Re: A small cartesian closed concrete category

[Paul Taylor <pt08@PaulTaylor.EU>]

Peter Easthope asked,

> Is there a cartesian closed concrete category which
> is small enough to write out explicitly?  It would be
> helpful in learning about map objects, exponentiation,
> distributivity and etc.   Can such a category be made
> with binary numbers for instance?

How about finite sets and functions?

Not just a CCC but an elementary topos.

I'm not sure what you mean by "binary numbers", but the powerset
of  n  is  2^n   (I wonder why Cantor introduced this notation?),
and the subsets of  n  are n-digit binary numbers.

As for more general function spaces, maybe it's worth an
undergraduate exercise to see whether there's a neat
representation.

NBB:  You don't need even to have heard of domain theory
to find examples of CCCs!

Paul Taylor