Re: Inevitability of ordering products

[James Borger <borger@math.mit.edu>]

On Sun, 11 Feb 2001, John Duskin wrote:

> Bill Lawvere, in contrast, noticed that when the working axioms of
> set-theory were rephrased in purely "category-theoretic" terms, that
> they, amazingly, all became "first order" statements , thereby
> raising the question of an entirely new way to look at foundational
> questions in which the pesky membership paradoxes could not arise nor
> even be formally expressible. He, in contrast to Grothendieck,
> "pushed" the much more radical move of, effectively, "banning all use
> of Hom-sets" and thereby  made the divide crystal clear.

Can someone give a reference to an elaboration of this point of view?
Since I am not a real category theorist and have at best a weak
understanding of foundations, something written for the mainstream
mathematician would be even better.

Thanks in advance.

Jim Borger