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.
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
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
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
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 26, 2015. 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 10, 2017. 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 6, 2018. http://arxiv.org/abs/1802.03426.