Invitation to Applied Category Theory

What Hacker News says

1. photon_linesMay 2022
   Great introductory books along with videos:

     - Mathematics and Its History (John Stillwell)
     - Journey through Genius: The Great Theorems of Mathematics (William Dunham)
     - Proofs Without Words: Exercises in Visual Thinking (Roger B. Nelsen)
     - The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities (William Dunham)
     - Odds & Ends: Introducing Probability & Decision with a Visual Emphasis (Jonathan Weisberg)
     - Introduction to Probability (Joseph K. Blitzstein, Jessica Hwang)
     - The Secret Life of Equations: The 50 Greatest Equations and How They Work (Richard Cochrane)
     - Euler's Gem: The Polyhedron Formula and the Birth of Topology (David S. Richeson)
     - 3Blue1Brown Essence of Linear Algebra: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab 
     - 3Blue1Brown Differential Equations: https://www.youtube.com/playlist?list=PLZHQObOWTQDNPOjrT6KVlfJuKtYTftqH6 
     - Dynamics: The Geometry of Behavior (Ralph Abraham, Christopher Shaw)
     - Geometry, Relativity and the Fourth Dimension (Rudolf Rucker)
     - 3Blue1Brown Essence of Calculus: https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr 
     - Calculus for the Practical Man (J.E. Thompson)
     - Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Harry M. Schey)
     - Who Is Fourier? a Mathematical Adventure
     - Physics, Topology, Logic and Computation: A Rosetta Stone (John C. Baez, Mike Stay)
     - An Illustrated Guide to Relativity (Tatsu Takeuchi)
     - The Mathematics Of Quantum Mechanics (Martin Laforest)
     - A Student's Guide to Maxwell's Equations (Daniel Fleisch) or if 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)

   Show morethread
2. chermiDec 2021
   You didn't ask me, but piggybacking anyway. Some of these I've been going back to for years starting back in my PhD, working through some ideas as I have time. Some I have recently been learning new things from.

   Approximately in that order below:

   Too many stat mech books, but honestly favorite is this old one. If you want a real challenge try to read to the OG Gibbs. Thermodynamics and an Introduction to Thermostatistics

   Lectures On Phase Transitions And The Renormalization Group

   Probability Theory: The Logic of Science

   Information Theory, Inference and Learning Algorithms

   Information, Physics, and Computation

   Elements of Information Theory

   Pattern Recognition and Machine Learning

   The Nature of Computation

   Principles 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

   Show morethread
3. benrbrayApr 2021
   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

   Show morethread
4. zozbot234Apr 2021
   Newer work from the same author: Seven Sketches in Compositionality: An Invitation to Applied Category Theory https://arxiv.org/abs/1803.05316
   thread
5. mathcassFeb 2021
   I have a disclaimer. I'm not an expert in category theory at all. However, my primary background is in mathematics and I've "looked over the basics" as they say.

   If you'll allow me to dodge the question just a little bit, I'd recommend that you dive in and see what it feels like to start learning it. The way I think that could proceed is to a) go find a book, lecture, video, or other resource you'd like to engage with, and b) start devouring it. If you run into conceptual difficulties, start looking online for ways to explain that difficult concept to yourself so that you can proceed.

   Hopefully that isn't flippant, but I've found myself in similar situations and I wish I'd just gone and started in this direction.

   To try to answer the core question, I think if you have a high school background in logic and the ability to think abstractly, that's the only real prerequisite for learning category theory. Many of the advanced concepts in category theory are really explanations for how concepts in algebra, analysis, etc (<- sub-fields of mathematics) are grounded in category theory. In this sense, I find that folks gain a better understanding of category theory because they'll start to see similar patterns in their respective parts of mathematics. So, what makes studying it difficult is that many of the examples of "what a category is" are from various parts of math. This can be a big hurdle, but the works of Spivak are very good about presenting 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 without understanding category theory

   - This StackExchange answer[3] has some other useful information

   [1] https://arxiv.org/abs/1302.6946

   [2] https://arxiv.org/abs/1803.05316

   [3] https://math.stackexchange.com/questions/21128/when-to-learn...

   Show morethread
6. max68Sep 2020
   These guys wrote "An Invitation to Applied Category Theory." It's an awesome book, and I'm super excited for these lectures.
   thread