Dear John,
It seems all the hard work is packed into the formalism that underlies the proof.
I cannot resist describing a key idea of my proof. It is to construct categories from homotopy types rather than from sets. The notion of category is homotopy essentially algebraic: "A category is essentially the same thing as a complete Segal object X satisfying an extra condition: the (source, target) map X_1-->X_0 times X_0 is a 0-cover (a map is a 0-cover if its homotopy fibers are discrete). This is like constructing the "natural" (or folk") model structure on Cat from a model structure on simplicial diagrams of spaces (spaces = simplical sets). A similar description applies to (weak) n-categories. The Stabilisation Hypothesis was a great conjecture. Let me congratulate you and Jim Dolan for formulating it. Best, André -------- Message d'origine-------- De: categories@mta.ca de la part de John Baez Date: dim. 16/05/2010 14:44 À: categories Objet : categories: Re: The stabilisation theorem André wrote: Too simple to be true?
No, I always hoped for a simple proof! And this proof is not "too simple". It seems all the hard work is packed into the formalism that underlies the proof. And that's how it should be, I think. So, I'm happy. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]