Academic literature on the topic 'Formal category theory'
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Journal articles on the topic "Formal category theory"
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Vickers, P., J. Faith, and N. Rossiter. "Understanding Visualization: A Formal Approach Using Category Theory and Semiotics." IEEE Transactions on Visualization and Computer Graphics 19, no. 6 (June 2013): 1048–61. http://dx.doi.org/10.1109/tvcg.2012.294.
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Fradi, Mouna, Faïda Mhenni, Raoudha Gaha, Abdelfattah Mlika, and Jean-Yves Choley. "Conflict Resolution in Mechatronic Collaborative Design Using Category Theory." Applied Sciences 11, no. 10 (May 14, 2021): 4486. http://dx.doi.org/10.3390/app11104486.
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Due to the multitude of disciplines involved in mechatronic design, heterogeneous languages and expert models are used to describe the system from different domain-specific views. Despite their heterogeneity, these models are highly interrelated. As a consequence, conflicts among expert models are likely to occur. In order to ensure that these models are not contradictory, the necessity to detect and manage conflicts among the models arises. Detecting these inconsistencies at an early stage significantly reduces the amount of engineering activities re-execution. Therefore, to deal with this issue, a formal framework relying upon mathematical concepts is required. The mathematical theory, namely category theory (CT), is considered as an efficient tool to provide a formal and unifying framework supporting conflict detection and management. This paper proposes a comprehensive methodology that allows conflict detection and resolution in the context of mechatronic collaborative design. CT is used in order to explicitly capture the inconsistencies occurred between the disparate expert models. By means of this theory, the conflicts can be detected and handled in an easy and formal way. Our proposed approach is applied to a collaborative scenario concerning the electro-mechanical actuator (EMA) of the aileron.
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Gillibert, Jean, and Christian Retoré. "Category theory, logic and formal linguistics: Some connections, old and new." Journal of Applied Logic 12, no. 1 (March 2014): 1–13. http://dx.doi.org/10.1016/j.jal.2014.01.001.
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Blanc, Anthony, Ludmil Katzarkov, and Pranav Pandit. "Generators in formal deformations of categories." Compositio Mathematica 154, no. 10 (August 30, 2018): 2055–89. http://dx.doi.org/10.1112/s0010437x18007303.
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In this paper we use the theory of formal moduli problems developed by Lurie in order to study the space of formal deformations of a$k$-linear$\infty$-category for a field$k$. Our main result states that if${\mathcal{C}}$is a$k$-linear$\infty$-category which has a compact generator whose groups of self-extensions vanish for sufficiently high positive degrees, then every formal deformation of${\mathcal{C}}$has zero curvature and moreover admits a compact generator.
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Bénabou, Jean. "Fibered categories and the foundations of naive category theory." Journal of Symbolic Logic 50, no. 1 (March 1985): 10–37. http://dx.doi.org/10.2307/2273784.
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Any attempt to give “foundations”, for category theory or any domain in mathematics, could have two objectives, of course related.(0.1) Noncontradiction: Namely, to provide a formal frame rich enough so that all the actual activity in the domain can be carried out within this frame, and consistent, or at least relatively consistent with a well-established and “safe” theory, e.g. Zermelo-Frankel (ZF).(0.2) Adequacy, in the following, nontechnical sense:(i) The basic notions must be simple enough to make transparent the syntactic structures involved.(ii) The translation between the formal language and the usual language must be, or very quickly become, obvious. This implies in particular that the terminology and notations in the formal system should be identical, or very similar, to the current ones. Although this may seem minor, it is in fact very important.(iii) “Foundations” can only be “foundations of a given domain at a given moment”, therefore the frame should be easily adaptable to extensions or generalizations of the domain, and, even better, in view of (i), it should suggest how to find meaningful generalizations.(iv) Sometimes (ii) and (iii) can be incompatible because the current notations are not adapted to a more general situation. A compromise is then necessary. Usually when the tradition is very strong (ii) is predominant, but this causes some incoherence for the notations in the more general case (e.g. the notation f(x) for the value of a function f at x obliges one, in category theory, to denote the composition of arrows (f, g) → g∘f, and all attempts to change this notation have, so far, failed).
