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.
- 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: 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.
- 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
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.