 ай бұрын
Is this true even if the space is not complet 😮
@bigzigtv706
10 ай бұрын
A monad is just a monoid in the category of endofunctors, can you explain this please
@nameq
10 ай бұрын
CATEGORY THEORY WAS CREATED TO NORMALIZE TERMINOLOGY ACROSS DIFFERENT ALGEBRAS. IS THAT NOT ENOUGH
@nameq
10 ай бұрын
if you learn it you will learn other areas of math a whole lot quicker! because there's always some dork who would exhaustively explain any area of math in categorical terms so if you know them you will pick up the theory faster and with less doubts! its roots (as in how it was created) lie in abstract algebra (the abstractest of them!) so arguing that it has "practical" applications should not be the focus! its main application is communication
@nameq
10 ай бұрын
i have no idea about the competiotion though so sorry if i m missing something
@TensorLiquidExp
8 ай бұрын
It is never enough for dumbasses. When it comes to paradigm change, there are always people who insist we evaluate the new paradigm in the old paradigm's perspective, when they should've done the opposite. Remember people used to think Galois' idea was worthless because it doesn't actually solve any equation with some root formula (lol) The only way you can claim CT doesnt have 'applications' is by insisting on avoiding Categorical language entirely which is a very contrived and stupid gymnastic way to look at structures and their relations I don't know who still do it. Many people expect a 'clever trick' to solve some hard problems, CT is not simply that, it's a new language. Your formulate the "impossible" problems in a new theory (e.g. Grothendieck's schemes) built on top of this language, then you can see its ingenuity (e.g. proof to FLT)
@marufmamun6592
10 ай бұрын
I love that something like this exists at all for algebraic topology😆 The Grothendieck phonk was the icing on the cake
@officiallyaninja
10 ай бұрын
3:10 I wasn't expecting to see NL here 💀
@devrim-oguz
11 ай бұрын
Here we go again…
@aleksrandompianostuff8749
11 ай бұрын
This video was needlessly jargon heavy, main ideas were obscured and not explained well, the retraction was defined with the ray going the wrong way…so many issues :( The actual category theoretic idea behind the proof is much simpler than this video shows
@TheGuzzler679
11 ай бұрын
sick Platinum preppy
@baronvonbeandip
11 ай бұрын
Also, yes, we always stan Grothendieck. A real legend amongst legends.
@baronvonbeandip
11 ай бұрын
Category theorists are the most online of the mathematicians. Their memes go hard
@__________________________8790
11 ай бұрын
The first picture is just gold!
@Lammot
11 ай бұрын
hm. what?
@karvasker3819
11 ай бұрын
recently had to learn a lot of this to understand a paper titled "A remarkable identity for lengths of curves", recommendations working magic
@alejorabirog1679
11 ай бұрын
lol. nice
@conrada5
11 ай бұрын
One of the greatest mathematics expositions of our time
@joelgomez9073
11 ай бұрын
The GTM memes are killing me. I love it
@kaiservenom270
11 ай бұрын
So... I'll want some fries too.
@takatino7556
11 ай бұрын
northernlion mentioned !?!?!?!?!?!?!!!111
@diffusegd
11 ай бұрын
I am a applied mathematician and I am satisfied.
@yaminnew2953
11 ай бұрын
You messed up the definition of g. Its not continous on the boundary, the way you defined it in the video. Also, I don't think this really illustrates the power of category theory so much as cat theory is a convenient language to phrase the homotopy invariance of pi_1. You don't really need cat theory to do this proof.
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