I am an Electrical Engineer. I do not know why I am watching this video, but I am experimenting brain damage trying to understand this nonsense. Even do, I like it.
Good quality video, but I feel like it's only really useful as a review if you already basically know category theory. Really feels like you try to cover too much ground here with a lot of very confusing bits that needed more explanation. You can't really do an "intro" to category theory without spending a lot more time making certain things clear. A lot of the huge leaps in this presentation don't make any sense to anyone who hasn't already studied a good bit of category theory and other advanced maths
0:50 this is my way of approaching the world. I am a top down guy. This is why I appreciate this clip as an introduction. I get the high level stuff and could just drill into the details. My natural inclination is to sort and sieve details to get the generalizations! 😃
14:44 agree on the screwdriver 😂😂😂 That also means that you should not spend too much time figuring out how to make a screwdriver… Especially if you are making a sandwich 🥪 😂😂😂 Thank you for for that one 😂😂😂 Next time I do my screwdriver analogy! 😂😂😂
6:36 up to this point it actually was a very good explanation. Quite a bit easier than reading it in formal language in any language, but especially challenging in French language! 👍
10:10 A category theorist is someone who can say "such that the diagram cmmutes" and seriously believe that this does not need any further explanation whatsoever.
I'm trying to awlf-study this stuff so that I can, later, try to apply it to cliodynamics, behavioral economics, quantitative finance, and economic anthropology. But, so far, I've found Category Theory HARD. Your video helped me understand it better. I hope that you keep making these sorts of videos.
Wow - from basic definitions to functors and natural transformations and on to infinity categories in less than 10 minutes! Quite remarkable. Really hope you choose to make more videos, because this was one of the best introductions to CT that I have come across!
I have a hard time believing that anyone who did not understand category theory before this video would understand it afterwards. Poor pedagogy because it is just providing vocabulary instead of making an effort to explain. Virtually no examples. Exactly what is wrong with some mathematics education. Designed to appeal to a tiny fraction of those who might be capable of understanding it. No effort to motivate the problem these theories are trying to solve.
The individual speaking in this video is gender-neutral or gender-fluid, has colored hair and spends lots of time editing gender studies topics on Wikipedia...It is working on a generalization of gender theory called "Gender Dynamics," and will introduce concepts such as "gendoids" and "gendons" that operate in Gender Spaces with axioms governing their "gendorphisms." It will surely win a Fields Medal for this groundbreaking work that combines Genitalia with Topology, Analysis and Algebra.
Profound! And some reflections: ... abstract algebra by nature is -emm- abstract so easily lends itself to transformations by "changing the labels of like things"? algebraists look for standards between mathematical things? Mathematical things depend a lot on labels applied to them and so remain consistent when labels are changed? analysts on the other hand seem to be drawn to things of inconsistency especially when analysis gives explanation for the inconsistencies? And at this point attract research funding because pointwise events do not readily lend themselves to generalities until those generalities are identified or reduced by a new analytical definition of some sort I agree there is a horribly magnificent something living in math that seems to show a rainbow effect: the closer one approaches the more rapidly the rainbow disappears or re-locates Q: Is Category Theory the way to go? A: hell yeah! It seems a very good way to go Excellent work!
Great (very) high-level intro, thank you! 😁 I'd love to see a series of videos, at various levels. Suggestion to everyone doing Category theory: use the *"semicolon" notation* for the composition of morphisms. I think it's much more intuitive to say (f ; g) than the reversed (g o f) I got more interested in Category theory upon learning about Lawvere’s fixed point theorem, and its applications: mind-blowing about the many famous diagonal arguments that can be derived from it! www.uibk.ac.at/mathematik/algebra/staff/fritz-tobias/ct2021_course_projects/lawvere.pdf
3:20 ".. Isomorphism, which is exactly what you think it is.." If I didn't know exactly what it was, I don't think I'd have any understanding of it. Is a bijection exactly what you'd think it is?
