@@Eyesomorphic Please make a course where you teach Type theory but do it by simultaneously teaching ALL the prerequisites and building blocks that we need to know from logic and proof theory. I would be so happy paying for a course if you can make it just as intuitive and visual as this video.
tbh i thought my real weapon was a combination of logical reasoning and math theorems.. i used a lot of statistics and logic to check how likely a statement is to be true or not given for example, if the person claims that 10 rare conditions were simultanously true, that's probably bullshit. but if it was a smaller set of conditions, or there is proof that some of them are true, the situation changes. or for example, using advanced counting and probabilities to win card games and impress ppl
@@Eyesomorphic Graph Theory is the abstraction of relationships? **Put down glasses** I've studied to PhD all for this and yet I'm still a single dog. The graph, does not work!
@@jacobsjdin4057You can access it for free online if you'd prefer, but obviously buying the book and supporting his work is great too. It was a culmination of Bartosz's posts made on the website I listed in the description. He has a lecture series as well that follows the same content
Yes, I was introduced into Category by Bartosz's UA-cam series many years ago, didn't understand all but later from other books/videos then came back to Bartosz whose videos the BEST.
This video is a pearl in the middle of the internet ocean. It's fascinating how you explain how some subjects of math are the abstraction of things we already use in Simple math. As a student of computer science i apreciate a lot this work
learning about lambda calculus is how the magic of abstraction "clicked" for me. Being able to define problems away is just mind-blowing to me still lol. "This function is a number now because I say it is" is just amazing
That's really reassuring! Keep an eye out for the next installment in this series, I took a rather long hiatus but there's a new video in the works currently! Thanks again
Instantly subbed, this is one of the most “eye” opening videos on mathematics that I’ve seen so far, you took an “abstract” concept and broke it down in a very digestible way, one could say you used abstraction to minimize the number of elements it takes to convey the underlying structure of “the utility of abstraction within mathematics” lol. Thank you for the video!
I have been a haskell programmer for quite a while, shared this video with some friends as I think it makes Category Theory really approachable! Well done!
As a first-year Math Degree student, I can that almost all (if not all) Mathematics can be described by the art of Abstraction. For example, if you want to prove "The sum of even numbers is even" you could try to check one by one, but you'd just never end because there're infinity even numbers. Instead, you can consider work with only two objects "A" and "B", which are two representatives of all integers that verify the property of being even (formally, if we consider the universe "Ω" to be set of all intergers: "∃n(A=2n)" and "∃m(B=2m)"). In other words, we've just removed all particular characteristics of individual even integers to stay only with what characterizes an "even integer"; we've made abstraction. Where the magic lies is that if you manage to prove any property with "A" and "B" (such that "A+B" is even), you're proving it for any two even numbers (actually, "killing infinit many birds with one shot"). 🔥
I’ve watched like 5 introductions to category theory, but your analogy of what algebra is to numbers is what category theory is to composition was the priming I needed. Heck! I learnt algebra before. And I know how I learnt algebra. For me learning algebra involved doing a lot of examples and then creating algorithms for it once I got a good grasp of the subject. So yesterday I started with an exercise heavy book to category theory (spivaks category theory for the sciences) and it’s exactly what I need to understand it. He introduces ologs that are the first real objects I studied seriously that don’t fulfill composition. Thanks a ton on getting me started!
That's great to hear! It took me at least 10 different books and lecture series to fully get to grips with the principles of category theory, and I guess this video is the culmination of that, and the progression that felt most intuitive to me. Good luck on your quest!
I dont regret a single second of watching this video, you completly changed my perception of not only mathematics, but the whole reality. Thank you for this amazing content, you defenitely deserve a sub! 👏
Great video. A young kid could understand this, and it would likely turn them into mathematicians! The world needs more mathematicians, especially now. Bravo.
