Re: Sets vs. categories as a foundation

In <[EMAIL PROTECTED]>, on 11/28/2003
   at 12:50 PM, [EMAIL PROTECTED] (George Greene) said:

>This is a very set-centric view.
>I thought the whole purpose of bothering with
>category theory in the first place was to escape this view.

No. Category theory is a tool for other branches of Mathematics,
whether you take categories as fundamental or take sets as
fundamental.

>My point is simply that if you have ZFC, what do
>you need categories for? 

Because you can prove things once in Category Theory and then apply
them to various branches of Mathematics. Your question is like asking
what you need groups for.

>"The category of sets" starts to get viciously circular. 

Why is that an issue? You can do Set Theory without the Axiom of
Foundation.

-- 
     Shmuel (Seymour J.) Metz, SysProg and JOAT

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