The main result of this paper may be stated as a construction of “almost representations” μn and μ̃n for the presheaves Obn and Õbn on the C-systems defined by locally cartesian closed universe categories with binary product structures and the study of the behavior of these “almost representations” with respect to the universe category functors. In addition, we study a number of constructions on...

We define and study the property of local diagonality for partial algebras and also a pair of related properties. We show that each of the three properties, together with idempotency, gives a cartesian closed initially structured subcategory of the category of all partial algebras of a given type. MSC 2000: 08A55, 08C05, 18D15

In this sequel to [HM02], we explore some of the global aspects of the category of paracategories. We establish its (co)completeness and cartesian closure. From the closed structure we derive the relevant notion of transformation for paracategories. We set-up the relevant notion of adjunction between paracategories and apply it to define (co)completeness and cartesian closure, exemplified by th...

We show that the cartesian closed category of compactly generated Hausdorff spaces is regular, but is neither exact, nor locally cartesian closed. In fact we find a coequalizer of an equivalence relation which is not stable under pullbacks.

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.

We present here ”the” cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps smooth curves to smooth curves and real analytic curves to real analytic curves. Under mild completeness conditions the second requirement can be replaced by: real analytic along affine lines. Enclose...

The aim of this paper is to establish some Cartesian closed categories which are between the two Cartesian closed categories: SLP (the category of L-domains and stable functions) and DI (the full subcategory of SLP whose objects are all dI-domains). First we show that the exponentials of every full subcategory of SLP are exactly the spaces of stable functions. Then we prove that the full subcat...

Inspired by a construction of Escardó, Lawson, and Simpson, we give a general construction of C-generated objects in a topological construct. When C consists of exponentiable objects, the resulting category is Cartesian-closed. This generalizes the familiar construction of compactly-generated spaces, and we apply this to Krishnan’s categories of streams and prestreams, as well as to Haucourt st...

This paper presents two categories of effective continuous cpos. We define a new criterion on the basis of a cpo as to make the resulting category of consistently complete continuous cpos cartesian closed. We also generalise the definition of a complete set, used as a definition of effective bifinite domains in [HSH02], and investigate what closure results that can be obtained.

Information systems with witnesses have been introduced in [13] as a logic-style representation of L-domains: The category of such information systems with approximable mappings as morphisms is equivalent to the category of L-domains with Scott continuous functions, which is known to be Cartesian closed. In the present paper a direct proof of the Cartesian closure of the category of information...