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López, Luis. "On the (Non)complementarity of θ-Theory and Checking Theory." Linguistic Inquiry 32, no. 4 (October 2001): 694–716. http://dx.doi.org/10.1162/002438901753373050.
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Chomsky (1995) proposes that the θ system and the checking system form two complementary modules. As a consequence both subjects and objects must form nontrivial chains to check their formal features with a functional category (T and v, respectively). I argue that objects and exceptional-Case-marking subjects check their formal features with a lexical verb, whose domain is therefore both θ role assigning and feature checking. I showthat discarding the complementarity assumption in this manner results in a more “bare” theory of the computational system as well as several empirical advantages.
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Mabrok, Mohamed A., and Michael J. Ryan. "Category Theory as a Formal Mathematical Foundation for Model-Based Systems Engineering." Applied Mathematics & Information Sciences 11, no. 1 (January 1, 2017): 43–51. http://dx.doi.org/10.18576/amis/110106.
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Sukharev, A. "The unobservable as an economic category." Obshchestvo i ekonomika, no. 3 (2022): 35. http://dx.doi.org/10.31857/s020736760019060-5.
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The definition of the unobservable in the field of science is given. The ideas about the unobservable in philosophy, physics, economics, etc. are presented. In economic science, the unobservable is presented in two perspectives: as unobservable objects and processes and as constructed categories (concepts) designed to reflect the essential aspects of economic life. The role of abstractions in economic theory is shown. Economic theory is a collection of unobservable abstractions, and its development takes place on the basis of the construction of new abstractions. The system of abstractions, being a formal system, forms a particular economic theory, and the aggregate of those represents a general economic theory. A hypothesis about the internal non-contradictoriness of private economic theories is stated.
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Li, Hong, and Xiao Ping Ma. "Granular Structure Merging Algorithm Based on Category Theory." Applied Mechanics and Materials 128-129 (October 2011): 390–96. http://dx.doi.org/10.4028/www.scientific.net/amm.128-129.390.
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In order to solve the problem of conversion from the finer level of granularity to the coarser level of granularity, this paper proposes a formal method for Granular structure merging based on category theory. Firstly, it takes the granular structure as the granular object and the granular structure mapping as the granular morphism, then the granular object and the granular morphism compose the granular structure category. Secondly, it uses the granular morphism and the granular pushout to achieve the granular structure merging , then gets the granular structure merging algorithm (GrSM). Finally, the author illustrates the method with the concrete examples, which solves the granular structure merging issue. This method has a solid mathematical foundation and methodology, which is worth further study.
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Wang, Yonghao. "Law as an important category in the ancient Chinese formal criticism." Frontiers of Literary Studies in China 4, no. 1 (February 12, 2010): 117–37. http://dx.doi.org/10.1007/s11702-010-0006-1.
Full textDissertations / Theses on the topic "Formal category theory"
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Shen, Gongqin. "Formal Concepts and Applications." Case Western Reserve University School of Graduate Studies / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=case1121454398.
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Paradis, Philippe. "On the Rational Retraction Index." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23111.
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If X is a simply connected CW complex, then it has a unique (up to isomorphism) minimal Sullivan model. There is an important rational homotopy invariant, called the rational Lusternik–Schnirelmann of X, denoted cat0(X), which has an algebraic formulation in terms of the minimal Sullivan model of X. We study another such numerical invariant called the rational retraction index of X, denoted r0(X), which is defined in terms of the minimal Sullivan model of X and satisfies 0 ≤ r0(X) ≤ cat0(X). It was introduced by Cuvilliez et al. as a tool to estimate the rational Lusternik–Schnirelmann category of the total space of a fibration. In this thesis we compute the rational retraction index on a range of rationally elliptic spaces, including for example spheres, complex projective space, the biquotient Sp(1) \ Sp(3) / Sp(1) × Sp(1), the homogeneous space Sp(3)/U(3) and products of these. In particular, we focus on formal spaces and formulate a conjecture to answer a question posed in the original article of Cuvilliez et al., “If X is formal, what invariant of the algebra H∗(X;Q) is r0(X)?”
