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If you’re curious about this stuff and don’t know where to begin, the first chapter of Fong & Spivak, “An Invitation to Applied Category Theory: Seven Sketches
by benrbray 6y ago
If you’re curious about this stuff and don’t know where to begin, the first chapter of Fong & Spivak, “An Invitation to Applied Category Theory: Seven Sketches in Compositionality” [1] also introduces category-theoretic ideas using partial orders.
Edit: After the Fong & Spivak book, the book by Emily Riehl, "Category Theory in Context" is an excellent next step, although it requires some mathematical maturity.
[1]: https://arxiv.org/abs/1803.05316 https://arxiv.org/abs/1803.05316
- ironSkillet 6y agoI highly recommend looking through this for anyone curious. I thought the section on databases was especially interesting. Many database operations (join, schema change, etc) fit very neatly into category theory language.
- benrbray 6y agoI agree, the database angle is fascinating! There's an interesting CSTheory.SE answer here [1] with some pointers to further reading, written by one of the creators of the Datafun [2] query language. [1] https://cstheory.stackexchange.com/questions/38221/is-there-a-relationship-between-relational-algebra-calculus-and-category-theory https://cstheory.stackexchange.com/questions/38221/is-there-... [2] http://www.rntz.net/datafun/ http://www.rntz.net/datafun/
- ABeeSea 6y agoCategory Theory in Context is such a great book. Kudos to Dover’s Aurora publishing arm for a great, original book at such a great price. Always love dover and adding additional new contents to the back catalogue of reprints is amazing. The book does constantly reference other branches of mathematics (algebra, topology, etc) for example. Probably not strictly necessary to have that background to follow the book, but helpful.
- ajarmst 6y agoFor non-mathematicians (although some post-secondary maths is probably required), I'd also recommend Spivak's "Category Theory for the Sciences" (MIT Press, 2014) and Milewski's "Category Theory for Programmers" (available online at https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/ https://bartoszmilewski.com/2014/10/28/category-theory-for-p...). I liked it enough to buy the hardcover.
- pjungwir 6y agoA few years ago I took a printout of Fong & Spivak with me on vacation to Greece. I really enjoyed the first few chapters---and my wife got to make fun of my leisure reading choices. :-) I wish they sold a bound copy, because at home among so many other things to read, it's tough to remember to pick up that stack of papers. EDIT: I take it back, you can buy it now!: https://www.amazon.com/Invitation-Applied-Category-Theory-Compositionality/dp/1108711820/ https://www.amazon.com/Invitation-Applied-Category-Theory-Co...