Welcome to UA-cam, Eyesomorphic! Stunningly simple and accessible presentation that couls invite more people into this beautiful area of study. Hope you could go deeper into category theory and present useful results in a similarly accessible fashion. Looking forward to them!
Apparently this is your very first video (on this channel). Obviously the algorithm knows what I like. The channel name is awesome. Isomorphism explains everything. Looking forward to the N+1 video.
What a beautiful introduction to category theory. As an applied guy who knows nothing about this subject, I enjoyed it a lot ! You got yourself a new subscriber, looking forward to your future videos :)
instant subscribe! i got my b.s. in mathematics last year, but real life hasn’t given me much time to keep up with reviewing what i learned in undergrad. this video made me feel like i was in one of my theory classes again! ❤
When I was 14, my relationship with functions was "it just a name we give to an expression" like we give π to 3.141592..., or e give to 2.7182... When I turned 15, I started to learn programming and it completely change my mind about how functions work. Yes sure it still is a name we give for an expression but the way we can use any kind of input and any kind of output that make me surprised, then I did a little research and I found out that functions in math is also the same, they're freedom, you can do what ever you want; don't just stop at the Natural numbers or Real numbers, start making your own numbers like a set with even numbers, or a set with prime numbers, or a set with your family members and we can make a function on those sets too. That kind of freedom make me love math❤ The way you explain everything reminded me of that feeling, feeling of I can do what I want with math. I hope you can keep up the good work!! And welcome to youtube🎉
Such an amazing video that explains category theory in a remarkable way. I have been looking for category theory videos but I never found any with this level of articulation and quality. Your hard work to put together explanations and graphics deserve great applause 👏
Wow, man, you're really really good at this, your approach to mathematics and your skill to teach in a simple way with many examples is amazing. Please, keep making videos, there's nothing like this on UA-cam.
Thank you for creating this! I've watched several intro to category theory videos and even started some books and courses, but this is by far the best explanation I've seen!
@@Eyesomorphic Please, continue such an amazing work. We need explanations like yours and 3b1b, making math much more approachable. You actually inspired me to learn more about Category Theory :) It blew my mind the same way, as the Group Theory did with its relation to physics and the conservation laws. On the side note. What is the answer for the question about the composite function of “isInteger” follows “sqrt”? I am a programmer and you got me curios, isn’t it a function, which checks whether a given integer is a square of another integer?
@@hellomylittleboy The function isInteger ∘ sqrt is indeed one that maps an integer to true if it a square number! Well done! Hopefully this small exercise demonstrates how the heart of programming is simply chaining together smaller functions into larger, more complex ones. This is why we can model them so well as a category!
Beautiful presentation of category theory. I enjoyed how Alice and Bob's speech colors were mapped to a (for Alice) and b (for Bob) respectively as a way of abstraction which then allowed me to understand the rest of the video, as though you created a rhetorical category to be an analogy to mathematical categories.
Hey, this video is seriously incredible. I remember you commented one of my videos a couple weeks ago and I knew recognised your name. Seriously this video is legions in quality above mine and genuinely congrats and good luck in the future!
This video has really helped me on a personal level, I've been undergoing changes in my thinking pattern recently, influnced by formal logic, and abstraction was a huge part of it. I've being trying to articulate my process of thinking, but I think this video on abstraction really hits the nail on the head. Thank you.
unbelievable simple clear explanation of abstraction and category theory fundamentals. I really thank you for your effort, I would absolutely like to see more of these please. Thank you again
Beautiful simple, clear explanation! Thank you for abstracting math education to its essence. I believe a ‘top down’ approach to math is as important as building a bottom up foundation - it helps to build motivation, and provides a framework to hang the whole of math. Would love to see your take on linear algebra, calculus, geometry, etc, and how they are different aspects of the same concepts.
Outstanding! I just stumbled across this channel and have become a fan from watching this first vid. Great job and best wishes for a long string of successors!
