## 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.