Since I’m hanging out with a bunch of category theorists every Wednesday, web finds with “category theory” in them keep attracting my attention. A couple of weeks ago, I came across this book draft posted on arXiv:
At first I thought, cool!, a new book on logic of diagrams or something. But then I read the abstract and intro, and it’s of course not about that at all. A sketch is a certain kind of graph that lets you define mathematical structures categorically. They were introduced by Charles Ehresmann. I’d links to an introduction on the web, but the only introductory thing I could find is a short paper by Wells. (The MacTutor biography of Ehresmann doesn’t even mention sketches…) So: still cool, but a lot harder for me to understand.
The other item was
which ‘summarizes and compares a number of set-theoretic foundations for category theory, and describes their implications for the everyday use of category theory.’ More elementary, and I look forward to reading it. Alas, I don’t know when I’ll find the time.