Category Theory

The GHZ/W-calculus contains rational arithmetic

by Shibdas Roy

Logique, calcul et représentation : du point de vue des monades

by Sylvain Cabanacq

It's just an abstract - Full paper following very soon...

2D-LTFT

by Elden Elmanto

"Aristotle's Argument that Goods are Irreducible." In Just the Arguments: 100 of the Most Important Arguments in Western Philosophy, edited by M. Bruce and S. Barbone. Blackwell, 2011.

by Jurgis (George) Brakas

JUST THE ARGUMENTS "[is] a survey and presentation of 100 of the most important arguments in Western philosophy, wherein experts will write brief encyclopedia-like entries presenting arguments in their essence, including a representative quotation, explication of the context and the aim of the argument, and the argument's logical form."

An Institutional Theory for #-Components

by Francisco Carvalho-Junior

Electronic Notes in Theoretical Computer Science
Volume 195, Pages 113–132
January 2008

Proceedings of the Brazilian Symposium on Formal Methods (SBMF 2006)

The # (hash) component model has been proposed to bring the advantages of a component-based perspective of software... more The # (hash) component model has been proposed to bring the advantages of a component-based perspective of software for the development of high performance computing applications, targeting computer architectures enabled for grid, cluster and capability computing. In simple terms, it is a component model for general purpose parallel programming targeting distributed architectures. This paper presents an institutional theory for #-components, which has originated the idea of introducing parameterized and recursive abstract component types in # programming systems, making possible a general notion of skeletal programming.

A categorical characterization for the compositional features of the # component model

by Francisco Carvalho-Junior

ACM SIGSOFT Software Engineering Notes Homepage
Volume 31 Issue 2, March 2006
ACM New York, NY, USA

SAVCBS '05 (Proceedings of the 2005 conference on Specification and verification of component-based systems)

The # programming model attempts to address the needs of the high performance computing community for new paradigms... more The # programming model attempts to address the needs of the high performance computing community for new paradigms that reconcile efficiency, portability, abstraction and generality issues on parallel programming for high-end distributed architectures. This paper provides a semantics for the compositional features of # programs, based on category theory.

Relative contributions of kind-and domain-level concepts to expectations concerning unfamiliar exemplars

by Nathalie Bedoin

Two inferential routes allow children to produce expectations about new instances of ontological categories like... more Two inferential routes allow children to produce expectations about new instances of ontological categories like ‘animal’ and ‘artefact’. One is to generalise information from a “look-up table” of familiar kind-concepts. The other one is to use independent expectations at the level of ontological do¬mains. Our ex¬periment pits these two sources of information against each other, using a sentence-judgement task associating proper¬ties with images of famil¬iar and unfamil¬iar artefacts and animals. “Strange” properties are com¬patible with the ontological concept, but not encountered in any familiar kind. A look-up strategy would lead children to reject them and an independent expectation strategy to accept them. In both domains we find a difference in reaction to strange properties associated with familiar vs. unfamiliar items, which shows that even young children do use independent domain-level information. We also find a U-shaped curve in propensity to use such abstract information. Also, animal categories are the object of much more definite domain-level expectations, which supports the notion that the animal domain is more causally integrated than the artefact domain.

Towards arrow-theoretic semantics of ontologies: conceptories

by Osman Bineev

In context of efforts of composing category-theoretic and logical methods in the area of knowledge representation we... more In context of efforts of composing category-theoretic and logical methods in the area of knowledge representation we propose the notion of conceptory. We consider intersection/union and other constructions in conceptories as expressive alternative to category-theoretic (co)limits and show they have features similar to (pro-, in-)jections. Then we briefly discuss approaches to development of formal systems built on the base of conceptories and describe possible application of such system to the specific ontology.

Una introducción al análisis categorista de la lógica

by Luis Estrada-González

Si ese viejo profesor no creyera que la teoría de categorías es una vieja moda francesa, diría que este artículo es... more Si ese viejo profesor no creyera que la teoría de categorías es una vieja moda francesa, diría que este artículo es una buena aproximación a lo que todo lógico educado debería saber de teoría de topos.

TQFTs and Higher Dimensional Algebra

by Shay Logan

This paper introduces the tools of higher category theory in a very general and loose way, then demonstrates their use in studying TQFTs.

Object

by henry laycock

I have converted my own copy of this 2010 piece, which appears in the Stanford Encyclopedia of Philosophy, from WP into PDF for this document.
A LIVE-LINKS COMPLETE BIBLIOGRAPHY FOLLOWS
http://philpapers.org/sep/object/

ABSTRACT. The Frege / Russell account of the object-concept is here called into question. The most general category or... more ABSTRACT. The Frege / Russell account of the object-concept is here called into question. The most general category or concept of an object is a formal one -- a logico-semantic category which is not (as is commonly supposed) exhaustive of what may be thought or said to be. Bona fide objects, whether abstract or concrete, must be countable - 'no entity without identity' (and hence without distinctness). But stuff or matter is not countable and cannot be understood in terms of objects. The issue is significant, if only because the predicate calculus rests upon the object-concept: non-count nouns have no place within the notation

The Universal Hopf Cyclic Theory

by Atabey Kaygun

Graded category structure in Chinese-English bilinguals

by Jyotsna Vaid

Ward, T., Kolomyts, Chu, A., Vaid, J., & Heredia, R. (2009). International J Creativity and Problem Solving.

