7 ms·
Applied Category Theory
- signa11 9y agofor programmer's there is this : https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/ https://bartoszmilewski.com/2014/10/28/category-theory-for-p... as well.
- alvarosevilla95 9y agoHaving taken the course, I definitely recommend it. Great content and Bartosz is just a great guy to listen to
- voidhorse 9y agoBartosz is great. You can also find a filmed series of his lectures on category theory on Youtube.
- unao 9y agohttp://math.mit.edu/~dspivak/teaching/sp18/ http://math.mit.edu/~dspivak/teaching/sp18/
- jfaucett 9y agoThis looks like a great resource. I really think the chapter difficulty idea is a good one and wish more math books adopted this approach. On another pedagogical note and as someone who reads a lot of math texts, I wish math textbooks would spend way more time on introducing the intuition (geometrical if in any way possible) of the ideas before or simultaneous with going into the formulas, theorems, and details. This not only vastly improves comprehension but I find having a geometrical understanding ( even if rough and partially incorrect) greatly helps in me being able to later derive the same formulas and theorems. Having written about various math topics over the years I know its much more difficult to follow this approach, so I don't blame anyone for not going out of their way to imbue intuition, but its still something I wish more mathematicians who teach would advocate for.
- benrbray 9y agoOne book I can think of that has a similar chapter/difficulty curve is Boyd & Vandenberghe's "Convex Optimization" book, http://stanford.edu/~boyd/cvxbook/ http://stanford.edu/~boyd/cvxbook/.
- currymj 9y agoi've seen a number of math-but-sort-of-CS textbooks putting the dependency graph for chapters in the introduction, so you know what you can get away with skipping and what must be done first. i agree about geometric intuition, as long as there's a wall of separation between the intuition+motivation and the main results. it frustrates me when an important result is only proved in the context of a motivating example where i don't have the background. usually this is when a math book dips into physics or engineering for whatever reason.
- ThoAppelsin 9y agoThis description of teaching is a lot like how 3blue1brown does his videos on YouTube: https://m.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw https://m.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw I am not affiliated, just love how he geometrically visualizes the concepts of math, and how he focuses on he intuition.
- danield9tqh 9y agoUnfortunately from reading the first couple of chapters it seems like this textbook doesn't do an excellent job of favoring graphics over formula. It's acceptable but really nothing stellar. I don't think it does the title of 'Applied Category Theory' justice. It is still very much theoretical.
- j2kun 9y agoConveying intuition is about way more than using graphics. It's about storytelling. I've seen people focus on graphics and fail in a hundred ways, while overwhelming theoretical works shine due to the focus on the narrative.
- asavinov 9y agoFunctional Programming and Category Theory: http://nikgrozev.com/2016/03/14/functional-programming-and-category-theory-part-1-categories-and-functors/ http://nikgrozev.com/2016/03/14/functional-programming-and-c...
- empath75 9y agoAs an interested amateur usually I find these ‘beginner’ texts laughably impenetrable, but I had no problems following this all the way through chapter one, at least. It uses fairly simple language all the way through with lots of diagrams.
- hollerith 9y agoI wish more PDFs written by academics had one column, not two, per page. The 2-column arrangement is harder for me to navigate when reading on a mobile device. (The OP has one column.)
- lou1306 9y agoI wish HTML/EPUB was as popular as PDF in academia... That would solve so many problems for mobile reading.
- seanmcdirmid 9y agoTwo columns works great for paper, trying to read A4 or letter sized one column is painful because the lines are too long. But it doesn’t make sense for mobile (at least non tablets).
- sadar_ 9y agoAs a mathematician, usually I find attempts to apply abstract mathematical concepts to concrete real-world concepts clumsy and hurting both the abstraction and the concrete thing. Is this the case with this text?
- nine_k 9y agoIf one cannot apply mathematics to concrete things, what use does the mathematics have, besides mental gymnastics? If mathematics is applied poorly to reality, it's usually because an inadequate model is used, not because attempting this is a wrong thing to do.
- andrepd 9y agoMathematics is not all about models, or real world applications. Pure mathematics is an end, in an of itself, for knowledge if not anything else.
- sadar_ 9y agoFirst of all, when I said concrete things I did not mean for example theoretical physics concepts. I mean things like economics[0] or philosophy[1]. I am saying that mathematical abstraction is not the right tool to get a better understanding for a lot of subjects. My questions was asking if this is an instance of someone with a categorical hammer and seeing categorical nails everywhere, or that it is a super natural fit. Most mathematicians (I know) do mathematics for the mathematics. It is in itself a goal that does not need an external use. So yes, mathematics for a lot of mathematicians is just mental gymnastics that turned out to be very useful. Probably the reasons for some people's love for math and the usefulness are related. [0] https://www.quora.com/Are-there-applications-of-group-theory-in-economics https://www.quora.com/Are-there-applications-of-group-theory... [1] https://en.wikipedia.org/wiki/Alain_Badiou#Mathematics_as_ontology https://en.wikipedia.org/wiki/Alain_Badiou#Mathematics_as_on...
- tupshin 9y agohttps://arxiv.org/abs/0903.0340 https://arxiv.org/abs/0903.0340
- danharaj 9y agoDavid Spivak has done lots of cool work on applying category theory to many concrete systems like databases [1]. Brendan Fong has worked on applying category theory to things that act like interconnected networks, such as electrical circuits. This fits into a larger ambitious program that John Baez is part of to use category theory to understand physical systems that are still much too complicated to understand with current mathematical tools, such as ecosystems. Fong's thesis is on my reading list [2]. The two authors are doing great research, like this investigation of the algebra of backpropagation [3]. I really look forward to reading this too! [1] https://arxiv.org/abs/0904.2012 https://arxiv.org/abs/0904.2012 [2] https://arxiv.org/abs/1609.05382 https://arxiv.org/abs/1609.05382 [3] https://arxiv.org/abs/1711.10455 https://arxiv.org/abs/1711.10455
- thraway180306 9y agoAbout ML-related research, Fong also piqued my interest earlier with his categorification of almost PGMs. Though it didn't inspire him or anyone to bring effective methods of algebra to PGM and improve the base theory, making the exercise really shine. So like with many categorification research it's just a 72-page statement „it can be done”. Brendan Fong (2012) Causal Theories: A Categorical Perspective on Bayesian Networks https://arxiv.org/abs/1301.6201 https://arxiv.org/abs/1301.6201
- tome 9y agoI made a Haskell Postgres library inspired by David Spivak's work: https://github.com/tomjaguarpaw/haskell-opaleye/ https://github.com/tomjaguarpaw/haskell-opaleye/
- kummapp 9y agoI would prefer this kind of notion with the categories: https://github.com/kummahiih/python-domain-equations https://github.com/kummahiih/python-domain-equations but seems like, I am the only one who likes simplicity
- jpfed 9y agoSo the text looks promising but, just as importantly, can someone just make a whole cookbook with diagrams like that?
- defen 9y agohttp://www.cookingforengineers.com/ http://www.cookingforengineers.com/ has a a slightly more primitive version in their recipes. Example: http://www.cookingforengineers.com/recipe/58/Peanut-Butter-Cookies http://www.cookingforengineers.com/recipe/58/Peanut-Butter-C... (scroll down to just before the comments)
- codekilla 9y agoThis is really great! For those interested, another book on the way is: http://www.sci.brooklyn.cuny.edu/~noson/MCtext.html http://www.sci.brooklyn.cuny.edu/~noson/MCtext.html. I've read Noson's other book on Quantum Computing and it was really clear, with lot's of examples.
- jesuslop 9y agoYeah the other book is very sweet and accesible, and quantum computing is very amenable to the monoidal category treatment as Coecke shows pleasantly in 'Picturing Quantum Processes', 110710422X.
- bitforger 9y agoI'd like to buy a hard copy of this... is it in print anywhere? Alternatively I'll just print the whole thing out I suppose.
- dragon96 9y agoThe associated video lectures can be found on the course homepage here: http://math.mit.edu/~dspivak/teaching/sp18/ http://math.mit.edu/~dspivak/teaching/sp18/
- zombieprocesses 9y agoWikibooks has a very basic intro to category theory/haskell. https://en.wikibooks.org/wiki/Haskell/Category_theory https://en.wikibooks.org/wiki/Haskell/Category_theory