Відео

Waiting, tnx

Very good addition to contemporary UA-cam mathematics material

nice, do more pelase

What does the expression λx.f x mean at 14:36, when x has not been defined in our context like with the λ-abstraction and β-reduction rules?

Wow, the connection between the conditional and functions blew my mind! But I'm a bit confused about the nature of what exactly HoTT is and its connection to logic. As I understand it, HoTT is not built on first-order logic like ZF, but rather logic "comes with" HoTT. So are inference rules like modus ponens part of HoTT? and does HoTT have a list of rules and axioms like ZF? Also if i'm not mistaken, we're also using the Deduction theorem to prove statements in this video, correct ? (Is that also part of the specification for HoTT?)

Really enjoying this video series so far. Coming at this from a professional software engineer POV with a casual interest in mathematics, it's easy to follow (thank god you didn't go too deep on topology or else I'd be lost). Never even occurred to me that type systems could be used for something this powerful.

Fucking Legend

Gonna swim in -the- a Specific Ocean

Will you do videos on linear logic?

In grad school, it was especially the algebraists who never said WHY we should be interested in the subject. What is the psychology here?

I want to learn type theory enough, to understand HoTT. Should I start with your videos or study something else before?

HOLY COW SCOOB THAT CAN'T BE PROPOSITIONAL LOGIC THAT'S M-M-M-M-M-MAGIC!

You are an extremely good teacher. Clearly, you have put a lot of effort into making this and it shows. You are not boring like many others and you really made me enthusiastic about the uses of HoTT. Thank you!!!!

dude it`s just awesome how simple you make this topic

Nottingham? You should do a video with Brady Haren!

Lmao I watched part 2 yesterday

I F***ING LOVE PRODUCT TYPES WOOOOOOOO

This is so cool I finally found a good series on HoTT

TOOB SQUARED!!!

I've seen lectures on a little bit of type theory that looked more like pure math than computer science. I've also gotten a little bit of that from chatgpt under the right prompts. Are there any text books that give a mathematical treatment of type theory with little to no mention of computer science? Thanks in advance

Can we in a way see \beta and \eta as adjunction units and counits in a sense?

This is exactly what I was looking for. It clicked at 8:26. Thanks so much!

I really love the presentation style and examples overall, it really gives the series its own personality. Keep up the good work!

Hott starting from basic type theory (for non-programmers)? Seems like a long way to go…

These videos are amazing thank you and please keep going

0:50 - of course there is: (string | number) - and you cannot do anything with it, until you check which it is (except pass it around, ala T)

I don't like math being a social activity. Convincing a bunch of apes does not constitute a proof to me. I hated that at Uni. - Where is the proof that your proof is correct? - Oh, you convinced me? Good job, but I'm just a stupid monkey, why should that matter? - Sure, if a monkey finds inconsistency, that is great, but if not, how is that a proof? - That's not math. That's rhetoric, and we all know how well that can go...

1:12 - I wish this was considered even for primary school maths, lol. - That is the the takeaway most students have from just learning any algebra.

10:24 I feel like your use of the word "faithful" here was a bit of a hint :)

Look what I found today 🎉

Beta and Eta Wooooooooo let's go!!!

Best HoTT channel is back!

Best HoTT content. Please keep going!

Yyaaaaayyy. Been waiting for this series. Making my way through the HoTT book currently. Thanks!

Eyyy first! I love your videos; you make this insanely high-level content feel so easy and intuitive

It's better to typehint your function def reactorTempFactor(n: float) -> float Your version was kinda type correct it just has a return type of float | str or a union type of a string and a number

It would actually be "Was ist und was soll HoTT?", because HoTT is singular ;)

This is great stuff, thanks

Absolutely brilliant video series! Subscribed.

1:29 The Game of the Century: Byrne - Fischer (1956)

Loved this video. But the sound that the marker makes on paper is a bit irritating

For introduction rule for beta I suggest providing the type for the conclusion of the inference rule.

Great video. Why do the rules only let us form application terms when the contexts of the function and argument are equal? If the contexts are different, is there a way to merge them together to allow the application?

Your tagging of the agda commands on screen is a fantastic idea. Loving these videos, can't wait til you get to Cubical Agda :)

Question: if = is judgmental equality in Agda, what about the fact that we can have a proof that two values are equal as an argument to a function, say? fn :: {A : Type} {a b : A} -> (a tripleEquals b) -> (b tripleEquals a) fn refl = refl The (a tripleEquals b) type is a proof that the two values are the same, which if I'm following correctly, means that they compute to the same thing, therefore are judgmentally equal. But we need to have tripleEquals in the type signature. Is the equality type also a representation of judgmental equality?

I found this series today, binged the whole thing, and I love it. I am now going to learn agda. Thank you so much.

At 6:33 (ua-cam.com/video/97twa7KgQ6k/v-deo.htmlsi=fUEOt3_Obyk2RV-c&t=393), I am slightly confused about the rule (Gamma |- a : A)/(Gamma |- a = a : A). I believe the type of a = a should be Prop (or Type)? What am I missing here?

Dear Jacob, this was purely amazing.

Very cool

many things in computer science is homo. Homoiconicity, homomorphisms, homotopy type theory. Its very interesting