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Lawrence, Nicholas. "A Brief Introduction to Transcendental Phenomenology and Conceptual Mathematics." Thesis, Södertörns högskola, Filosofi, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:sh:diva-32873.
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By extending Husserl’s own historico-critical study to include the conceptual mathematics of more contemporary times – specifically category theory and its emphatic development since the second half of the 20th century – this paper claims that the delineation between mathematics and philosophy must be completely revisited. It will be contended that Husserl’s phenomenological work was very much influenced by the discoveries and limitations of the formal mathematics being developed at Göttingen during his tenure there and that, subsequently, the rôle he envisaged for his material a priori science is heavily dependent upon his conception of the definite manifold. Motivating these contentions is the idea of a mathematics which would go beyond the constraints of formal ontology and subsequently achieve coherence with the full sense of transcendental phenomenology. While this final point will be by no means proven within the confines of this paper it is hoped that the very fact of opening up for the possibility of such an idea will act as a supporting argument to the overriding thesis that the relationship between mathematics and phenomenology must be problematised.
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Worth, Andrew Christopher. "English Coordination in Linear Categorial Grammar." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1451933040.
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Bellet, Thomas. "Transformations de graphes pour la modélisation géométrique à base topologique." Thesis, Poitiers, 2012. http://www.theses.fr/2012POIT2261/document.
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De nombreux domaines comme le jeu vidéo, l’architecture, l’ingénierie ou l’archéologie font désormais appel à la modélisation géométrique. Les objets à représenter sont de natures diverses, et leurs opérations de manipulation sont spécifiques. Ainsi, les modeleurs sont nombreux car tous spécialisés à leur domaine d’application. Or ils sont à la fois chers à développer, souvent peu robustes, et difficilement extensibles. Nous avons proposé dans la thèse l’approche alternative suivante :– fournir un langage dédié à la modélisation qui permet de définir les opérations quelque soit le domaine d’application ; dans ce langage, les objets sont représentés avec le modèle topologique des cartes généralisées, dont nous avons étendu la définition aux plongements ; les opérations sont elles définies par des règles de transformation de graphes, issues de la théorie des catégorie ;– garantir les opérations définies dans le langage à l’aide de conditions de cohérence ; une opération dont la définition vérifie ces conditions ne produit pas d’anomalie ;– développer un noyau de modeleur générique qui interprète ce langage ; les opérations définies sont directement appliquées dans le modeleur, sans implantation dans un langage de programmation ; l’outil assure également la vérification automatique des conditions du langage pour prévenir un utilisateur lorsqu’il propose une opération incohérente.Le langage et le modeleur développés se sont révélés performants à la fois en termes de temps de développement et en termes de temps machine. L’implantation d’une nouvelle opération par une règle ne prend que quelques minutes à l’aide des conditions du langage, au contraire de l’approche classiGeometric modeling is now involved in many fields such as: video games, architecture, engineering and archaeology. The represented objects are very different from one field to another, and so are their modeling operations. Furthermore, many specific types of modeling software are designed for high programing costs, but with a relatively low rate of effectiveness.The following is an alternative approach:– we have conceived a dedicated language for geometric modeling that will allow us to define any operation of any field; objects in this language are defined with the topological model of generalized maps, this definition has been extended to the embedding informations; here the operations are defined as graph transformation rules which originate from the category theory;– we have ensured operation definitions with consistency conditions; these operations that satisfy those conditions do not generate anomalies; – we have designed generic modeling software to serve as an interpreter of this language; the operation definitions are directly applied without the need for more programing; the software also automatically checks the language conditions and warns the user if he designs a non-consistent operation.The provided language and software prove to be efficient, and all for a low programing cost. Designing a new operation takes only minutes thanks to the language conditions, as opposed to hours of programming and debugging with the past approach
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Cantali, Rodrigo Ustárroz. "Da forma ao contexto : a importância dos elementos contextuais na evolução histórica da categoria do contrato." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2018. http://hdl.handle.net/10183/185070.
