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 therefore missing some important tools from my toolbox if I don’t look it up.

## To Read

The traditional vector (or should I say arrow?) for transmitting for 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: Jerermy Kun’s Algebraic Topology series

John Baez has 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 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 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 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.

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

The inevitable Math overflow question

Andrea Asperti and Giuseppe Longo. Categories, Types and Structures. Category Theory for the working computer scientist

John D Cook, Visualizing category concept dependencies

Baez, John C., Brendan Fong, and Blake S. Pollard. 2015. “A Compositional Framework for Markov Processes,” August. http://arxiv.org/abs/1508.06448.

Heunen, Chris, Ohad Kammar, Sam Staton, and Hongseok Yang. 2017. “A Convenient Category for Higher-Order Probability Theory,” January. http://arxiv.org/abs/1701.02547.

Leinster, Tom. 2016. *Basic Category Theory*. http://arxiv.org/abs/1612.09375.

McInnes, Leland, John Healy, and James Melville. 2018. “UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction,” December. http://arxiv.org/abs/1802.03426.