Years ago Dana Scott gave us a minimal non-trivial exponential category (CCC), *S*. Besides the terminator it has just one (non-isomorphic) object, D. (Necessarily, DxD = D = D^D.) The obvious question has been repeatedly asked: what finite numbers larger than two can appear as the number of isomorphism types? It was asked again a couple of weeks ago at Vancouver. The question is a good one but needs a formulation. As it stands it allows an annoyingly easy answer: take any finite Heyting algebra and view it as a category. Herewith is a failed attempt for such a formulation. Let's first knock out the Heyting algebras by demanding strong connectivity (given any ordered pair of objects there's a map from the first to the second). Let's demand the Cantor-Bernstein-Schroeder property (objects that appear as retracts of each other are isomorphic). It and finiteness say that for every object, A, there's an integer such that the (n+1)-fold cartesian power of A is isomorphic to the n-fold power. So let's go a bit further and demand that n = 1, that is, every object is a Jonnson-Tarski object (isomorphic to its own cartesian square). Given these conditions if we use the existence of retractions to order the isomorphism types (CBS says precisely that such is a partial ordering, not just a pre-ordering) then cartesian products deliver least upper bounds (unfortunately we are stuck with denoting the bottom of this semi-lattice as 1). Proposition: Every join semi-lattice appears as the poset of isomorphism types of a strongly connected Cantor-Bernstein-Schroeder Jonnson-Tarski exponential category. Because: Given a join semi-lattice, L, in the L-fold cartesian power of the Scott category (which we'll realize as the set of functions from L to *S*) construct the desired category as the full subcategory of "characteristic functions of principle ideals", that is, objects of the form f_x: L --> *S* where x is an element in L and f_x (y) = 1 iff x is less than or equal to y . (Note that any full subcategory of a cartesian power of *S* is closed under exponentiation: *S* satisfies the equation X^Y = X hence so does any of its cartesian powers.) So maybe the question is: What finite numbers appear as the numbers of isomorphism types in _subdirectly irreducible_ strongly connected exponential categories?