Category Theory: An Introduction to Abstract Nonsense

Correction: Universal Property of Quotients requires ker(f) to contain ker(pi)

0:00 Motivation
1:33 Basics in Category Theory
4:14 Group Objects
5:08 Functors
8:17 Universal Properties
11:57 Proof using Category Theory
13:27 Shortcomings of Category Theory

[nestorv]

I finally understand why category theory is nonsense. Thanks

[arisweedler]

This is an incredible video. I am a programmer and I fell into a category theory rabbit hole a while back when trying to fully grok what a monad is. I get that now, but I got bit by the category theory bug.

It should be no surprise that, as a programmer, I just enjoy learning about a combination of novel ways to abstract and build the most powerful building blocks - so every problem becomes a familiar or common one. Category theory is just… fun to have as a mental model. I’ve really enjoyed a series by Bartosz Milewski, but it helps to take a step back every once in a while. Also it helps to have the ability to give an intro to this stuff without sharing a 10 hour playlist.

This is the most coherent overall explanation I have seen to date, and I think only a small percent of the content went over my head (my background in math mostly ends after college level calculus/discrete math/some linear algebra, and then a TON of pop-math youtube videos: 3b1b, mathologer, reducible, numberphile, etc.).

Wanted to say - thanks for creating this! I enjoyed it a lot :)

[TepsiMorphic]

Please make more high level math videos. They are in demand! Your content is amazing!

[notsojharedtroll]

That is a nice reference referring to the domain of algebras as the "caliphate". Al Juarismi would be proud.

[mr.champion]

0:54 There's another version of this map that I saw which reflects that very idea. It replaces the "coast of category theory" with the "coast of universal algebra", and promotes category theory to a "moon", with the intent that the moon creates the waves in the ocean of logic

[LolSumor]

I understood next to nothing, but this was a fun and entertaining to watch.

[raka]

this is the best introductory video on CT in youtube, it goes a little deeper still being fun to watch

[feynmanschicken]

9:40 correction: Universal Property of Quotients requires ker(f) to contain ker(pi)

[MultiAblee]

I am currently doing my masters in pure math and I have a bunch of algebraic topology etc under my belt and I have to say. I love that this was high level and at the same time approachable. Would love a deeper dive into more Category Theory or matter of fact any other higher level concepts in the future!

[Quince]

Thank you for time and energy spending to explain complicated ideas in a simple languave.

[alessandrobertulli]

I can clearly see you put a lot of effort in this group, and the result can be seen (tho I couldn't understand everything, given my layman's math background). Great work, thanks!

[snk-js]

as a developer and after watching this and other videos about category theory many times, I just end up in a conclusion that this is just consistent and composable way of programming and defining entities that could be used to create strongly-typed-well-defined systems

[bissbort]

This is the most underrated channel I've seen for a while. Keep up the great work!

[SimGunther]

Hope this doesn't come true, but the idea that you'd "make only ONE awesome video on the channel and choose not to elaborate on it" would be sour because you have such awesome potential for 1M+ subs!

[madlarch]

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!

[Duskull]

I really loved the map of mathematics at the beginning

[Hans_Magnusson]

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!

😃

[raheem]

Very fundamental, great Motivations

Extremely well simplified.
Worth keeping the work up for sure

[snk-js]

is a new way of speaking mathematics in high level, humanity needed this for sake

[meccamiles]

The caliphate of algebra.... beautiful piece of rhetoric, particularly given the historical genesis of algebra :)