On the information-theoretic structure of distributed measurements

by David Balduzzi

Developments of Computational Models 2011, to appear Elec Proc Theoretical Comp Sci

The internal structure of a measuring device, which depends on what its components are and how they are organized,... more The internal structure of a measuring device, which depends on what its components are and how they are organized, determines how it categorizes its inputs. This paper presents a geometric approach to studying the internal structure of measurements performed by distributed systems such as probabilistic cellular automata. It constructs the quale, a family of sections of a suitably defined presheaf, whose elements correspond to the measurements performed by all subsystems of a distributed system. Using the quale we quantify (i) the information generated by a measurement; (ii) the extent to which a measurement is context-dependent; and (iii) whether a measurement is decomposable into independent submeasurements, which turns out to be equivalent to context-dependence. Finally, we show that only indecomposable measurements are more informative than the sum of their submeasurements.

Lecciones de la degeneración (O: ¿Qué hay de malo con la trivialidad?)

by Luis Estrada-González

Versión 4. He expandido la sección 3 y la parte de cómo se obtiene el trivialismo en un topos degenerado ahora es, creo, mucho más clara. Cualquier comentario es bienvenido.

Structural Algebraic Compactness

by Adam Eppendahl

Rejected by CALCO 2005

Alas, the motivating examples of algebraically compact categories are not algebraically compact and the enriched... more Alas, the motivating examples of algebraically compact categories are not algebraically compact and the enriched setting does not directly support the theory of algebraic compactness. We show that the structural setting, the same setting developed independently for models of linear logic, directly supports the theory of algebraic cocompleteness. We extend the structural setting to a bistructural setting that supports the full theory of algebraic compactness. These results provide a precise, elementary theory that includes Freyd's original theory together with the domain-theoretic models that motivated it, without reference to enriched, indexed or internal categories. We then describe how the structural setting fits together with the more sophisticated enriched and internal settings in which domain-theoretic models are commonly studied.

Syntactic Multicategories and Categorical Combinators for Linear Logic

by Valeria de Paiva

Categories and Types for Axiomatic Domain Theory

by Adam Eppendahl

PhD Thesis

Domain Theory provides a denotational semantics for programming languages and calculi containing fixed point... more Domain Theory provides a denotational semantics for programming languages and calculi containing fixed point combinators and other so-called paradoxical combinators. This dissertation presents results in the category theory and type theory of Axiomatic Domain Theory.
Prompted by the adjunctions of Domain Theory, we extend Benton's linear/nonlinear dual-sequent calculus to include recursive linear types. and define a class of models by adding Freyd's notion of algebraic compactness to the monoidal adjunctions that model Benton's calculus.
We observe that algebraic compactness is better behaved in the context of categories with structural actions than in the usual context of enriched categories. We establish a theory of structural algebraic compactness that allows us to describe our models without reference to enrichment. We develop a 2-categorical perspective on structural actions, including a presentation of monoidal categories that leads directly to Kelly's reduced coherence conditions.
We observe that Benton's adjoint type constructors can be treated individually, semantically as well as syntactically, using free representations of distributors.
We type various of fixed point combinators using recursive types and function types, which we consider the core types of such calculi, together with the adjoint types. We use the idioms of these typings, which include oblique function spaces, to give a translation of the core of Levy's Call-By-Push-Value. The translation induces call-by-value and call-by-name translations of the core of Plotkin's Fixed Point Calculus.
Following Freyd, we construct a canonical fixed point operation from the algebras provided by the algebraic compactness of our models. Our analysis of Freyd's construction exposes a remarkable property of morphisms from coalgebras to algebras: morphisms from Gp to s correspond one-for-one to morphisms from p to Hs, where p is a coalgebra for HG and s an algebra for GH. We give an application of this property to the transposition of recursive coalgebras in Taylor's categorical theory of recursion where G is not left adjoint to H.
We develop a theory of parametric transformations corresponding to the uniformity property characterizing canonical fixed points and use this to derive abstract conditions on categories of domains which ensure that the interpretation of fixed point combinators coincides with the canonical fixed point operation.

A Mathematical Derivation of a Risk Assessment Procedure

by Marco Benini

Co-authored with Sabrina Sicari

Risk assessment is a well-established engineering practise widely applied on technological systems. Despite its... more Risk assessment is a well-established engineering practise widely applied on technological systems. Despite its spread, few attempts have been made to formalise its basis in order to provide a non-empirical foundation. In this article we introduce a formal analysis of risk assessment in an algebraic framework, considering also the case of multiple experts. Results about the reliability and the applicability of the framework will be derived according to the structural properties of the problem formalisation.

[IAENG International Journal of Applied Mathematics,
volume 40 issue 2, 13 May 2010, Pages 52-62]

From Computing Machineries to Cloud Computing: The Minimal Levels of Abstraction of Inforgs through History

by Marco Benini

Co-authored with Federico Gobbo

[HAPOC-11] [HAPOC-11]