Papers › Proof Theory of Partially Normal Skew Monoidal Categories
Proof Theory of Partially Normal Skew Monoidal Categories
Tarmo Uustalu, Niccolò Veltri, Noam Zeilberger
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The skew monoidal categories of Szlach\'anyi are a weakening of monoidal categories where the three structural laws of left and right unitality and associativity are not required to be isomorphisms but merely transformations in a particular direction. In previous work, we showed that the free skew monoidal category on a set of generating objects can be concretely presented as a sequent calculus. This calculus enjoys cut elimination and admits focusing, i.e. a subsystem of canonical derivations, which solves the coherence problem for skew monoidal categories. In this paper, we develop sequent calculi for partially normal skew monoidal categories, which are skew monoidal categories with one or more structural laws invertible. Each normality condition leads to additional inference rules and equations on them. We prove cut elimination and we show that the calculi admit focusing. The result is a family of sequent calculi between those of skew monoidal categories and (fully normal) monoidal categories. On the level of derivability, these define 8 weakenings of the (unit,tensor) fragment of intuitionistic non-commutative linear logic.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections