I think knot theory is particularly helpful here but I'll let Yetter and Freyd reply further. Jim Stasheff jds@math.upenn.edu Home page: www.math.unc.edu/Faculty/jds On Thu, 16 Mar 2006, Vaughan Pratt wrote:
Category theory, and for that matter modern (as opposed to elementary) algebra, is to mathematics as mathematics is to physics, and for that matter to computer science. Whereas mathematics organizes reasoning about the phenomena studied by physicists and computer scientists, algebra and category theory perform a similar function for mathematics.
In any setting organization is desirable, and arguably necessary on occasion. But the use of algebra and category theory to organize physics and computer science is a double whammy here. One should therefore be doubly sympathetic of those physicists and computer scientists who want to know what substantive contribution is being made to their subject and can't evaluate the answers because they are one if not two levels removed from the necessary abstractions.
Vaughan Pratt