Intensional Double Glueing, Biextensional Collapse, and the Chu Construction.

Abstract: The superficial similarity between the Chu construction and the Hyland-Tan double glueing construction G has been observed widely. This paper establishes a more formal mathematical relationship between the two. We show that double glueing on relations subsumes the Chu construction on sets: we present a full monoidal embedding of the category chu(Set, K) of biextensional Chu spaces over Κ into G(Rel ^K ), and a full monoidal embedding of the category Chu(Set, K) of Chu spaces over Κ into IG(Rel ^K ), where we define IG, the intensional double glueing construction, by substituting multisets for sets in G. We define a biextensional collapse from IG to G which extends the familiar notion on Chu spaces. This yields a new interpretation of the monic specialisation implicit in G as a form of biextensionality. [Copyright &y& Elsevier]