Basic Category Theory

What Hacker News says

1. seanhunterApr 2026
   If you want to learn category theory in a way that is more orthodox, a lot of people recommend Tom Leinster’s Basic Category Theory, which is free[1]. I’m going to be working through it soon, but the bit I’ve skimmed through looks really good if more “mathsy” than things like TFA. It also does a better job (imo) of justifying the existence of category theory as a field of study.

   [1] https://arxiv.org/pdf/1612.09375

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2. jesuslopNov 2022
   Agreed on the institute and Spivak. But CWM is, er, for working mathematicians. Leinster's Basic Category Theory, or Awodey Category theory are more unassuming.
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3. bmachoOct 2022
   > And actually.. since a vector space has an underlying set, it seems to me that to do a direct sum on a vector space, you must first do a direct sum on the set (that is, do a disjoint union), and then do other things to map the rest of the structure of a vector space into the sum.

   No.

   > So, somehow, a disjoint union (of the underlying set) becomes a cartesian product (of the whole vector space)?

   No. If anything it is the other way: the cartesian product of the underlying sets becomes the (equivalent of) "disjoint union" of the vector spaces.

   > (Is there somewhere to read about this to gain intuition?)

   I don't think you want that. But there definitely are some category theory textbooks, and introductory pdfs. E.g. Tom Leinster Basic Category Theory is a textbook, and it aims to give you intuition. https://arxiv.org/abs/1612.09375

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4. 363849473754Aug 2022
   for proofs i really liked two sources: susanna epps’s discrete math book and also rosen’s discrete math text (though epp’s is friendlier for the beginner)

   supplement those books with these lecture videos:

   https://youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNo...

   they appear to follow rosen but they’re the same topics you’d see in epp

   if you’re the complete beginner go with epp and then use rosen as a supplement.

   if you are an advanced undergraduate in math but don’t know category theory then:

   https://math.jhu.edu/~eriehl/context.pdf

   or

   Basic Category Theory by Tom Leinster

   (even though i’ll list a bunch more resources below i’d probably start with leinster and work up enough math maturity to push through it.)

   i also liked this: https://arxiv.org/pdf/1912.10642.pdf

   if you don’t know advanced math then there is an upcoming (not yet released book) called “the joy of abstraction”

   i cannot attest for the book as i haven’t read it but may be good for true beginners:

   https://www.cambridge.org/us/academic/subjects/mathematics/l...

   (click “look inside”)

   they say “no formal mathematical background needed”

   you can read the description and see if that is something that would be of interest to you.

   this guy has videos + a book

   https://youtu.be/fY02LIW8fvk

   there are a lot of books like “category theory for programmers”, “programming in categories” and the “seven sketches” books along with lecture recordings and videos that you may find helpful.

   category theory for programmers might be the easiest of those three books. i worked a bit out of the programming with categories (http://brendanfong.com/programmingcats_files/cats4progs-DRAF...) book and ignored all the haskell sections and just focused on the math parts (this is a distinct book from “category theory for programmers”. people confuse the two due to the names and the fact they both use haskell).

   if you know category theory and want to learn topology then there is “ Topology A Categorical Approach” by bradley et al.

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5. omarantoMar 2021
   What book will suit you depends on your background. If you have a solid background in math, say an undergraduate degree in math, my favorite book is Emily Riehl's Category Theory in Context [1] (the "context" in the title refers to a background in math).

   If you don't know that much math, I'd recommend Tom Leinster's Basic Category Theory [2] or Steve Awodey's Category Theory [3] (particularly if you have some background in computer science or programming).

   [1] https://math.jhu.edu/~eriehl/context.pdf

   [2] https://www.maths.ed.ac.uk/~tl/bct/

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6. autopoiesisAug 2019
   It sounds like you would be interested in the book / course '7 Sketches in Compositionality' by David Spivak and Brendan Fong, which studies precisely those ideas categorically, with a particular focus on systems that you might broadly call 'computational': http://math.mit.edu/~dspivak/teaching/sp18/

   It has been discussed on Hacker News at least a couple of times previously -- fairly recently, even. You might be interested to look at these discussions:

   https://news.ycombinator.com/item?id=20376325

   https://news.ycombinator.com/item?id=19701767

   Edit to add:

   You might also be interested to learn that categorical approaches to linguistics typically take as their starting point monoidal categories, in which there are notions of 'parallel' as well as 'sequential' composition. It turns out that the usual categorical semantics for linguistics shares a lot with the categorical semantics for quantum mechanics: roughly, meanings are vectors, like quantum states. You can read more about doing (finite-dimensional) quantum mechanics entirely using string diagrams (the formal diagrammatic calculus of monoidal categories) in the work of Bob Coecke, who also played a large part in originating these approaches to linguistics.

   For example, on the quantum side, an excellent book is 'Picturing Quantum Processes' [0]. And on the linguistics side, the paper linked in the article is a good start: https://arxiv.org/abs/1003.4394

   [0] Not freely available, but some slides are at https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf

   Edit, again:

   There is also of course Bartosz Milewski's book / blog series 'Category Theory for Programmers', which introduces category theory from the perspective of Haskell and C++ programming: https://bartoszmilewski.com/2014/10/28/category-theory-for-p...

   But the best introduction to category theory I have read is Leinster's book, 'Basic Category Theory': https://arxiv.org/abs/1612.09375

   And as you might have guessed, I do agree with your statement!

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