# Category theory

November 25, 2011 — April 18, 2016

I don’t know anything about category theory, but asides about it occur so often in my daily reading that I really should; moreover, since I frequently see it applied to formal syntax and network descriptions, two areas I am interested in, I am 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 dotcom times: category theory for functional programming

Mazzola, G. (2002). The Topos of Music.

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’ newest course

May as well file it here: Jeremy Kun’s Algebraic Topology series

John Baez presents a wealth of, to my innocent mind, provocative uses of this category thingy

- Diagrams
- Elevator pitch (Possibly an elevator to the core of the earth)
- Networks (Once again, a to-me amazingly general take on networks, although perhaps that should not be surprizing 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 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

Bartosz Milewski’s Category Theory for Programmers

- or Phillip 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, Stanford’s Encyclopedia of philosophy article looks good and has a killer bibliography
- Alexander Kurz’s listing
- The inevitable Math overflow 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

## 2 References

*arXiv:1508.06448 [Math-Ph]*.

*arXiv:1701.02547 [Cs, Math]*.

*Basic Category Theory*.

*arXiv:1802.03426 [Cs, Stat]*.