Re: A small cartesian closed concrete category

["Matt Hellige" <matt@immute.net>]

On Thu, Feb 14, 2008 at 9:46 PM, Fred E.J. Linton <fejlinton@usa.net> wrote:
> On Thu, 14 Feb 2008 10:07:27 PM EST, PETER EASTHOPE <peasthope@shaw.ca>
>  asked:
>
>  > Is there a cartesian closed concrete category which
>  > is small enough to write out explicitly?
>
>  try the skeletal version of the full category of "sets of cardinality < 2"
>  having as only objects the ordinal numbers 0 and 1.
>
>  Here 0 x A = 0, 1 x A = A, 0^1 = 0, 0^0 = 1, 1^A = 1.
>  In other words, B x A = min(A, B), B^A = max(1-A, B).
>

Or, in case that's too small, what about any short chain? For
instance, let S = {0,1,2,3} and say there exists a morphism a -> b iff
a < b. I believe this is cartesian closed, and I believe it can easily
be understood as concrete. This should be enough to give non-trivial
product and exponentiation, but you can still draw the whole diagram.

Matt

-- 
Matt Hellige / matt@immute.net
http://matt.immute.net