Category theory - The Dan MacKinlay family of variably-well-considered enterprises

To Read
References

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

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 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
- 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

References

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.