Giuseppe Rosolini

TCS Journal 2014 Journal Article

Sobriety for equilogical spaces

• Anna Bucalo
• Giuseppe Rosolini

The category of equilogical spaces, as well as the exact completions of the category of T 0 -spaces and of the category of topological spaces, offers locally cartesian closed extensions of the category of topological spaces. Hence in any one of such categories, it is straightforward to consider spaces of continuous functions without bothering about ensuring that they be topological spaces. We test this fact with the notion of sober topological space, producing a synthetic characterization of those topological spaces which are sober in terms of a construction on equilogical spaces of functions.

TCS Journal 2004 Journal Article

Preface

• Lars Birkedal
• Martín Escardó
• Achim Jung
• Giuseppe Rosolini

TCS Journal 2002 Journal Article

Fixpoint operators for domain equations

• John Power
• Giuseppe Rosolini

We investigate fixpoint operators for domain equations. It is routine to verify that if every endofunctor on a category has an initial algebra, then one can construct a fixpoint operator from the category of endofunctors to the category. That construction does not lift routinely to enriched categories, using the usual enriched notion of initiality of an endofunctor. We show that by embedding the 2-category of small enriched categories into the 2-category of internal categories of a presheaf topos, we can recover the fixpoint construction elegantly. Also, we show that in the presence of cotensors, an enriched category allows the fixpoint construction.

CSL Conference 2001 Conference Paper

An Abstract Look at Realizability

• Edmund Robinson
• Giuseppe Rosolini

Abstract This paper is about the combinatorial properties necessary for the construction of realizability models with certain type-theoretic properties. We take as our basic construction a form of tagging in which elements of sets are equipped with tags, and functions must operate constructively on tags. To complete the construction we allow a form of closure under quotients by equivalence relations. In this paper we analyse first the condition for a natural monoidal structure to be product structure, and then investigate necessary conditions for the realizability model to be locally cartesian closed and to have a subobject classifier.

TCS Journal 2001 Journal Article

Domains in H

• Marcelo P. Fiore
• Giuseppe Rosolini

We give various internal descriptions of the category ω- Cpo of ω-complete posets and ω-continuous functions in the model H of Synthetic domain theory introduced in Fiore and Rosolini (J. Pure Appl. Algebra 116 (1997) 151–162). It follows that the ω-cpos lie between the two extreme synthetic notions of domain given by repleteness and well-completeness.