Seven Sketches in Compositionality
by Unknown author
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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 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 mathema
on “Category Theory: Orders” ↗Definitely “Seven Sketches in Compositionality”! [1] ——— [1] https://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf
on “Ask HN: Which mathematics books taught you the most in your career?” ↗If anyone is interested in Applied Category Theory, definitely check out the Topos Institute in Berkeley [1]. They do weekly seminars that they post on youtube and a really intriguing blog. I must say that David Spivak is a treasure to hear speak. 7 Sketches in Compositionality [2] was my introduction into Category Theory (written by Spivak and Brendan Fong, another member of Topos), and it really
on “Applied category theory in chemistry, computing, and social networks [pdf]” ↗Check out “Seven Sketches in Compositionality“ by Spivak and Fong. You can find a free copy provided by the authors online. It is an introductory book to applied category theory.
on “A Brief Guide to a Few Algebraic Structures” ↗What kinds of graphs? There are a number of graphical representations that turn out to be incredibly useful in category theory, but they're far from equivalent. IIRC, https://arxiv.org/abs/1803.05316 introduces some of them.
on “To Dissect a Mockingbird: A Graphical Notation for the Lambda Calculus (1996)” ↗If I could give my high school self only one math book, it would have to be Seven Sketches in Compositionality by Fong and Spivak. Did every exercise over winter break in college and realized along the way that I had been hustling through math courses and olympiad problems without appreciating any beauty in the…
on “Ask HN: Recommend a maths book for a teenager?” ↗…to Embedded Systems, Second Edition: A Cyber-Physical Systems Approach Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control An Invitation to Applied Category Theory: Seven Sketches in Compositionality BTW, feel free to ask for recommendations in physics, especially stat mech, simulation/computation, condensed matter theory
on “Ask HN: What do you read for general knowledge?” ↗Recently, I stumbled upon a book "Seven Sketches in Compositionality: An Invitation to Applied Category Theory" where the authors decided to design the difficulty of the chapters like this: https://i.ibb.co/349JLsf/difficulty.jpg (image from the book) I like this approach…
on “You're not dumb, the prerequisites are bullshit” ↗Somewhat less of a "textbook", but good at showing applications of category theory - Fong, Spivak: Seven Sketches in Compositionality https://arxiv.org/abs/1803.05316 (Notably, this includes application to a "graphical" treatment of fairly-elementary linear algebra, which a different HN user is mentioning even as I write this, as a part of math where CT cannot possibly be useful and will only eve
on “A monad is a monoid in the category of endofunctors, what’s the problem?” ↗I am currently reading it, it is very nicely written and accessible. Each chapter starts off gently so you can skip to the next whenever you feel lost, only to come back later. So far: introduction/preorders, monoidal preorders/wiring diagrams, categories/application to database schemas. For those reading on a ebook, the book sources are available on its arxiv page https://arxiv.org/abs/1803.053
on “Applied Category Theory” ↗aside from 3Blue1Brown : I think category theory will give you an unique point of view of math, also basic logic and philosophy are very important for a good and solid foundation on math intuition. https://arxiv.org/abs/1803.05316 along with their youtube lectures. very basic but refreshing: https://www.youtube.com/playlist?list=PL8dPuuaLjXtNgK6MZucdY... if you are a programmer or developer:
on “Ask HN: Best resources to gain math intuition?” ↗Yeah, +100 I have this same problem in general. FWIW, the only real practical example I've seen (which has been rather serendipitous for me) is the "Seven Sketches in Compositionality" linked in the comments below applying category theory to databases. You can even play with the actual an implementation (written Java) to see some real world code here: https://github.com/CategoricalData/CQL…
on “Category Theory for Programmers (2014) [pdf]” ↗David Spivak and Brendan Fong have been doing lots of work at MIT to evangelize applied category theory. See their recent books/classes: Seven Sketches in Compositionality: An Invitation to Applied Category Theory https://arxiv.org/abs/1803.05316 Applied Category Theory mini-course: https://ocw.mit.edu/courses/mathematics/18-s097-applied-cate... Programming with Categories mini-course (with Bar
on “Ask HN: What are you learning?” ↗I would recommend "Seven Sketches in Compositionality", as it does not progressively get harder, but each chapter starts off very easily. So you can catch up, if you got lost. It is available here: https://arxiv.org/abs/1803.05316
on “Infinity Category Theory Offers a Bird’s-Eye View of Mathematics” ↗Seven Sketches in Compositionality is easily the best book to get started on Category Theory. Learning something becomes highly fun and enjoyable when the authors/lecturers are deliberately trying to make it so. Most books on anything…
on “Category Theory: Lecture Notes and Online Books” ↗