Factorisation Systems on Domains

We present a cartesian closed category of continuous domains containing the classical examples of Scott-domains with continuous functions and Berry's dI-domains with stable functions as full cartesian closed subcategories. Furthermore, the category is closed with respect to bilimits and there is an algebraic and a generalised topological description of its morphisms. 1 Introduction There are two kinds of morphism that are studied in classical domain theory, Scott-continuous ones and stable ones. Berry introduced stable maps to model sequentiality in the -calculus [Ber78]. A stable map, in addition to being continuous (i.e. preserving directed suprema), also preserves bounded binary infima. So, for first order the stable functions are a subset of the continuous ones, but at higher order types the continuous and the stable function space become incomparable. Stability captures sequentiality to some extend, e.g. POR is not a stable function, yet the stable model of PCF fails to be fully..