Tuesday, May 7, 2013
Small survey of Category Theory introductions
Some time ago a friend asked for a good introductory work on Category theory. I never did answer his question to my satisfaction, as the stuff I picked up on the subject was here and there as I needed it, and I thought there was never any succinct introductory work.
Well, I thought wrongly.
Above link ... links to the seminal summa, available for you if you wish to pursue this delightful area of research into expressivity in mathematics.
Also, of course, there's the working-quantum-physicist's introduction at:
Having a working knowledge of quantum computation is not necessary, probably not even helpful, but a very nice introduction is Quantum Computation and Quantum Information by Nielsen and Chuang, if you wish to see the source from where I got to categories and Category Theory.
Dr. Baez's work starts off lightly and playfully, but then gets pretty deep pretty quickly, as he goes into the Groupoid/Topoid theoretical application of Category Theory, but that's to be understood, as quantists are always concerned about (super-)symmetries, and I, not so much, as I look for the more practical application of Categories in Monoids and the Relational Calculus, but there it is.
I do, of course, have more advanced works on this topic if you wish to research further, and there's always this blog, where I look at the logical implications of cat theory (heh: 'logical' 'implications' ... Math humor). There is, e.g., an introductory article on monads and their computational application at: