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