Minus the background music that causes unnecessary additional mental busyness, top notch production 👌 (your proper diction/pronunciation paired with quality explanation are more than enough on their own)
Thank you for amazing video and especially for reference to a course by Bartosz Milewski! I tried to study Category Theory twice before, and gave up both times. Thanks to your video I found Bartosz' lectures (here on UA-cam) on Category Theory, and they are much more accessible than materials I used before - so I'll give it another try. This video was very inspirational for me. Thank you!
Really good video (and the perfect name for the channel), I hope you continue to post. That said, I would say that category theory is the abstraction of abstraction. Composition is what links an abstraction to another. Also, the functorial nature of the whole shebang should be a really good sequel.
I wish my lecturer just show us this video when I first started taking a class on category theory. I spent way too long trying to understand very abstract concepts without much of an idea as to why I should care - this video would have helped a lot!
What a beautiful video. When something is presented simply enough, it’s truth is revealed in all forms. Your section on rationals and reals got me thinking of kolgomorov complexity in a whole new light. Your section on composing functions got me thinking of computable functions and how one can apply category theory to complexity theory. I imagine that was unintended, but welcome for sure. Cheers to you, this is inspiring work. You’ve won a new subscriber. I hope to see more of your videos in the future.
Glad that it felt intuitive! I spent quite a bit of time thinking of the most natural way to describe sets and functions without using any unnecessary notation, so I'm happy my example 'clicked' for you! Thanks for the subscription :)
Thank you for the great video! Explanations are very clear and easy to follow. I wasn’t lost for a second. Great job! This video is similar to my favourite book about the subject: Conceptual Mathematics by Lawvere and Schanuel. Despite great respect I have towards Bartosz Millewski’s work, I would recommend the book over his lectures.
I did my undergrad thesis on adjoint functors and my Master degree thesis on the homotopy theory of differential graded categories. Congratulations for the work and the views!
That was a very nice video, and easy to understand. I would love to see some more on this subject in order to develop the various concepts of this theory.
You caught my attention by just one video and you also made me impressed of this. I've never seen this topic before. I'll might use this in my journey in mathematics as a second year highschool student. Hope you can make more videos like this.
this is my first time seeing this video and thinking of this topic. I understood things that I never thought of before or learned. I am taking functional programming class next semester and I will see how the small snippet of abstraction on functional programming here will help me. Thank you for the great content.
Really beautiful i loved it! Thanks a lot, can't wait to learn more! Would love to hear more about category theory if you want to consider it (but i see you provided an awesome list to learn more!). I wish you the best going forward ❤
This is possibly the best intro category theory video in the category of intro category theory videos
Welcome to UA-cam! Fantastic presentation. Absolutely looking forward for a long and prosperous playlist, Eyesmorphic. Thank you for existing!
That means a lot! Thanks
@@Eyesomorphic Please make a course where you teach Type theory but do it by simultaneously teaching ALL the prerequisites and building blocks that we need to know from logic and proof theory. I would be so happy paying for a course if you can make it just as intuitive and visual as this video.
@@Eyesomorphichave a nice day and be wise ☕️🍰🍸
@@Eyesomorphicintuition is hugging you deeply, warmly and passionately
tbh i thought my real weapon was a combination of logical reasoning and math theorems.. i used a lot of statistics and logic to check how likely a statement is to be true or not given for example, if the person claims that 10 rare conditions were simultanously true, that's probably bullshit. but if it was a smaller set of conditions, or there is proof that some of them are true, the situation changes. or for example, using advanced counting and probabilities to win card games and impress ppl
Man this is UA-cam gold. You gotta become a regular. I would be so happy to grab i was in the first 60 views.
Thanks! I'll definitely try to make some more videos, I've already got an idea for another one. Glad you enjoyed :D
@@Eyesomorphic Graph Theory is the abstraction of relationships? **Put down glasses** I've studied to PhD all for this and yet I'm still a single dog. The graph, does not work!
@@ultimaxkom8728 clever 😂
Brag*?
