## 8 Citations

### Proof Theory of Partially Normal Skew Monoidal Categories

- MathematicsACT
- 2020

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

- MathematicsNCL
- 2022

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

- MathematicsLFMTP
- 2020

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.

### LNL polycategories and doctrines of linear logic

- MathematicsArXiv
- 2021

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)

- MathematicsDagstuhl Artifacts Ser.
- 2022

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

- Computer ScienceJ. Log. Comput.
- 2021

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)

- Computer Science
- 2019

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.

## References

SHOWING 1-10 OF 35 REFERENCES

### A Sequent Calculus for a Semi-Associative Law

- MathematicsFSCD
- 2017

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.

### Coherence for Skew-Monoidal Categories

- MathematicsMSFP
- 2014

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

- MathematicsMathematical 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.

### Skew monoidales, skew warpings and quantum categories

- Mathematics
- 2012

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…

### Monads need not be endofunctors

- MathematicsLog. Methods Comput. Sci.
- 2010

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

- MathematicsJournal of Pure and Applied Algebra
- 2018

### Associahedra, tamari lattices and related structures : Tamari memorial festschrift

- Mathematics
- 2012

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…