Category theory
2011-11-25 — 2025-10-04
Wherein a curated bibliography and guide to learning is presented, with emphasis on applications to formal syntax, networks, and functional programming, and pointers to textbooks, lectures and online courses.
I don’t know anything about category theory, but asides about it occur so often in my daily reading that I really should. I frequently see it applied to formal syntax and network descriptions — two areas I’m interested in. As such, I’m probably missing some important tools from my toolbox if I don’t look it up.
1 To Read
The traditional vector (or should I say arrow?) for transmitting this stuff in these internetty times: category theory for functional programming
In music: Mazzola (2002b)
Chris Aldrich’s UCLA Category Theory Summer Study Group
Emily Riehl: Category theory in context is the free version of a book coming out soon, recommended to accompany Baez’s newest course
May as well file it here: Jeremy Kun’s Algebraic Topology series
John Baez presents a wealth of provocative uses of this category thingy, at least to my innocent mind
- Diagrams
- Elevator pitch (Possibly an elevator to the core of the earth)
- Networks (Once again, an amazingly general take on networks to me, although perhaps that should not be surprising given the generality of the tool)
- a tale of n-Categories
Maarten Fokkinga, A Gentle Introduction to Category Theory—the calculational approach
Barr and Wells
- Toposes, Triples and Theories
- Category Theory for Computing Science which is a highly recommended textbook with a cheap cover price, but it’s only sold through a tedious shipping process at extortionate rates by the University of Montreal. (Don’t bother looking on Abebooks, it’s about $US130 there too. I imagine a thriving bootleg market for this one.)
Abstract and Concrete Categories: The Joy of Cats is a reprint online textbook by Jiří Adámek, Horst Herrlich, George E. Strecker
David Spivak’s Category Theory for Scientists/the Sciences
- as OCW
- as arXiv post: Spivak (2013)
- as open-access textbook
Bartosz Milewski’s Category Theory for Programmers
- or Philip Wadler, Category theory for the working hacker
[…] on why category theory is relevant for developers, discussing the principle of Propositions as Types connecting propositions and proofs in logic, and types and programs in computing.
- The nLab
- Tom Leinster’s Category Theory textbook
- Steve Awodey’s Category Theory textbook
- Everyone’s secret alma mater, good old Wikiversity, has an Introduction to Category Theory
- On a similar bent, the Stanford Encyclopedia of Philosophy article looks good and has a killer bibliography
- Alexander Kurz’s listing
- The inevitable MathOverflow question
- Andrea Asperti and Giuseppe Longo — Categories, Types and Structures: Category Theory for the Working Computer Scientist
- Eugenia Cheng’s YouTube lecture channel
- John D. Cook, Visualizing Category Concept Dependencies