Disclaimer: Followup may not include breaks (like fact 16)

@@louiswong921 NOOO

Sometimes the Funnest part is the truth...

Yup. Thanks! 👋👍😀👍👍👍

And it was good indeed. I saw it first. Or at least watched it ig.

Thats wild mate, like "a tensor is an object that transforms like a tensor"

@@VincentKun A vector is an element of a vector space

I'm pretty sure I've heard the latter way more often than the former. I never realized there's a natural transformation between them in the categories of jokes.

A monad is a category where objects are the image of some functor F and the arrows are of type A -> F(B). The requirement that a monad forms a category implied in particular that composition of those arrows (however it might work) ought to be associative and there ought to be an identity arrow, often called „pure“ (or „return“ if you look at it from the point of view of operational semantics).

@@markuspfeifer8473 You're referring to a Kleisli category of a monad.

It was never told that it was a joke ;)

@@Sciencedoneright read fact 1 again (oh wait is it a liar paradox?)

​@@KIT8882 oh 😂 I forgot, haha

Genius, isn‘t it

Read this comment right after that

it's the moment, when you realise that the "coco" in "coconut" is a double inversion, making it redundant and can therefore be safely removed... leaving you with just "nut"

@@mini_bomba but I’d like to remove excluded middle please, so coco doesn’t necessarily get you back to the same place

So a cocone is just a ne?

@@reo101 we are the coauthors who say ne! NE! NE! NE!

@@DiracComb.7585 Ah, a constructivist!

As your coposter, I couldn't agree more.

I see no correlation in the replies to this comment and the original comment!

Uncreator, unpostor, unrrelation, unmment

If category theorists were in charge of naming things, children would be called "co-parents".

@@strangeWaters they did start as haploid cells cooperating via copulation

Apache Spark is written using functional programming in Scala. Spark is the most widely used computing infrastructure for big data machine learning. Functional programming is very suited to parallel computing.

@@jimbocho660 yeah but thats nerd shit

have you heard of... Rust? :D

@@koacado Rust is many things, most of which I like, but it is not a functional programming language.

Beautiful short code. If you understand it... *IF(!)* you understand it...

Nah a comathematician turns theorems into coffee. Therefore, coffee is isomorphic to theorems, and so my proof for the Riemann hypothesis is... a half shot of Espresso

This is my favourite joke in mathematics, glad to see it here.

Wouldn’t it turn ffee into cotheorems?

@@jonasvanderschaaf no, arrows must be reversed! (the joke is on the common saying "a mathematician is a device that turns coffee into theorems"

@@c.a.7058 you're right of course, I must have been tired from trying to understand what the everliving **** the Yoneda lemma actually means

Every second that passes you know less math. We all do.

Well technically new math is developed at faster pace than you can consume, so every second you know less _part_ of totality of math whether you watch this video or not

There is no math. There is only maths

It's an example of coeducation. Everyone knows you learn less in a coeducational dorm.

Don't worry. I spent 4½ years studying Category Theory in grad school. I 𝘥𝘦𝘧𝘪𝘯𝘪𝘵𝘦𝘭𝘺 know less math now than I did when I started that journey.

You're object of an elementary topos

@@Salmanul_ it's stalin

cool but having a picture of a genocidal dictator as your pfp is kinda cringe

just tell them that a monad is a monoid in the category of endofunctors

@@ilonachan so true

Or just the worlds most abstract and theoretical set up for a your mum joke.

Yeah I sensed that terminal object before I even finished laughing!

Only if I also remain full and essentially surjective on objects. (Sorry, it’s another category theory joke, couldn’t resist.)

@@OliverLugg so if you transcend everything you just get insane? Nice Easter egg @god (just a joke this is a great video)

@@mrOverYeff this whole vid is a joke lol

and he did....

*cohelpful

@Oliver Gottkehaskamp i'll have to disagree... This has been EXTREMELY helpful for my facial muscles; they did some work-out during this video like they haven't done in weeks (or maybe even months). xD

@@irrelevant_noob You missed the joke I'd say. Maybe check the video title again ;)

@@scialomy That fella just implied that the video is not doing its job correctly :^)

365th like

help

@@VerilyVeritasValio no

If there’s a black whole, is there a black separate?

@@eddie-roo that would just be a black cowhole

@@Dong_Harvey a co-whole is just a cow-hole

"I use Haskell, BTW" Haskell and Arch Linux are isomorphic!

This is extremely true.

That coauthor joke worked on so many levels lol

He just followed up with a real one!

It's cocategory theory

That's actually a proof technique in category theory called diagram chasing. You just ramble and point at parts of a diagram while pontificating about preimages and morphisms. For example that's how you prove the snake lemma and it's an incredibly annoying proof to do any other way. Like writing it down is incredibly tedious so most authors only do one part and leave the rest as an exercise.

@@abebuckingham8198 I remember the first time I saw diagram chasing. I's a frightened undergrad until that moment, when I realised I was allowed to do that sort of thing. Just draw the shapes that make sense in your mind, gesture vaguely at the blackboard, saying "See?"

