The Sequent Calculus of Skew Monoidal Categories

  title={The Sequent Calculus of Skew Monoidal Categories},
  author={Tarmo Uustalu and Niccol{\`o} Veltri and Noam Zeilberger},

Proof Theory of Partially Normal Skew Monoidal Categories

This paper develops sequent calculi for partially normal skew monoidal categories, which are skew monoid categories with one or more structural laws invertible, and proves cut elimination and shows that the calculi admit focusing.

Proof Theory of Skew Non-Commutative MILL

Monoidal closed categories naturally model NMILL , non-commutative multiplicative intuitionistic linear logic: the monoidal unit and tensor interpret the multiplicative verum and conjunction; the

Deductive Systems and Coherence for Skew Prounital Closed Categories

The coherence problem for skew prounital closed categories is solved by showing that the sequent calculus admits focusing and presenting two reduction-free normalization procedures for the natural deduction calculus: normalization by evaluation and hereditary substitutions.

Eilenberg-Kelly Reloaded

LNL polycategories and doctrines of linear logic

It is shown that free algebras for LNL doctrines can be presented by a sequent calculus, and that every morphism of doctrines induces an adjunction between their 2-categories of alge bras.

How to Take the Inverse of a Type (Artifact)

In functional programming, regular types are a subset of algebraic data types formed from products and sums with their respective units. One can view regular types as forming a commutative semiring

Type inhabitation of atomic polymorphism is undecidable

This paper shows that type inhabitation for $\mathbf{F_{at}}$ is undecidable by codifying within it an Undecidable fragment of first-order intuitionistic predicate calculus, adapting and modifying the technique of Urzyczyn’s purely syntactic proof of the undecidability of type inhabitations for $F$.

Principles of Program Verification for Arbitrary Monadic Effects. (Principes de la Vérification de Programmes à Effets Monadiques Arbitraires)

The goal of this thesis is to devise a principled semantic framework for verifying programs with arbitrary monadic effects in a generic way with respect to rich specifications, for properties such as program equivalence.



A Sequent Calculus for a Semi-Associative Law

A sequent calculus with a simple restriction of Lambek's product rules is introduced that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words induced by a semi-associative law.

Skew-monoidal categories and bialgebroids

Coherence for Skew-Monoidal Categories

A variation of monoidal categories called skew-monoidal cat- egories where the unital and associativity laws are not required to be isomorphisms, only natural transformations is motivated, and a proof of this coherence proof is presented.

Deductive systems and categories

  • J. Lambek
  • Mathematics
    Mathematical systems theory
  • 2005
The author plans to pursue this subject further by investigating standard constructions on the category of categories in general, and by looking at special deductive systems, in particular at the propositional calculus and its relation to Curry's theory of combinators.

Triangulations, orientals, and skew monoidal categories☆

Skew monoidales, skew warpings and quantum categories

Kornel Szlach\'anyi recently used the term skew-monoidal category for a particular laxified version of monoidal category. He showed that bialgebroids $H$ with base ring $R$ could be characterized in

Skew-closed categories

Monads need not be endofunctors

A generalization of monads is introduced, called relative monads, allowing for underlying functors between different categories, and it is shown that the Kleisli and Eilenberg-Moore constructions carry over to relative monad and are related to relative adjunctions.

Free skew monoidal categories

Associahedra, tamari lattices and related structures : Tamari memorial festschrift

Tamari lattices originated from weakenings or reinterpretations of the familiar associativity law. This has been the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central