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Esta dissertação propõe-se a analisar as influências do contexto da relação contratual na delimitação das obrigações das partes. Sustenta-se que os contratos sempre funcionam em contextos sociais específicos, que influenciam o significado das relações contratuais. Analisa-se como o Direito pode reconhecer e valorar o ambiente social e econômico de certas condutas adotadas pelas partes ao longo da relação obrigacional. Trata-se, consequentemente, de uma pesquisa voltada para as fontes das obrigações, no sentido de se averiguar se o contexto pode ser considerado como uma fonte de efeitos normativos para a relação contratual, especialmente nas relações de âmbito civil-empresarial. O problema do contexto como possível fonte de efeitos normativos é apresentado a partir de duas perspectivas: a primeira, mais ampla, é relativa ao desenvolvimento da teoria das fontes das obrigações e da função exercida pelo contexto da relação no desenvolvimento do que hoje se denomina Teoria Geral dos Contratos; a segunda, mais restrita, é referente à delimitação das obrigações em uma relação contratual a partir dos elementos contextuais da relação. Ao final, procura-se demonstrar que o contexto da relação contratual se apresenta como elemento influente na determinação do momento em que obrigações contratuais são contraídas e na delimitação das obrigações contraídas.This dissertation has as its central theme the analysis of to what extent the context of the contractual relations influences the delimitation of contractual obligations. It is argued that contracts always function in specific social contexts, which influence the meaning of contractual relations. This study seeks to analyze how the law can acknowledge and value the social and economic environment of certain behaviors adopted by the parties along the obligatory relationship. It is, therefore, a study that addresses the question of whether the context can be considered as a source of normative effects for the contractual relationship, especially in civil-commercial relationships. The problem of context as a possible source of normative effects is presented from two perspectives: the first one, broader, concerning the development of the theory of sources of obligations and the function exerted by the context of the relations in the development of what is now called General Theory of Contracts; the second one, more restricted, regarding the delimitation of the obligations in a contract from the contextual elements of the relationship. This study aims, in the end, to demonstrate that the context of the contractual relationship is an influential element both in determining when contractual obligations arise and in delimiting the contractual obligations.
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Bueno-Soler, Juliana 1976. "Semantica algebrica de traduções possiveis." [s.n.], 2004. http://repositorio.unicamp.br/jspui/handle/REPOSIP/279780.
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Orientadores: Marcelo Esteban Coniglio, Carlos CaleiroDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Kuang, Heng. "Towards a Formal Reactive Autonomic Systems Framework using Category Theory." Thesis, 2013. http://spectrum.library.concordia.ca/977901/1/PhD_Thesis_Final_Heng.pdf.
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Software complexity is the main obstacle to further progress in IT industry, as the difficulty of managing complex and massive computing systems goes well beyond IT administrators’ capabilities. One of the remaining options is autonomic computing, which helps to address complexity by using technology to manage technology in terms of hiding and removing low level complexities from end users.
Real-time reactive systems are some of the most complex systems that have become increasingly heterogeneous and intelligent. Thus, we want to add autonomic features to real-time reactive systems by building a formal framework, Reactive Autonomic Systems Framework (RASF), which can leverage specification, modeling and development of Reactive Autonomic Systems (RAS). With autonomic behavior, the real-time reactive systems are more self-managed to themselves and more adaptive to their environment.
