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The multiplicative fragment of Linear Logic is the formal system in thisfamily with the best understood proof theory, and the categorical models whichbest capture this theory are the fully complete ones. We demonstrate how theHyland-Tan double glueing construction produces such categories, either with orwithout units, when applied to any of a large family of degenerate models. Thisprocess explains as special cases a number of such models from the literature.In order to achieve this result, we develop a tensor calculus for compactclosed categories with finite biproducts. We show how the combinatorialproperties required for a fully complete model are obtained by this glueingconstruction adding to the structure already available from the originalcategory.

Constructing Fully Complete Models of Multiplicative Linear Logic