Dear categorists, A small category C has finite products just when the representables in [C^op, Set] are closed under finite products. It is cartesian closed just when the representables are closed under finite products and internal hom. It seems natural, therefore, to consider a notion of "cartesian closedness without finite products": categories in which the representables are closed in [C^op, Set] under internal hom but not necessarily under finite products. This amounts to giving, for each pair of objects X and Y, an object [X, Y] together with a universal natural transformation C(-, [X, Y]) x C(-, X) -> C(-, Y). Such categories will be closed in the sense of Eilenberg-Kelly without necessarily being monoidal: let us call them "universally closed" for now. Obviously, any cartesian closed category is universally closed; and categorical proof theory gives us a class of non-degenerate examples built from the syntax of (classical) sequent calculi with implication but no product. The question now arises as to whether there are any non-syntactic examples of universally closed categories which are not cartesian closed. The most likely place seems to me to be domain theory, but I have been unable to track anything down. Does anyone have any pointers? Thanks, Richard.