Formal methods are proven approaches to ensure the correct operation of complex interacting systems. However, many current formal approaches do not have appropriate mechanisms to specify RAS and have not addressed well on verifying self-management behavior, which is one of the most important features of the RAS. The management of evolving specifications and analysis of changes require a specification structure, which can isolate those changes in a small number of components and analyze the impacts of a change on interconnected components. Category theory has been proposed as a framework to offer that structure; it has a rich body of theory to reason about objects and their relations. Furthermore, category theory adopts a correct by construction approach by which components can be specified, proved and composed in the way of preserving their properties.
In the multi-agent community, agent-based approach is considered as a natural way to model and implement autonomic systems, as the ability of an autonomous agent can be easily mapped to the self-management behaviors in autonomic systems. Thus, many ideas from the Multi-Agent Systems (MAS) community can be adapted to implement the autonomic systems, such as the self-management behavior, automatic group formation, interfacing and evolution.
Therefore, in terms of achieving our research goal, we need to i) build an architecture and corresponding communication mechanism for modeling both reactive and autonomic behavior of the RAS, ii) formally specify the architecture, communication and behavior above using category theory, iii) design and implement the architecture, communication as well as behavior of the RAS model by the MAS approach with its implementation and iv) illustrate our RASF methodology and approach with case studies.
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Marczyński, Grzegorz. "Specifications of Software Architectures using Diagrams of Constructions." Doctoral thesis, 2014.
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Formal methods promise the ultimate quality of software artifacts with mathematicalproof of their correctness. Algebraic specification is one of such methods, providingformal specifications of system components suitable for verification of correctnessof all individual steps in the software development process, and hence of the entiredevelopment process and of the resulting program.In this thesis we propose a new approach to algebraic specifications of software architectures,called diagrams of construction specifications. Constructions, as introducedhere, model parameterised modules, with dependency relation captured directly onsignature symbols. They give a uniform treatment of first- and higher-order parameterisation,and are equipped with a single sum operation which subsumes the moststandard operations on parameterised modules. We introduce specifications for suchconstructions, study their compositionality properties, and define a notion of refinementfor constructor specifications. Diagrams of construction specifications capturedesign and development of modular software architecture, based on decomposition andrefinement of construction specifications.Throughout the thesis we illustrate new concepts and problems discussed by means ofsimple examples; a somewhat longer example is also added to summarize our presentation.Metody formalne umożliwiają uzyskanie najwyższej jakości procesu wytwarzania oprogramowaniaprzez dostarczenie matematycznych dowodów jego poprawności. Jedną ztakich metod są specyfikacje algebraiczne, które podają sposób formalnej specyfikacjiposzczególnych komponentów systemu informatycznego oraz weryfikacji poprawnościwszystkich kroków procesu wytwarzania oprogramowania i w rezultacie dają możliwośćzapewnienia poprawności zarówno całego procesu, jak i samego wynikowego programu.W niniejszej rozprawie proponuje się nowe podejście do algebraicznych specyfikacji architekturoprogramowania zwane diagramami specyfikacji konstrukcji. Wprowadzonejest pojęcie konstrukcji, które są modelami sparametryzowanych modułów wraz z relacjązależności wyrażoną bezpośrednio na symbolach z ich sygnatur. Konstrukcjezapewniają jednolite podejście do parametryzacji pierwszego i wyższych rzędów. Jedynąoperacją na konstrukcjach jest suma, która z powodzeniem zastępuje większośćstandardowych operacji na modułach sparametryzowanych. W rozprawie przedstawianesą specyfikacje konstrukcji, przeprowadzane są badania ich kompozycjonalnościoraz definiowane jest pojęcie uściślenia (ang. refinement) specyfikacji konstrukcji. Diagramyspecyfikacji konstrukcji pozwalają modelować strukturę i rozwój modularnycharchitektur oprogramowania opartych na dekompozycji i uściślaniu specyfikacji konstrukcji.W całym tekście podawane są liczne małe przykłady wprowadzanych pojęć i dyskutowanychproblemów. Na koniec przytoczony jest nieco dłuższy przykład ilustrującykilka kroków rozwoju architektury prostego systemu informatycznego.
