At 11:09 PM 12/17/2009, John Baez wrote:
I think it's premature to introduce category theory in the undergrad curriculum.
I think there are enough very interesting simple examples of categories that the language and diagrams could be introduced to high school students. For example, lists are terrific examples for discussion of the free monoid functor, its unit, and counit, but they don't have to be called by their official names. And tables give a 2-dimensional version of that discussion, with an exchange law that is simple but interesting. Kinship trees or the trees used in high school probability class can be used to talk about partially ordered sets, but they don't have to be called that. The idea would be to get diagrams into the student consciousness, so they learn about connecting the dots. Advanced high school students know about multiplication of matrices, so they could learn something about arrows standing for linear transformations, and composition of arrows corresponding to matrix multiplication. The slogan is, "algebra is the geometry of notation," and high school students can learn to look at and play with diagrams. I bet some kind of school-yard game could be based on diagram chasing. As I see it the greater problem is that high school mathematics teachers need more education. Therefore, I am preparing a book with no calculus beyond the AP level, but using Robinson infinitesimals, Kolmogorov probability spaces, and Eilenberg-Mac Lane categories wherever these things come up simply and naturally in a certain context to do with biology. It has been announced for pre-order at amazon.com by World Scientific and should be available in April, 2010. The work-in-progress is available for examination (and feedback to me!) upon request. Ellis D. Cooper [For admin and other information see: http://www.mta.ca/~cat-dist/ ]