Category Theory for Programmers
by Bortosz Milewski, Bartosz Milewski · first published 2018
65% recommend28% neutral6% critical
Why HN recommends it
Free, programmer-oriented route into category theory that needs only programming experience; code examples in Haskell, C++, OCaml and Scala. Also helps explain Haskell's underlying ideas, with a lecture series too.
Summarised by Claude from recommending comments
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If anyone is looking to get into Category Theory as a programmer, I would recommend giving Bartosz Milewski's Category Theory for Programmers a shot[0]. Quite good, and you can read it as a blog post on that site or get the ebook/physical book to leaf through. For a more theoretical/less applied approach that's still relevant to computer science/programming,…
on “Applied Category Theory” ↗This is a really exciting area. See also the Cambria project [1] and the HN discussion from yesterday [2]. See [3,4] for a great introduction to category theory for programmers--we are all indebted to Milewski / Fong / Spivak / et al. for making this topic more accessible. [1] https://www.inkandswitch.com/cambria.html [2] https://news.ycombinator.com/item?id=24699615 [3]…
on “Generalizing 'jq' and Traversal Systems using optics and standard monads” ↗I've tried getting into Category Theory many times over the past few years and the only thing that actually worked is Category theory for Programmers by Bartosz Milewski (lectures[1], book[2]) 1. https://www.youtube.com/playlist?list=PLbgaMIhjbmEnaH_LTkxLI... 2. https://bartoszmilewski.com/2014/10/28/category-theory-for-p...
on “Category Theory: Orders” ↗…mathematically. In programs, we compose lots of things (functions, types, objects, systems...), and being able to abstract that away is valuable. Bartosz Milewski has been putting together a nice series ("Category Theory for Programmers") for a little while now, that seems to be pretty well-received and may give you the answer you're looking for: http://bartoszmilewski.com/2014/10/28/category-theory-for-pr...
on “Category Theory abstractions for Clojure” ↗…about the way complex numbers and quaternions are used to computing spatial rotations. I'm not personally a fan of category theory, but if abstractions are your thing you might enjoy Bartosz Milewski's Category Theory for Programmers. Along similar lines (and circling back to type theory), there's CMU's Software Foundations series of books[1]. If you are interested in cryptography, you might really enjoy reading Chris Peikert's A…
on “An Artificially Created Universe: The Electronic Computer Project at IAS (2012)” ↗Riehl's "Category Theory in Context" is great. It's one of those books where every page really takes a couple hours to fully absorb. It pairs well with Milewski's "Category Theory for Programmers" [1] series, which is comparatively lighter and gives some concrete examples. [1] https://bartoszmilewski.com/2014/10/28/category-theory-for-p...
on “Ask HN: Technical Summer Reading List” ↗…mathematics professor teacher and he suggested this book: Conceptual Mathematics by Lawvere[1] The book teaches category theory to, smart, highschool students. It's a great start. After that I went with: Category Theory for Programmers by Bartosz Milewski [2] Next I would go with anything by David Spivak. Now I understand that: A monad is not scary, it's just a monoid in the category of endofuctors" ;) [1] https://www.amazon.com/-/es/F-William-Lawvere/dp/052171916X…
on “Ask HN: How to Get into Category Theory?” ↗Category theory for programmers by Bartosz Milewski [0] is another great resource geared more towards how programmers can leverage it in their work. 0. https://bartoszmilewski.com/2014/10/28/category-theory-for-p...
on “Category Theory Illustrated – Logic” ↗…http://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf for others. Category theory: Categories and Toposes: Visualized and Explained - Southwell Conceptual Mathematics: A First Introduction to Categories - Lawvere Category Theory for Programmers - Milewski (if you like functional programming) Programming with Categories - Fong, Milewski, Spivak (if you like functional programming) Category Theory in Context - Riehl There are a few others by…
on “Physics Student Earns PhD at Age 89” ↗See also Bartosz Milewski's very nice WIP blog series[1] on category theory for programmers. [1] http://bartoszmilewski.com/2014/10/28/category-theory-for-pr...
on “Category theory for beginners” ↗He was pretty directly referencing Dr. Milewski, I'm sure. He's a relatively famous C++ guy from my understanding who of late has been doing this whole category theory for programmers series. Which is a shame because the whole series is gold.
on “Categories for Programmers: The Yoneda Lemma” ↗category theory for programmers lecture series - bartosz milewski, 67 videos - https://www.youtube.com/channel/UC8BtBl8PNgd3vWKtm2yJ7aA philosophy and (existentialist) psychoanalysis lectures - corey anton, 610 videos - https://www.youtube.com/channel/UCKVncWM_TniOhlwwQHyu1ug…
on “Ask HN: What are the good channels on YouTube to learn?” ↗…Philosophy https://www.youtube.com/playlist?list=PL9GwT4_YRZdBf9nIUHs0z... Then this category theory keeps popping up everywhere, completly incomprehensible, seems like mathematicians are gone mad. I found that this lectures help like no others to catch up to them. Category theory for programmers by Bartosz Milewski https://www.youtube.com/playlist?list=PLbgaMIhjbmEnaH_LTkxLI...
on “Ask HN: What talks or videos do you suggest to watch on a long flight?” ↗…"Category Theory for the Working Hacker" by Philip Wadler is a great talk if you're interested in learning more: https://www.youtube.com/watch?v=gui_SE8rJUM Also recommend checking out Bartosz Milewski's "Category Theory for Programmers": https://github.com/hmemcpy/milewski-ctfp-pdf
on “The Simple Essence of Automatic Differentiation [pdf]” ↗With some consistent dedicated effort you could maybe go through Category Theory for Programmers https://github.com/hmemcpy/milewski-ctfp-pdf
on “A monad is a monoid in the category of endofunctors, what’s the problem?” ↗