Re: Categories ridiculously abstract

["Robert J. MacG. Dawson" <Robert.Dawson@STMARYS.CA>]

Tom Leinster wrote:
> 
> Michael Barr wrote:
> >
> > And here is a question: are categories more abstract or less abstract than
> > sets?
> 
> A higher-dimensional category theorist's answer:
> "Neither - a set is merely a 0-category, and a category a 1-category."
> 
> There's a more serious thought behind this.  Sometimes I've wondered, in a
> vague way, whether the much-discussed hierarchy
> 
> 0-categories (sets) form a (1-)category,
> (1-)categories form a 2-category,
> ...
> 
> has a role to play in foundations.  After all, set-theorists seek to found
> mathematics on the theory of 0-categories; category-theorists sometimes talk
> about founding mathematics on the theory of 1-categories and providing a
> (Lawverian) axiomatization of the 1-category of 0-categories; you might ask
> "what next"?  Axiomatize the 2-category of (1-)categories?  Or the
> (n+1)-category of n-categories?  

	Surely we should start with the set of (-1)-categories? <gd&r>

	-Robert Dawson