40.2k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- National Institute of Chemical Physics and BiophysicsEE28 papers
- University of TartuEE15 papers
- Istituto Nazionale di Fisica Nucleare, Sezione di PadovaIT10 papers
- University of OxfordGB10 papers
- University of PaduaIT10 papers
- University of CambridgeGB9 papers
- Aalto UniversityFI8 papers
- Centre National de la Recherche ScientifiqueFR8 papers
- European Organization for Nuclear ResearchCH8 papers
- University of HelsinkiFI8 papers
- King's College LondonGB7 papers
- Reykjavík UniversityIS6 papers
32 papers · 1 filter
Cyclic Nonassociative Bilinear Logic With Additive Constants as Extension of Full Nonassociative Lambek Calculus
Paweł Płaczek, Cheng-Syuan Wan
Cyclic Linear Logic (CyMALL, CyBL) is a compromise between Commutative Linear Logic (MALL) and Noncommutative Linear Logic (Bilinear Logic, BL). We do not admit commutativity of th…
Monoid Structures on Indexed Containers
Michele De Pascalis, Tarmo Uustalu, Niccolò Veltrì
Containers represent a wide class of type constructions relevant for functional programming and (co)inductive reasoning. Indexed containers generalize this notion to better fit the…
Order in Partial Markov Categories
Elena Di Lavore, Mario Román, Paweł Sobociński +1
Partial Markov categories are a recent framework for categorical probability theory that provide an abstract account of partial probabilistic computation with updating semantics. I…
The calculus of neo-Peircean relations
Filippo Bonchi, Alessandro Di Giorgio, Nathan Haydon +1
The calculus of relations was introduced by De Morgan and Peirce during the second half of the 19th century, as an extension of Boole's algebra of classes. Later developments on qu…
Semi-Substructural Logics with Additives
Niccolò Veltri, Cheng-Syuan Wan
This work concerns the proof theory of (left) skew monoidal categories and their variants (e.g. closed monoidal, symmetric monoidal), continuing the line of work initiated in recen…
Canonical Gradings of Monads
Flavien Breuvart, Dylan McDermott, Tarmo Uustalu
We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable con…
Monoidal Width
Elena Di Lavore, Paweł Sobociński
We introduce monoidal width as a measure of complexity for morphisms in monoidal categories. Inspired by well-known structural width measures for graphs, like tree width and rank w…
What Makes a Strong Monad?
Dylan McDermott, Tarmo Uustalu
Strong monads are important for several applications, in particular, in the denotational semantics of effectful languages, where strength is needed to sequence computations that ha…
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…
Normalization by Evaluation for the Lambek Calculus
Niccolò Veltri
The syntactic calculus of Lambek is a deductive system for the multiplicative fragment of intuitionistic non-commutative linear logic. As a fine-grained calculus of resources, it h…
Inductive and Coinductive Predicate Liftings for Effectful Programs
Niccolò Veltri, Niels F. W. Voorneveld
We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution…
On Doctrines and Cartesian Bicategories
Filippo Bonchi, Alessio Santamaria, Jens Seeber +1
We study the relationship between cartesian bicategories and a specialisation of Lawvere's hyperdoctrines, namely elementary existential doctrines. Both provide different ways of a…
String Diagrammatic Electrical Circuit Theory
Guillaume Boisseau, Paweł Sobociński
We develop a comprehensive string diagrammatic treatment of electrical circuits. Building on previous, limited case studies, we introduce controlled sources and meters as elements,…
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…
Functorial Semantics for Partial Theories
Ivan Di Liberti, Fosco Loregian, Chad Nester +1
We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case,…
A Foundation for Ledger Structures
Chad Nester
This paper introduces an approach to constructing ledger structures for cryptocurrency systems with basic category theory. Compositional theories of resource convertibility allow u…
Concurrent Process Histories and Resource Transducers
Chad Nester
We identify the algebraic structure of the material histories generated by concurrent processes. Specifically, we extend existing categorical theories of resource convertibility to…
From Equations to Distinctions: Two Interpretations of Effectful Computations
Niels Voorneveld
There are several ways to define program equivalence for functional programs with algebraic effects. We consider two complementing ways to specify behavioural equivalence. One way…
Constructing Higher Inductive Types as Groupoid Quotients
Niccolò Veltri, Niels van der Weide
In this paper, we study finitary 1-truncated higher inductive types (HITs) in homotopy type theory. We start by showing that all these types can be constructed from the groupoid qu…
Codensity Lifting of Monads and its Dual
Shin-ya Katsumata, Tetsuya Sato, Tarmo Uustalu
We introduce a method to lift monads on the base category of a fibration to its total category. This method, which we call codensity lifting, is applicable to various fibrations wh…
Rule Algebras for Adhesive Categories
Nicolas Behr, Pawel Sobocinski
We demonstrate that the most well-known approach to rewriting graphical structures, the Double-Pushout (DPO) approach, possesses a notion of sequential compositions of rules along…
Graphical Sequent Calculi for Modal Logics
Minghui Ma, Ahti-Veikko Pietarinen
The syntax of modal graphs is defined in terms of the continuous cut and broken cut following Charles Peirce's notation in the gamma part of his graphical logic of existential grap…
A Universal Construction for (Co)Relations
Brendan Fong, Fabio Zanasi
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits an…