I feel like the proper way to communicate a diagram chase is a flipbook. But the journals won't let me staple one to my paper :(

Economics?

230th like

Achieving ignorance is the beginning of understanding.

@@walterbushell7029 achieving KNOWN ignorance, rather?

You co-learnt the material

You are obviously therefore in the category of people who are easily trapped by theories about nothing. Bon voyage to lala land.

Welcome to the study of Category Theory. It's like that all the way down.

the joke gets better the more you think about it

oh god I didn't get it until I saw this comment... that's hilarious

To be fair, you have to have a very high IQ to understand Fact 23. The humour is extremely subtle, and without a solid grasp of theoretical mathematics most of the jokes will go over a typical viewer's head. There's also Oliver Lugg's nihilistic outlook, which is deftly woven into his characterisation- his personal philosophy draws heavily from Alexander Groethendieck's literature, for instance. The fans understand this stuff; they have the intellectual capacity to truly appreciate the depths of these jokes, to realise that they're not just funny- they say something deep about LIFE. As a consequence people who dislike Fact 23 truly ARE idiots- of course they wouldn't appreciate, for instance, the humour in Oliver's existential catchphrase "What about maps between Functors ?," which itself is a cryptic reference to Samuels and Saunders paper What about maps between Natural Transformations?[Berlin 1969, Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques]. I'm smirking right now just imagining one of those addlepated simpletons scratching their heads in confusion as Lugg's genius wit unfolds itself on their television screens. What fools.. how I pity them. 😂 And yes, by the way, i DO have a Fact 23 tattoo. And no, you cannot see it. It's for the ladies' eyes only- and even then they have to demonstrate that they're within 5 IQ points of my own (preferably lower) beforehand. Nothin personnel kid 😎

@@misiraly this is some of the most adept mathematical shitposting I've ever witnessed

Fact 17 even more-so

remind me to never touch Haskell

As a hobbyist Haskell programmer still in high school this video made some sense but I didn't understand the Yoneda Lemma stuff (heard of it but have never bothered to look into it)

@@shmoobalizer To be fair, you don't actually need to know any category theory to use Haskell. It got a lot of concept from category theory, but the theoretical background is meaningless as far as actual programming is concerned.

@@shmoobalizer NEVER touch Haskell !!!!

@@markhathaway9456 thx

Monads are very useful for encapsulating state and sequencing, and the monad operations form a category.

its also not really an application of category theory, as it is not useful itself :D

@@SteveBobbington i know there's a pun in there somewhere but: Just beacuse B is not useful, that doesn't mean A→B isn't an application. For example: suppose that the above statement is true. One application of math is to calculate demand for food (A→B), and one application of that calculation is to not waste food (B→C), and one application of not wasting food is increasing the amount of useable food (C→D), and one application of increasing the amount of useable food is increasing humans' lifespan (D→E), and one application of increasing humans' lifespan is making more jokes (E→F), and one application of jokes is... Well, jokes are useless things, and that makes E→F not an application, and that makes D→E not an application... and that makes A→B not an application. So now, do you believe math doesn't have any applications? I think I ran into two fallacies (if that is even the right word), 1- I conflated math having a use in calculating with math having only one use. But more importantly, 2- I measured "usefulness" of a given thing by the number of applications it has. which, you know, causes anything that is not evantually an application of itself to fail (teaching history helps students to become history teachers so that they teach students so that....) "=" useful, but things that evantually end aren't.

@@xXJ4FARGAMERXx *screams*

​@@NXTangldoesn't everything form a category? Isn't that the entire point of category theory?

Should I get a phd in category theory just so I can get paid to spout silly sentences like these?

i have no idea if what you said is true but im liking this anyways for how absurd it sounds

Based Grothendieck

@@taggerung_ Truth is sometimes stranger than fiction and with mathematical geniuses, truth is sometimes far stranger than even Theater of the Absurd. To borrow from Hardy's comment on receiving Ramanujan's initial correspondence: I couldn't make-up such things; nobody would have the imagination to dream up such things. By the way, I have a great photo of Sammy Eilenberg reclining on his sofa, contemplating mathematics in his Greenwich Village apartment and using Chola bonzes as paperweights on his piles mathematics reprints. Those sort of Chola bronzes sell at $500,000 to $2,000,000 at auction these days, and he was well aware of their value. And Grothendieck was quite the eccentric sometimes self-publishing in mimeograph format. I have one of his rare mimeographed books (in French) and sadly, it's fading.

I like that in the question of one space or two between sentences that you went for the meme "why don't we have both?"

my favorite mathematician together with Conway

Do you still have it? Maybe the slides or something? This really interested me, I would so go to a talk about this topic

@@karen-7057 I can't find it. I did it about 10 years ago and it's not in my GDrive, MSDrive, slides, slideshare...neither on my website. I still remember the content though. It showed the link between complex numbers, the plane and matrix. It also showed the relation between a sum number game and 3 in a row (tic-tac-toe). Also shown how to write for loops as while loops. And how grey code can be found by navigating a n-dimentional square. Also, SQL vs Set theory (But I learned that this one breaks quickly and relational algebra is a better fit). Very simple stuff, but useful to understand for future analyst developers (that was the target audience).