Category theory for programmers is an amazing book, and I absolutely reccomend watching the lectures too!
Could you elaborate on why it’s an amazing book? I am considering bying
@@jacobsjdin4057You can access it for free online if you'd prefer, but obviously buying the book and supporting his work is great too. It was a culmination of Bartosz's posts made on the website I listed in the description. He has a lecture series as well that follows the same content
Yes, I was introduced into Category by Bartosz's UA-cam series many years ago, didn't understand all but later from other books/videos then came back to Bartosz whose videos the BEST.
This video is a pearl in the middle of the internet ocean. It's fascinating how you explain how some subjects of math are the abstraction of things we already use in Simple math. As a student of computer science i apreciate a lot this work
Thanks!
learning about lambda calculus is how the magic of abstraction "clicked" for me. Being able to define problems away is just mind-blowing to me still lol. "This function is a number now because I say it is" is just amazing
Unbelievable simplicity. Please keep on making new videos. This is pure gem.
That's really reassuring! Keep an eye out for the next installment in this series, I took a rather long hiatus but there's a new video in the works currently! Thanks again
Brilliant. Clean animations, thoughtful and clear exposition and a great topic. Can’t wait for more videos from Eyesomorphic.
I can't say it any better, so a great big DITTO!
Instantly subbed, this is one of the most “eye” opening videos on mathematics that I’ve seen so far, you took an “abstract” concept and broke it down in a very digestible way, one could say you used abstraction to minimize the number of elements it takes to convey the underlying structure of “the utility of abstraction within mathematics” lol. Thank you for the video!
I have been a haskell programmer for quite a while, shared this video with some friends as I think it makes Category Theory really approachable! Well done!
Is haskell any good for cryptography?
As a first-year Math Degree student, I can that almost all (if not all) Mathematics can be described by the art of Abstraction.
For example, if you want to prove "The sum of even numbers is even" you could try to check one by one, but you'd just never end because there're infinity even numbers.
Instead, you can consider work with only two objects "A" and "B", which are two representatives of all integers that verify the property of being even (formally, if we consider the universe "Ω" to be set of all intergers: "∃n(A=2n)" and "∃m(B=2m)"). In other words, we've just removed all particular characteristics of individual even integers to stay only with what characterizes an "even integer"; we've made abstraction.
Where the magic lies is that if you manage to prove any property with "A" and "B" (such that "A+B" is even), you're proving it for any two even numbers (actually, "killing infinit many birds with one shot"). 🔥
I’ve watched like 5 introductions to category theory, but your analogy of what algebra is to numbers is what category theory is to composition was the priming I needed.
Heck! I learnt algebra before. And I know how I learnt algebra. For me learning algebra involved doing a lot of examples and then creating algorithms for it once I got a good grasp of the subject.
So yesterday I started with an exercise heavy book to category theory (spivaks category theory for the sciences) and it’s exactly what I need to understand it.
He introduces ologs that are the first real objects I studied seriously that don’t fulfill composition.
Thanks a ton on getting me started!
That's great to hear! It took me at least 10 different books and lecture series to fully get to grips with the principles of category theory, and I guess this video is the culmination of that, and the progression that felt most intuitive to me. Good luck on your quest!
do you have a CS/Software background? if yes can we expect some CS related videos to from you in the future besides pure mathematics? @@Eyesomorphic
@@YuruCampSupermacy My background is in mathematical foundations for CS, so you can definitely expect some more CS orientated content in the future!
I dont regret a single second of watching this video, you completly changed my perception of not only mathematics, but the whole reality. Thank you for this amazing content, you defenitely deserve a sub! 👏
Great video. A young kid could understand this, and it would likely turn them into mathematicians! The world needs more mathematicians, especially now. Bravo.
As a math student, absolutely fantastic work!! Would love to see more
I can see how thoroughly you planned this video! Both the visualisation and the topic are beautiful!
This kind of math content is definetly worth a channel for!
