Category Theory

Some interesting on-line papers and books:

• Phil Scott, Rick Blute: Category Theory for Linear Logicians (2003)
• Jaap van Oosten: Realizability: a Historical Essay (2000)
• More on realizability
• Lawvere: Metric spaces, generalized logic and closed categories (1973)
• Yanofsky: A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points (2003)
• Girard, Lafont & Taylor's Proofs and Types (1989)
• McLarty: The Rising Sea: Grothendieck on Simplicity and Generality I (2003)

Excellent texts that unfortunately are not available on-line:

• Peter Johnstone's "Notes on Logic"

I did my PhD thesis on a language for "skeletons of proofs"; more precisely, on finding and expressing the skeletons of certain Category Theory / Type Theory proofs. Here are some links to people doing work that is somehow related to mine, but using approaches that are totally different:

• Backhouse, Bijsterveld, van Geldrop, van der Woude: Category Theory as Coherently Constructive Lattice Theory
• Huet and Saibi: Computational Category Theory
• Ehrard: The Differential Lambda-Calculus
• Fokkinga: A Gentle Introduction to Category Theory --- the calculational approach

My old math page - needs LOTS of updates

http://www.cs.bham.ac.uk/~pbl/ - call-by-push-value

http://www.math.mcgill.ca/triples/

Grothendieck:

• http://groups.google.com/groups?threadm=0t3t3bw3rrcd%40legacy
• http://www.fermentmagazine.org/rands/recoltes1.html
• http://www.grothendieck-circle.org/
• http://modular.fas.harvard.edu/sga/
• http://www.math.jussieu.fr/~maltsin/groth/Derivateurs.html
• http://kolmogorov.unex.es/~navarro/res/
• http://mapage.noos.fr/recoltesetsemailles/TdM.htm
• http://www.math.jussieu.fr/~leila/biographic.php