It is a well known result that the main practical application for Haskell is that it provides a practical application for category theory.

Autistic weeb has a useless masters in Algebraic Topology and Cohomology Theory? Not surprising. The period after WW2 has certainly been fruitful in the production of bullshit from pure mathematics and philosophy. Although some of the crap from the likes of Gregory Cantor came way earlier. Mathematics that doesn't describe numerical or value relationships in reality simply isn't mathematics.

@@BumboLooks Jesus christ, who hurt you? The first sentence of that reply was random baseless ad hominem attacks, and the rest just seems like pure speculation and one hell of an odd, bold take about what constitutes mathematics. Maths needn't inherently relate to reality. But almost any field of maths does somehow link in anyway, even if in a really obscure fashion. Maths isn't even easy to define - but I'd say "study of patterns", is good for a concise definition. Which essentially means anything goes, provided it's defined consistently. You can still look down on it, but it's mathematics nonetheless. Honestly you sound like somebody who got salty about not being able to understand some math once upon a time, and took that to mean that whoever came up with it was confused, rather than perhaps the person looking into it, and then that spiralled into a hatred for any and all modern mathematics, which seems to even have extended to philosophy because why the hell not? The only thing missing is a "back in my day" quip. Let people learn what they wanna learn - it's often not helping anyone, but it definitely ain't hurting anyone, either. Throwing insults at people can hurt, though - it's not a chore to just be nice, or at the least not be outright rude if unprompted? Or, you're just trolling - but I know you aren't, I just like to leave that option open as a catch-all.

​@@BumboLooksShouldn't you be pumping my septic tank right now? Maybe filling some potholes? 🤣

@@user-pi1vz1de3u What does that have to do with mathematics?

Only a pure math student would feel the need to put "(not applied)" lmao

I've never studied category theory and I've still found myself trying to read that somewhere

A monad is a monoid in the category of endofunctors.

it's a really good way of remembering it tho! You just write down the necessary commutative diagrams for a monoid in a strict monoidal category and then you instantiate it to End(C), and there you have it: the definition of a monad.

I'm summoning the tantacrul gang

This is so true #jank

Also my buddy MusicMelts wanted to say "Recalcitrant"

Categories are getting worse every year.

Good work, team!

If you wanna sound less friendly, you could say “rdially” instead of “cordially”

Correction: Category theory ➘ this exact video ➙ Terminal object ⇄ why Math in general ➚

Both of your comments are difficult to parse (at least on mobile) because of it being unclear what parts of it is due to wordwrap and such

Pretty sure “why” is the initial object for all maths.

@@Axman6 The initial object for lots of modern maths is a disjunction. PUBLISH v PERISH.

Yes, reminds me of cardinal numbers and dimensions.

Maths is a Ponzie scheme.

Not the "exact" same, remember FACT 8 (4:04). The ALMOST exact same. ;-)

Gory is an adjective.

Is this demonstrated in a 2-category? like how they have morphisms between morphisms?

@@mastershooter64 he made another video actually describing the various parts of category theory, but roughly: you can keep repeating this forever. every morphism is an object, so you can morph between those, and morph between those, and morph ...; idk the definition of a 2-category though

@@MrRyanroberson1 Guess you bailed out before fact 15 (6:22)? :-B

@@irrelevant_noob nah i just comment as i watch the video

@@MrRyanroberson1 still, did it take you 5 months to not advance past 7 minutes? :-s

Sooooooo by applying Yoneda lemma I can conclude that you might as well *not* to know what it means since your lack of wish to share the knowledge makes it behavioraly undistinguishable from the state that you claim

@@user-jr7ns3bl9c That would be true if not for the fact that a monad is actually a monoid in the category of endofunctors. Classic beginner mistake.

Aannddd I wrote this comment before u brought up Haskell lol

Why not a half group or group or sth?

Cozelenskyy started a cospecial cooperation and invaded Corussia.

cubes!

@@drdca8263 fair enough! :D happy new year

in fact we should think of a category of only existing of morphisms with thinking of the objects as identities

​@@marshmelo4832 This doesn't solve the fundamental problem I was referring to, because "all" morphisms still don't form a set. Besides, I don't think this point of view is generalizable to infinity-categories.

@@AlexanderShamov Why do all morphisms not form a set?

@@SpaghettiToaster If you learn the definition of a category and treat it the same way you would treat any other algebraic structure, you'll miss the all-important nuance: namely, that the naive notion of isomorphism of categories is "wrong". The "correct" notion is called equivalence of categories, and it's much weaker. Everything category theorists ever do is invariant under equivalence of categories. But neither the set of objects nor the set of "all" morphisms is invariant under it. The broader picture is that equality of elements of a set, isomorphism of objects in a category, and equivalence of categories are really just the beginning of a hierarchy of higher dimensional notions of "sameness", and the classical set-theoretic foundations only capture the first layer of this hierarchy. In order to "feel" the whole thing we will probably need to replace set theory with some version of homotopy type theory, but that is still work in progress.

@@AlexanderShamov I still don't see how elements categorized as "same" by whichever means do not form a set.