Welcome to UA-cam, Eyesomorphic! Stunningly simple and accessible presentation that couls invite more people into this beautiful area of study. Hope you could go deeper into category theory and present useful results in a similarly accessible fashion. Looking forward to them!
Apparently this is your very first video (on this channel). Obviously the algorithm knows what I like. The channel name is awesome. Isomorphism explains everything. Looking forward to the N+1 video.
What a beautiful introduction to category theory. As an applied guy who knows nothing about this subject, I enjoyed it a lot ! You got yourself a new subscriber, looking forward to your future videos :)
instant subscribe! i got my b.s. in mathematics last year, but real life hasn’t given me much time to keep up with reviewing what i learned in undergrad. this video made me feel like i was in one of my theory classes again! ❤
That's great to hear!
first comprehensible explanation of rational numbers I've ever heard. I'm 65.
May God richly bless you, sir.
beautifully reminiscent of 3Blue1Brown imo, looking forward to more! Gave me a really solidly improved understanding of category theory :)
When I was 14, my relationship with functions was "it just a name we give to an expression" like we give π to 3.141592..., or e give to 2.7182... When I turned 15, I started to learn programming and it completely change my mind about how functions work. Yes sure it still is a name we give for an expression but the way we can use any kind of input and any kind of output that make me surprised, then I did a little research and I found out that functions in math is also the same, they're freedom, you can do what ever you want; don't just stop at the Natural numbers or Real numbers, start making your own numbers like a set with even numbers, or a set with prime numbers, or a set with your family members and we can make a function on those sets too. That kind of freedom make me love math❤
The way you explain everything reminded me of that feeling, feeling of I can do what I want with math. I hope you can keep up the good work!! And welcome to youtube🎉
We have an absolute sigmachad here 🗿
Such an amazing video that explains category theory in a remarkable way. I have been looking for category theory videos but I never found any with this level of articulation and quality.
Your hard work to put together explanations and graphics deserve great applause 👏
Wow, man, you're really really good at this, your approach to mathematics and your skill to teach in a simple way with many examples is amazing.
Please, keep making videos, there's nothing like this on UA-cam.
This video is so well made, the best I've seen in a long while on pure maths. Amazing work!
The BEST introduction to category theory for a non mathematician like me. Can't wait for more videos by you.
That's very encouraging, thank you!
Spanish: Este video es una maravilla, en serio, poder explicar algo tan "abstracto" de una forma tan digerible es todo un arte. FELICITACIONES!!
¡Eso significa mucho! Gracias :)
I hope you're in top tier winners for #SoME3! Brilliant explanation . As a math student, absolutely fantastic work!! Would love to see more.
Nice Video! I am glad to see a new great UA-camr joining the platform and teaching concepts. Thank you for this piece of art.
such a great video, the best one i’ve seen so far on introducing category theory, i love it so much! also i love the channel profile picture and name
That's very kind, thanks!
Welcome to youtube!!
Really appreciate your dedication since day one.💖
Thank you for creating this! I've watched several intro to category theory videos and even started some books and courses, but this is by far the best explanation I've seen!
hands down one the best math videos I’ve ever seen on youtube
That's ever so kind!
@@Eyesomorphic Please, continue such an amazing work. We need explanations like yours and 3b1b, making math much more approachable. You actually inspired me to learn more about Category Theory :) It blew my mind the same way, as the Group Theory did with its relation to physics and the conservation laws.
On the side note. What is the answer for the question about the composite function of “isInteger” follows “sqrt”? I am a programmer and you got me curios, isn’t it a function, which checks whether a given integer is a square of another integer?
@@hellomylittleboy The function isInteger ∘ sqrt is indeed one that maps an integer to true if it a square number! Well done! Hopefully this small exercise demonstrates how the heart of programming is simply chaining together smaller functions into larger, more complex ones. This is why we can model them so well as a category!
This was my very first exposure to category theory and it was beautiful!.....Thank you.
