Robin Cockett - Double glueing

The glueing construction in the form of the Freyd covering is a well-known and useful tool in categorical logic. Recently Hyland and Tan showed how a variation of this construction, which they called the double glueing construction, could be used both to produce new models of linear logic and to establish the full completeness of certain existing models. These ideas were further generalized by Masahito Hasegewa in order to establish the full completeness of the translations between certain linear type theories.

The talk will discuss the generalization of these ideas to linearly distributive categories and indicate the connection between the double glueing construction and the Chu construction. In particular, a variation of the standard double glueing construction will be presented (which might be called Chu-glue). This latter construction, I claim, is the more natural construction when morphisms are understood to be linear functors.