Books on the topic "Formal category theory"
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Andrzej, Tarlecki, and SpringerLink (Online service), eds. Foundations of Algebraic Specification and Formal Software Development. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.
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Topological modular forms. Providence, Rhode Island: American Mathematical Society, 2014.
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Gray, J. W. Formal Category Theory: Adjointness For 2-Categories. Springer London, Limited, 2006.
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Landry, Elaine. Structural Realism and Category Mistakes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0018.
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Structural realists have made use of category theory in three ways. The first is as a meta-level formal framework for a structural realist account of the structure of scientific theories, either syntactic or semantic. The second is an appeal to the category-theoretic structure of some successful, successive or fundamental, physical theory to argue that this is the structure we should be physically committed to, either epistemically or ontically. The third is to use category theory as a conceptual tool to argue that it makes conceptual sense to talk of relations without relata and structures without objects. After a brief overview of structural realism, I consider how each appeal to the use of category theory stands up against the aims of the structural realist.
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Tarlecki, Andrzej, and Donald Sannella. Foundations of Algebraic Specification and Formal Software Development. Springer, 2014.
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Grim, Patrick, Gary R. Mar, and Paul St. Denis. The Philosophical Computer. The MIT Press, 1998. http://dx.doi.org/10.7551/mitpress/5347.001.0001.
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The authors present a series of exploratory examples of computer modeling, using a range of computational techniques to illuminate a variety of questions in philosophy and philosophical logic. Topics include self-reference and paradox in fuzzy logics, varieties of epistemic chaos, fractal images of formal systems, and cellular automata models in game theory. Examples in the last category include models for the evolution of generosity, possible causes and cures for discrimination, and the formal undecidability of patterns of social and biological interaction. The cross-platform CD-ROM provided with the book contains a variety of working examples, in color and often operating dynamically, embedded in a text that parallels that of the book. Source code of all major programs is included to facilitate further research. Bradford Books imprint
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Portner, Paul. Mood. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199547524.001.0001.
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The category of mood is widely used in the description of languages and the formal analysis of their grammatical properties. It typically refers to features of a sentence’s form (or a class of sentences which share such features), either individual morphemes or grammatical patterns, which reflect how the sentence contributes to the modal meaning of a larger phrase or which indicates the type of fundamental pragmatic function it has in conversation. The first subtype, verbal mood, includes the categories of indicative and subjunctive subordinate clauses; the second sentence mood, encompasses declaratives, interrogatives, and imperatives. This work presents the essential background for understanding semantic theories of mood and discusses the most significant theories of both types. It evaluates those theories, compares them, draws connections between seemingly disparate approaches, and with the goal of drawing out their most important insights, it formalizes some of the literature’s most important ideas in new ways. Ultimately, this work shows that there are important connections between verbal mood and sentence mood which point the way towards a more general understanding of how mood works and its relation to other topics in linguistics, and it outlines the type of semantic and pragmatic theory which will make it possible to explain these relations.
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Cheyne, Peter, Andy Hamilton, and Max Paddison, eds. The Philosophy of Rhythm. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199347773.001.0001.
