Category Theory
Category theory is the mathematics of mathematics. Okay, so then what is Mathematics? It’s the logical study of how logical things work. Thus category theory is the logical study of how logical things work.
Category makes logical connections between things
A family tree is an example of category theory. It provides a way of representing relationships.
Category theory and composition explained using family trees. #ylj18 pic.twitter.com/f4Wn4doIV9
— Geoffrey Huntley (@GeoffreyHuntley) May 21, 2018
Object and morphisms
Communicative squares
#ylj18 Commutative squares with Super Smash Bros pic.twitter.com/LILzxGJM6Q
— Andrae Muys (@etymon) May 21, 2018
Factors of 42
Mind slightly detonated. Visualizing number factors relationships in higher dimensions, and deriving an abstraction leading to general principle. “Maths is getting fed up with washing the dishes and inventing a dishwasher” - @DrEugeniaCheng #ylj18 pic.twitter.com/cjLfNwEaqv
— Christopher Biggs (@unixbigot) May 21, 2018
Cube of privilege
A cube of privilege #YLJ18 pic.twitter.com/ZAcX6KuhKv
— Vaibhav Sagar (@vbhvsgr) May 21, 2018
The principle of Sameness
8 + 1 = 1 + 8
2 x 5 = 5 x 2
(8+5) +5 = 8 + (5+5)
@DrEugeniaCheng says that doing math with numbers is boring, and we should look at using math in the kitchen where one equation doesn't necessarily equal the other (except cake, cake always works) #ylj18 🍰 pic.twitter.com/3prdodCgaN
— Amy 👩💻🐺 (@Amys_Kapers) May 21, 2018
The concept of invertibility - “if I go over here can I go back?”
Universal Properties
Things can be isomorphic in one category but not another.
If you freeze water, it goes back to water. If you freeze an egg and
Whole categories can be isomorphic if the arrows look the same. The first row is isomorphic because the arrows go the same way, the bottom row isn’t isomorphic.
🌶️💯🌶️ #ylj18 pic.twitter.com/e7IMDjUw5x
— Vaibhav Sagar (@vbhvsgr) May 21, 2018
Visual Representation
Friend map
With this one slide you can introduce folks to category theory. Start at the bottom and do why why why until you get to the top. #ylj18 pic.twitter.com/n9xeq9iQkb
— Geoffrey Huntley (@GeoffreyHuntley) May 21, 2018
Cycles
Category theory: helping to explain why losing weight is complicated #ylj18 pic.twitter.com/65MgUS45AK
— Andrew Herron (@_spyder) May 21, 2018
We often ignore the side-effects of what we do, like the "waste" shown in red here. That's one reason we're in trouble. But category theory can make this process of ignoring into a functor! Then, left and right adjoints can help us "un-ignore": https://t.co/wUhc3YjKds pic.twitter.com/4Zp0B9gsoz
— John Carlos Baez (@johncarlosbaez) May 21, 2018
References
- https://arxiv.org/abs/1803.05316
