Ooh, sounds very promising. I can tell how excited you are in the intro, and I'm super glad I'm subscribed. I am coming from a "weird formal systems" and "philosophy of math" perspective, and I bet this'll be a very meaty dive into category theory. Thank you.
Thanks very much for the encouraging words. I wish I understood more about the philosophy of math, I bet it gives one an interesting perspective on category theory theory
I never understood that what is category, why is it invented? In which field it is essential? Why should we learn it? Your explanations are very interesting. So, please can I get your help for these questions?
A category is, in the most usual case, a collection of objects and, for each pair of objects, a collection of arrows between them. In the case of what are called "locally small" categories, the collection of objects forms a class, and the collection of arrows between any pair of objects forms a set. Categories now find use in virtually all areas of math, but they were originally used mostly in the field of algebraic geometry, and remain in most use in algebraic geometry, computer science, and mathematical logic. Most of the categories one would usually see are ones whose objects are sets with structure and whose arrows are functions between them which preserve that structure - the categories of sets, graphs, group, topological spaces, etc. all being examples.
I was randomly scrolling and then I saw this gift from the heavens. I do not know how it found a way to me. But it truly is a great gift.
your style make it feel like a story not a lecture, it very enjoyable to watch.
I'm so glad that you published these two videos now when I started to learn category theory.
Ooh, sounds very promising. I can tell how excited you are in the intro, and I'm super glad I'm subscribed. I am coming from a "weird formal systems" and "philosophy of math" perspective, and I bet this'll be a very meaty dive into category theory. Thank you.
Thanks very much for the encouraging words. I wish I understood more about the philosophy of math, I bet it gives one an interesting perspective on category theory theory
Maybe the biggest ahha moment is around 1:19:20
I never understood that what is category, why is it invented? In which field it is essential? Why should we learn it?
Your explanations are very interesting. So, please can I get your help for these questions?
A category is, in the most usual case, a collection of objects and, for each pair of objects, a collection of arrows between them. In the case of what are called "locally small" categories, the collection of objects forms a class, and the collection of arrows between any pair of objects forms a set. Categories now find use in virtually all areas of math, but they were originally used mostly in the field of algebraic geometry, and remain in most use in algebraic geometry, computer science, and mathematical logic. Most of the categories one would usually see are ones whose objects are sets with structure and whose arrows are functions between them which preserve that structure - the categories of sets, graphs, group, topological spaces, etc. all being examples.
Great video!
Thanks for uploading