Invitation to Applied Category Theory
by Brendan Fong, David I. Spivak · first published 2019
62% recommend38% neutral
Why HN recommends it
A gentle entry point to category theory for applied uses, with examples beyond pure mathematics. Readers praise it as a readable starting place, especially those wanting to see its use in science and engineering.
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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…
on “Category Theory: Orders” ↗…expertise in some area, the benefit of passive reading approaches zero. So I plan to write more and code more (mastering Julia for mathematics and CS) in 2020. A few titles I enjoyed this year: "An Invitation to Applied Category Theory" by Brendan Fong, David I. Spivak. It was fun to dig deeper into categories and read how you can apply thinking in them to different domains: databases, signal processing, circuits. Some mathematical…
on “Ask HN: Books You Read in 2019?” ↗…you're also interested in a visual guide, I wrote one as well: https://github.com/photonlines/Intuitive-Guide-to-Maxwells-Equations - Introduction to Elementary Particles (David J. Griffiths) - An Invitation to Applied Category Theory: Seven Sketches in Compositionality (Brendan Fong, David I Spivak) - Solving Mathematical Problems: A Personal Perspective (Terence Tao)
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗I liked “An Invitation to Applied Category Theory“, pdf is available here: [1] It is written in a more terse, mathematical language, but it is very clear and friendly for non-mathematicians. The authors provide interesting examples of applicability.…
on “Category Theory for Programmers (2014) [pdf]” ↗…of Cyber-Physical Systems Introduction 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?” ↗…"type" or "domain" of operation, but in a consistent way that preserves the compositionality-like properties OP talks about. A recent book exploring this topic is "Seven Sketches in Compositionality; An Invitation to Applied Category Theory" https://arxiv.org/abs/1803.05316 . (Despite the obvious reference to CT in the title, the work is quite accessible and the math involved is not much more complicated than that found in the linked blogpost.…
on “Why Operators Are Useful” ↗These guys wrote "An Invitation to Applied Category Theory." It's an awesome book, and I'm super excited for these lectures.
on “Programming with Categories” ↗…just the necessary category theory as well as giving you examples that aren't purely mathematical. Check out "Category theory for scientists (Old version)"[1] or "Seven Sketches in Compositionality: An Invitation to Applied Category Theory"[2]. They're books that I've studied and I really like how much effort the author has put in to make it accessible to non-mathematicians. Some parting thoughts. - You can understand Haskell & friends…
on “Ask HN: What mathematical background do I need to understand category theory?” ↗Newer work from the same author: Seven Sketches in Compositionality: An Invitation to Applied Category Theory https://arxiv.org/abs/1803.05316
on “Category theory is a universal modeling language” ↗I’m currently taking a category theory course based on Fong & Spivak’s textbook An Invitation to Applied Category Theory [1] and this reminds me of chapter 3 which introduces functors and natural transformations by way of using them to describe schemas, database instances and migrations. [1] https://arxiv.org/abs/1803.05316
on “Knowledge Graphs” ↗…might want to review the now classic IBM 360 Principles of Operation manual many years later; sadly, there a lot of books I wished I had kept but didn't. Keep reading. I'm currently working through An Invitation to Applied Category Theory by Fong and Spivak. Take classes. I found that taking real university courses really help me refresh things I learned years ago. Some are available online, but I am lucky enough to have a world class…
on “How do you handle your Aging in IT?” ↗…categorical databases. Go get your mind blown by CQL: https://www.categoricaldata.net/ It's "an open-source implementation of the data migration sketch from" the book "Seven Sketches in Compositionality: An Invitation to Applied Category Theory" which went by yesterday here: https://news.ycombinator.com/item?id=20376325 > The open-source Categorical Query Language (CQL) and integrated development environment (IDE) performs data-related tasks…
on “Data-Oriented Design (2018)” ↗…(https://www.appliedcategorytheory.org/) have something they call CQL, Categorical Query Language, https://www.categoricaldata.net/ ? They have a book out that talks about it, "Seven Sketches in Compositionality:An Invitation to Applied Category Theory", specifically Chapter 3 "Databases: Categories, functors, and universal constructions" https://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf
on “Adventure in Prolog Tutorial (2016)” ↗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 better, because most math books have…
on “You're not dumb, the prerequisites are bullshit” ↗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 Bartosz Milewski): http://brendanfong.com/programmingcats.html
on “Ask HN: What are you learning?” ↗