8 citations · 23 across the 6 of their papers we have counts for
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Proof Theory of Skew Non-Commutative MILL
Tarmo Uustalu, Niccolò Veltri, Cheng-Syuan Wan
Monoidal closed categories naturally model NMILL, non-commutative multiplicative intuitionistic linear logic: the monoidal unit and tensor interpret the multiplicative verum and co…
Proof Theory of Partially Normal Skew Monoidal Categories
Tarmo Uustalu, Niccolò Veltri, Noam Zeilberger
The skew monoidal categories of Szlachányi are a weakening of monoidal categories where the three structural laws of left and right unitality and associativity are not required to…
Deductive Systems and Coherence for Skew Prounital Closed Categories
Tarmo Uustalu, Niccolò Veltri, Noam Zeilberger
In this paper, we develop the proof theory of skew prounital closed categories. These are variants of the skew closed categories of Street where the unit is not represented. Skew c…
The Sequent Calculus of Skew Monoidal Categories
Tarmo Uustalu, Niccolò Veltri, Noam Zeilberger
Szlachányi's skew monoidal categories are a well-motivated variation of monoidal categories in which the unitors and associator are not required to be natural isomorphisms, but mer…
Interaction laws of monads and comonads
Shin-ya Katsumata, Exequiel Rivas, Tarmo Uustalu
We introduce and study functor-functor and monad-comonad interaction laws as mathematical objects to describe interaction of effectful computations with behaviors of effect-perform…
Directed Containers as Categories
Danel Ahman, Tarmo Uustalu
Directed containers make explicit the additional structure of those containers whose set functor interpretation carries a comonad structure. The data and laws of a directed contain…