Elementary Category Theory
I've been asked for an introduction to category theory, especially for people who are not advanced mathematicians. I've found a number of videos and other documents.
Two quick introductions -- what category theory is about and why it's useful.
Funny, but possibley unhelpful to the beginner:
A discussion on Quora:
A serious beginner's book on category theory:
- Conceptual Mathematics: a first introduction to categories, by f. William Lawvere and Stephen H. Schanuel
- When I first encountered category theory decades ago, it was extremely challenging to get into it, at least partially because the examples in the available books were all from highly esoteric fields of mathematics. Maybe the ideas were simple, but the explanations and examples were not.
I was delighted recently to find this book that started with elementary ideas and built category theory up gradually. It’s a good introduction to the subject, without assuming a lot of advanced math. You can buy an elegant printed copy from the usual booksellers, but a pdf is also available online.
- In the ACM digital library at https://dl.acm.org/doi/10.5555/1594905
- in the us archive
- on img.4plebs.org (but what is thie site?)
And about the relationshipe between category theory, type theory, and set theory. Each of these has been touted as a possible foundation for mathematics. Set theory is the oldest, and best-known of these. Category theory are is starting to see serious use in the theory of programming languages. And type theory is one of the tools often used nowadays in formal verification of proofs.