Intensional double glueing, biextensional collapse, and the Chu construction
نویسنده
چکیده
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 K into G(Rel), and a full monoidal embedding of the category Chu(Set,K) of Chu spaces over K into IG(Rel), 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.
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