categories: Re: Michael Healy's question on math and AI

[Michael Barr <barr@barrs.org>]

I mean the initial algebra for the theory with a nullary operation 0:1 -->
N and a unary operation s:N --> N.  1 stands for the terminal object
(empty product).

On Sun, 28 Jan 2001, Bill Halchin wrote:

> 
> 
> >For another example, consider the traditional definition of Z as the set
> >{0,{0},{0,{0}},{0,{0}{0,{0}}},...}
> >and contrast that to the categorical specification.
>      ^^^ Michael, to make things more explicit I take you
>       mean the category with one object N and two arrows, 0 & S,
>    such that
> 
>        0:N->N and s:N->N
> 
>    Yes?
> 
>    Regards,
> 
>    Bill Halchin