Category Theory

Last update: 21 Jul 2026 14:17
First version: 15 July 2026

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I have been resisting learning category theory since the mid-1990s, when it would show up in John Baez's "This Week's Finds in Mathematical Physics", and make my eyes glaze over. At some point, however, I am going to drink the Kool-Aid need to procrastinate in a truly epic fashion find a use for it. When I do, I want to have resources available. (Of course, one resource would be "go down the stairs from your office, turn left, and take Steve Awodey's class.") --- I should perhaps clarify that I do know what a category is, and have even solved (very basic) textbook exercises about them, I just don't get the point.

See also:
• Math I Ought to Learn
• Mathematical Logic

Not unambiguously recommended:
• Peter McCullagh, "What is a statistical model?", Annals of Statistics 30 (2002): 1225--1310 [Comments]

To finish, one of these decades:
• Paul M. Cohn, Universal Algebra

To read, applications in probability and statistics (my links):
• Tobias Fritz, "A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics", arxiv:1908.07021
• Bart Jacobs, Aleks Kissinger, Fabio Zanasi, "Causal Inference by String Diagram Surgery", arxiv:1811.08338
• Jürgen Jost, Hông Vân Lê, Tat Dat Tran, "Probabilistic morphisms and Bayesian nonparametrics", arxiv:1905.11448 [Information geometry]
• Felix Weitkämper, "Projective families of distributions revisited", International Journal of Approximate Reasoning 162 (2023): 109031

To read, applications to automata / formal languages / abstract computation:
• Jiri Adamek, Stefan Milius and Lawrence S. Moss, Initial Algebras and Terminal Coalgebras: The Theory of Fixed Points of Functors
• Jiri Adamek and Vera Trnkova, Automata and Algebras in Categories
• Benjamin C. Pierce, Basic Category Theory for Computer Scientists
• R. F. Walters, Categories and Computer Science

To read, applications in physics:
• Robert Geroch, Mathematical Physics [As an illustration of my not getting the point, I've read about half of this, and quite enjoyed it when he's expositing the actual mathematical tools, but the parts where he says (paraphrasing) "And we can see that these form a category because" come across as much bar-bar-bar, and I retain nothing at all.]

To read, not otherwise, or not yet, classified:
• Steve Awodey, Category Theory
• John Baez's Applied Category Theory Course
• Peter J. Cameron, Sets, Logic and Categories
• Brendan Fong and David I. Spivak, "Seven Sketches in Compositionality: An Invitation to Applied Category Theory", arxiv:1803.05316
• F. William Lawvere and Stephen H. Schaunel, Conceptual Mathematics: A First Introduction to Categories
• Tom Leinster, Basic Category Theory, arxiv:1612.09375
• Saunders Mac Lane, Categories for the Working Mathematician
• Colin McLarty, Elementary Categories, Elementary Toposes
• David I. Spivak, "Category theory for scientists", arxiv:1302.6946