Man, I'm still SO EAGER for another video! This video is absolutely beautiful, I can't wait for the next one, and the next ones!
Beautiful presentation of category theory. I enjoyed how Alice and Bob's speech colors were mapped to a (for Alice) and b (for Bob) respectively as a way of abstraction which then allowed me to understand the rest of the video, as though you created a rhetorical category to be an analogy to mathematical categories.
Hey, this video is seriously incredible. I remember you commented one of my videos a couple weeks ago and I knew recognised your name. Seriously this video is legions in quality above mine and genuinely congrats and good luck in the future!
I remember your video well, I thoroughly enjoyed it! Keep up the good work, and thanks for the kind words :D
This video has really helped me on a personal level, I've been undergoing changes in my thinking pattern recently, influnced by formal logic, and abstraction was a huge part of it. I've being trying to articulate my process of thinking, but I think this video on abstraction really hits the nail on the head. Thank you.
I have never subscribed and turned on notifications for a channel so fast.
unbelievable simple clear explanation of abstraction and category theory fundamentals. I really thank you for your effort, I would absolutely like to see more of these please. Thank you again
How very kind, do stay tuned for more videos :D
Best category theory introduction I’ve come across thus far!
Best intro to category theory I've seen, you get an instant new subscription from me!
This video blew my expectations. AWESOME. I hope to see many cool videos like this one from this channel now
Beautifully simple overview of a difficult area of mathematics. I'm looking forward to a deeper dive in future videos.
Beautiful simple, clear explanation! Thank you for abstracting math education to its essence. I believe a ‘top down’ approach to math is as important as building a bottom up foundation - it helps to build motivation, and provides a framework to hang the whole of math. Would love to see your take on linear algebra, calculus, geometry, etc, and how they are different aspects of the same concepts.
Outstanding! I just stumbled across this channel and have become a fan from watching this first vid. Great job and best wishes for a long string of successors!
Minus the background music that causes unnecessary additional mental busyness, top notch production 👌 (your proper diction/pronunciation paired with quality explanation are more than enough on their own)
Keep making videos man, you are destined to be right up there with numberphile, mathologer, and threeBlueOneBrown
Good luck with the channel! Has a lot of potential!
A video with an agile structure and a lean data posture. A job well done!
Thank you for amazing video and especially for reference to a course by Bartosz Milewski! I tried to study Category Theory twice before, and gave up both times. Thanks to your video I found Bartosz' lectures (here on UA-cam) on Category Theory, and they are much more accessible than materials I used before - so I'll give it another try. This video was very inspirational for me. Thank you!
Loved it. Subscribed. Looking forward to future videos, i can't believe your first video is of such high quality. kudos.
Really good video (and the perfect name for the channel), I hope you continue to post. That said, I would say that category theory is the abstraction of abstraction. Composition is what links an abstraction to another. Also, the functorial nature of the whole shebang should be a really good sequel.
Beautiful! Thank you for showing that beauty of “abstraction”😊
Apart from the superb technical content, the music chosen is very relaxing. Thank you for this wonderful creation.
Thanks! Had a friend compose it :)
Thanks from the composer! I'm hoping to compose some tracks for future videos as well, so let me know if you have any suggestions.
@@calebp6114Could you please upload it as a separate video or upload it on some music sharing website somehow? Or maybe sell it, I'd buy 🥺
This is not only a great introduction to Category Theory, but also a great introduction to Mathematics in general. 🔥
I hope you're in top tier winners for #SoME3! Brilliant explanation 👏🏼
One of the best math videos ive ever seen, so informative! I am truly thankful for being able to see it
After watching so many videos on Category Theory, this one is hands down my favorite. I have watched at it least 3 times.
Thanks for the kind words!
This is the most exciting math related video i have ever seen!
The channel we all needed, welcome!!!