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Spanning all cultures, rhythm is the basic pulse that animates poetry and music. The recent explosion of scholarly interest across disciplines in the aural dimensions of aesthetic experience—particularly in sociology, cultural and media theory, and literary studies—has yet to explore this fundamental category. Discussion of rhythm tends to be confined within the discrete conceptual domains and technical vocabularies of musicology and prosody. With its original essays by philosophers, psychologists, musicians, literary theorists, and ethno-musicologists, this volume opens up wider—and plural—perspectives. It examines formal affinities between the historically interconnected fields of music, dance, and poetry, addressing key concepts such as embodiment, movement, pulse, and performance. Questions considered include: What is the distinction between rhythm and pulse? What is the relationship between everyday embodied experience, and the specific experience of music, dance, and poetry? Can aesthetics offer an understanding of rhythm that helps inform our responses to visual and other arts, as well as music, dance, and poetry? What is the relation between psychological conceptions of entrainment, and the humane concept of rhythm and meter? This collection provides a unique overview of a neglected aspect of aesthetic experience, and will appeal across disciplinary boundaries. It examines formal affinities between the historically interconnected fields of music, dance, and poetry, addressing key concepts such as embodiment, movement, pulse, and performance. The book is conceived throughout to appeal to a cross-disciplinary readership.
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Colás, Alejandro. The International Political Sociology of Empire. Oxford University Press, 2018. http://dx.doi.org/10.1093/acrefore/9780190846626.013.335.
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There are two primary reasons why empires are central to our understanding of International Relations (IR). First, the empire has been replaced by juridically equal sovereign territorial states over the past century. Formal empires no longer exist, and only one head of state retains the title of Emperor—Akihito of Japan. The second reason why the study of empire matters to IR is that much of the conventional distinction between hierarchy and anarchy has been subject to various criticisms from a wide array of methodological and political perspectives. In particular, International Political Sociology (IPS) has offered a framework for critical analyses of phenomena such as systemic transformation, international unevenness, and global inequality, or war, violence, and racism in international politics. Since the end of the Cold War, new theorizations of empire have placed empire and imperialism at the center of debates in IR. Contemporary investigations of empire in IR, and IPS in particular, have dwelled on a number of political debates and methodological issues, including the nature of American imperialism, the link between IR and global history, and the relationship between empire and globalization. The category “empire” continues to both illuminate the pertinence of IR to social theory more generally and at the same time highlights the shortcomings of the discipline in addressing the causes and dynamics of global inequality, violence, and uneven development.
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Hellman, Geoffrey. Structuralism. Edited by Stewart Shapiro. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0017.
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The main types of mathematical structuralism that have been proposed and developed to the point of permitting systematic and instructive comparison are four: structuralism based on model theory, carried out formally in set theory (e.g., first- or second-order Zermelo–Fraenkel set theory), referred to as STS (for set-theoretic structuralism); the approach of philosophers such as Shapiro and Resnik of taking structures to be sui generis universals, patterns, or structures in an ante rem sense (explained in this article), referred to as SGS (for sui generis structuralism); an approach based on category and topos theory, proposed as an alternative to set theory as an overarching mathematical framework, referred to as CTS (for category-theoretic structuralism); and a kind of eliminative, quasi-nominalist structuralism employing modal logic, referred to as MS (for modal-structuralism). This article takes these up in turn, guided by few questions, with the aim of understanding their relative merits and the choices they present.
Book chapters on the topic "Formal category theory"
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Crole, Roy L. "Deriving Category Theory from Type Theory." In Theory and Formal Methods 1993, 15–26. London: Springer London, 1993. http://dx.doi.org/10.1007/978-1-4471-3503-6_2.
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Rodin, Andrei. "Hilbert: Making It Formal." In Axiomatic Method and Category Theory, 39–72. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00404-4_3.
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Rodin, Andrei. "Formal Axiomatic Method and the Twentieth Century Mathematics." In Axiomatic Method and Category Theory, 73–97. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00404-4_4.
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Sannella, Donald, and Andrzej Tarlecki. "Extended ML: An institution-independent framework for formal program development." In Category Theory and Computer Programming, 364–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/3-540-17162-2_133.
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Widmeyer, George R. "Towards a Formal Approach to Information Systems Design Theory Using Category Theory." In Lecture Notes in Computer Science, 371–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29863-9_27.
