0. Introduction. I t is well known that for much of the mathematics of topos theory, it is in fact sufficient to use a category C whose slice categories C/A are cartesian closed. In such a category, the notion of a 'generalized set', for example an 'Aindexed set', is represented by a morphism B^-A of C, i.e. by an object of C/A. The point about such a category C is that C is a C-indexed categor...

Perhaps the most important and striking fact of domain theory is that important categories of domains are cartesian closed. This means that the category has a terminal object, finite products, and exponents. The only problematic part for domains is the exponent, which in this setting means the space of continuous functions. Cartesian closed categories of domains are well understood and the unde...

Simpson, A.K., A characterisation of the least-fixed-point operator by dinaturality, Theoretical Computer Science 118 (1993) 301-314. The paper addresses the question of when the least-fixed-point operator, in a Cartesian-closed category of domains, is characterised as the unique dinatural transformation from the exponentiation bifunctor to the identity functor. We give a sufficient condition o...