Double glueing and models of linear logic

Many full completeness theorems have been established for fragments of linear logic since the notion was first defined by Samson Abramsky and Radha Jagadeesan in their 1992 paper. For the most part, these results are obtained on a case-by-case basis: the subject of each proof is precisely one category.

In this talk it is shown that certain double glueing constructions can transform tensor-generated compact closed categories with finite biproducts into stronger models of linear logic. By creating a `glueing' over homfunctors and using only standard linear algebra, we show that every such category can act as the basis of a fully complete model of unit-free MLL. We also discuss how the category of hypercoherence spaces can also be seen as a double-glued category, and that the associated construction may be generalised to help create a family of accurate unit-free MALL models.