David Leduc wrote: In "Towards a categorical foundation of mathematics", Makkai wrote that:
"This suggests that, possibly, the right approach to the definition of weak n-category is to aim at formulating all coherence conditions at once, regardless the fact that this might give a very "theoretical" definition. It would then be a separate, and still very important, project to find a (hopefully) finite and concise set of coherence conditions that would be enough to imply all coherence conditions."
It was 15 years ago! Did this approach give something?
Yes: most or all of the successful approaches to infinity-categories follow a philosophy of this general sort. You can find a lot of references here: http://ncatlab.org/johnbaez/show/Towards+Higher+Categories Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]