Category theory

1 To Read

• Mark Chu-Carroll:

  • a practical intro via implementing monoids
  • Category Intuition By Example
  • Leading up to Topoi: Getting Back to Categories
  • Fun with Functors

• 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.

• The catster’s lecture series, indexed

• 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

  • as OCW
  • as arxiv post
  • as open-access textbook

• 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