Section: New Results

Semi-Star-Autonomous Categories

Participants : Willem Heijltjes, Lutz Straßburger.

A curious aspect of Girard's proof nets for multiplicative linear logic without units is that, despite being a canonical representation of proof, their categorical semantics is not obvious—this in contrast to the situation with units, where star-autonomous categories form a natural semantics, but no canonical proof nets are known.

In the middle of the past decade several proposals for a categorical semantics of proof nets, a notion of semi-star-autonomous categories, were investigated: by Robin Houston and Dominic Hughes, by Kosta Došen, and by François Lamarche and Lutz Straßburger.

The present effort by Willem Heijltjes and Lutz Straßburger completes the notion in such a way that proof nets constitute the free semi-star-autonomous category.