I like that you use Propositions and Types as examples and not the usual suspects like Vector Spaces
This is a treasure trove, please continue this series! Category theory is shown in such a bad light and your videos help show it's versatility
Man never stop this series, it's awesome to have a niche maths subject explained that well on youtube. Can't wait for part 4
EYESOMORPHIC, UPLOAD AGAIN AND MY LIFE IS YOURS
To be perfectly honest, this is the first video of the series that I felt had real payoff, it is magical to see the cold definitions make sense in multiple places. This makes me all the more excited for the next one!
I just foun this channel and pff is gold; I'm in the 4th semester of undegrad pure math and having an insight of an advanced topic in such an intuitive way is amazing
Perhaps the best video about basics of Category Theory I have seen at least so far.
For the ordering category, there should be no terminal object, as for every number b there is some number b' > b, so for no object b every other object has a unique arrow to b. However, products exist, and if i understood this explanation correctly, for two objects a, b it should be the minimum of a and b: For every number c with c <= a and c <= b, we have c <= min(a, b), and as there is at most one arrow between each pair of objects, this arrow is unique. Also, this choice of product is unique, as for every other p with p <= a and p <= b we have either p = min(a, b) or there is no (unique) arrow from min(a, b) to p, but there are arrows from min(a, b) to a and to b, so p is not a product.
I bet you've been waiting to make that connection to your channel name for so long š
And when the world needed him the most... he returned...
I was puzzling over the final problem you posed for quite some time. Fantastic video that clearly introduces complicated topics, in an understandable manner. I hope you keep making these videos.
This channel has so much substance. And a certain aesthetic and theme. Its amazing!
This is a fantastic video, thank you for making it. I am currently studying the elementary theory of the category of sets and this has really helped my understanding of the universal construction.
Fantastic video. Category theory is one of my small obsessions. Thanks, Haskell.
Thank you so much for your videos! I've been reading about Category Theory for a while, but it never truly clicked until now. Finally, composition makes sense! I was stuck trying to grasp what a category is and how composition works, but your explanation cleared it up. And the terminal object ideaāwow! The idea that we donāt explicitly know what it is, only that everything points to thereāthatās mind-blowing. It feels almost Zen-like, like a kÅan.
This video helps the novice to understand the fundamentals of Category Theory, and that makes other such videos much more approachable.
This was outrageously good, Iāve read the definitions but this really made the ideas come alive, thank you so much!
Very much digging this functional lambda-calculus -esque style of video. The idea of syntactic manipulation amazes me
I love this so much. So pleasant and elegant. Sure as heck beats reading a book on it. I just struggle with having a much fun that way for this stuff. I think the built in stopping points are a positive.
@oserodal2702