Somehow this founds its way to me …. Of course we want you to make more videos. Excellent job, very cool, well orchestrated :)
I REALLY like your style, visuals are so perfect for following on
This is amazing, simple and comprehensive way to display explanation of the topic.
I wish my lecturer just show us this video when I first started taking a class on category theory. I spent way too long trying to understand very abstract concepts without much of an idea as to why I should care - this video would have helped a lot!
I'm glad to hear it!
What a beautiful video. When something is presented simply enough, it’s truth is revealed in all forms. Your section on rationals and reals got me thinking of kolgomorov complexity in a whole new light. Your section on composing functions got me thinking of computable functions and how one can apply category theory to complexity theory. I imagine that was unintended, but welcome for sure. Cheers to you, this is inspiring work. You’ve won a new subscriber. I hope to see more of your videos in the future.
First time I watch a video about category theory that actually makes sense. Thanks for this ❤
My god this was so eye opening and extremely thought out of. thank you for the effort brother.
Two minutes in and I know I'm gonna be watching every video you post :D
That intro was sick af
9 minutes in, That I can view 'age' as a function applied to a set 'people' just blew my mind. Insta subscribed
Glad that it felt intuitive! I spent quite a bit of time thinking of the most natural way to describe sets and functions without using any unnecessary notation, so I'm happy my example 'clicked' for you! Thanks for the subscription :)
A function gives an output from whatever input you defined it on, not just on numbers!
Thank you for the great video! Explanations are very clear and easy to follow. I wasn’t lost for a second. Great job!
This video is similar to my favourite book about the subject: Conceptual Mathematics by Lawvere and Schanuel. Despite great respect I have towards Bartosz Millewski’s work, I would recommend the book over his lectures.
The three first seconds of the video already made me subscribe. That intro has style, mate.
Please make more videos! Im so lost learning abstract math and this was such a nice way around it
Very clear and beginner friendly, waiting for More :)
Loved it! Looking forward to your upcoming videos!
Excellent video!. The explanation of the concept of abstraction was fantastic. Thank you so much!
I did my undergrad thesis on adjoint functors and my Master degree thesis on the homotopy theory of differential graded categories.
Congratulations for the work and the views!
awesome video! can’t wait to see the full potential of this channel
That was a very nice video, and easy to understand. I would love to see some more on this subject in order to develop the various concepts of this theory.
Always nice to revisit this video
How very generous! Hopefully the next video in the series is released next week, so keep an eye out for that. Thanks again!
This is a great video, it has really given me a new perspective on category theory, thanks!
You caught my attention by just one video and you also made me impressed of this. I've never seen this topic before. I'll might use this in my journey in mathematics as a second year highschool student. Hope you can make more videos like this.
Dang this was beautifully done! Thanks for the time you put into making such a nice presentation.
this is my first time seeing this video and thinking of this topic. I understood things that I never thought of before or learned. I am taking functional programming class next semester and I will see how the small snippet of abstraction on functional programming here will help me. Thank you for the great content.
You have created something beautiful
Very nice and simple ! Thank you !!! Hopping There will be others videos !!!
I hope to see more videos from you, I really loved the aesthetics and style of your video. This was great.
What a nice channel, I know this is a gold mine. Please post more.
I really like the visuals! The explanation was succinct as well! Please do continue!
One of the best math videos I have yet seen
i have a feeling this channel is going to explode. very good video. always sucked at math, but this was extremely interesting and informative.
it shows you how good this video is when an such a high percentage of people liked it. Well done!
Gold!👌 Looking forward to following this series!
I absolutely loved every single second of the video. This was just amazing.
Really beautiful i loved it! Thanks a lot, can't wait to learn more! Would love to hear more about category theory if you want to consider it (but i see you provided an awesome list to learn more!). I wish you the best going forward ❤
I really enjoyed the video, it was clear and i liked the examples you used. I really hope you will make more!
Excellent! Thank you for creating this video, it's a lovely way to express these relationships 🤩
Beautifully presented and crystal clear! Looking forward to more.