Re: The stabilisation theorem

[<joyal.andre@uqam.ca>]

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


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