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Nomura, Tatsuya. "Formal Description of Autopoiesis Based on the Theory of Category." In Advances in Artificial Life, 700–703. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44811-x_81.
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Romero Contreras, Arturo. "Husserl, Intentionality and Mathematics: Geometry and Category Theory." In When Form Becomes Substance, 327–57. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-83125-7_12.
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Pellissery, Sony, Saloni Jain, and Geo Varghese. "Access to Social Protection by Immigrants, Emigrants and Resident Nationals in India." In IMISCOE Research Series, 147–61. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-51237-8_8.
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AbstractIndia has a segmented social protection system. About 92% of workers in India are in unorganised sector, deprived of formal social security provisions. Those who are in formal sector receive very generous social protection arrangements close to that of welfare states in Europe, primarily influenced by the colonial legacy. Those in the informal sector primarily meet their social security needs from their disposable income. With expansive private welfare providers, the rich segment in the informal segment is able to afford this. Indian unskilled migrants, mainly in the Gulf region, have a range of benefits that are primarily to meet the civil rights, rather than social rights. Compared to this, Indian migrants in Western Europe and the Americas mainly benefit from the social security system in those countries. On the other hand, foreigners coming to India have limited social security arrangements. Since 2000, India has entered into bilateral agreements with several countries, which also recognise a new category of workers called ‘international workers’. These workers have their social security benefits primarily protected as in source country.
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Tabuns, Aivars. "Latvian Migrants in Foreign Labour Markets: Job Placement and Discrimination." In IMISCOE Research Series, 97–115. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12092-4_5.
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Abstract The majority of migrants from Latvia move abroad intending to work, and so fall into the category of ‘work migrants’. A crucial role in their job placement is played by an increasingly complex network of intermediaries. This includes formal employment agencies, more informal, social network-based mediators and even illegal service providers. Despite the agencies providing job placements abroad being subject to regulations, fraud and the mistreatment of jobseekers has emerged as a cause for concern. Even when there is no ill will from the intermediaries, immigrant workers often suffer discrimination from their employers, sometimes leading to a re-evaluation of their return migration plans. This chapter explores the employment conditions of Latvian migrant workers. It analyses the operation of private employment agencies offering employment abroad and, in more general terms, sheds light from the Latvian migrant workers’ perspective on their treatment by employers. In doing so, this analysis demonstrates that almost a fifth of those respondents who used the services of private employment agencies had experienced unfair treatment. Moreover, at least one in three Latvian migrant workers encountered some form of discrimination at work, and around one in six were in a precarious and vulnerable position due to the nature of their employment contract. The chapter concludes with recommendations for further studies and policy development.
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Djordjević, Ljubica. "Non-Territorial Autonomy and Minority Rights: Impact of the Self-Governing National Communities on Minority Protection in Slovenia." In Realising Linguistic, Cultural and Educational Rights Through Non-Territorial Autonomy, 139–53. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-19856-4_10.
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AbstractSlovenia’s highly developed system of national minority protection has several distinctive features, one of which is the existence of self-governing national communities (SGNCs) for the Italian and Hungarian communities. The model combines personal and territorial elements in an interesting way: self-governing communities can only be established on ‘ethnically mixed territories’, but they are elected solely by persons registered as belonging to the respective community. There is also a second tier: regional SGNCs, with indirectly elected members representing local SGNCs. Most of their competences (on both levels) fall under the category of ‘shared rule’, i.e. they participate in managing institutions (schools, for instance) or in decision-making by providing consent or opinion, while no state powers (for example, in education or culture) are entirely delegated to these bodies.The SGNCs are deeply entrenched in the Slovenian system of minority protection, but are often taken for granted and are rarely assessed with regard to their real impact. There is no systematic monitoring of their performance, and evidence-tracking of their work is scarce and scattered. Against this background, this paper is based on an analysis of the implementation monitoring of the Framework Convention for the Protection of National Minorities (FCNM) in Slovenia, and focuses on the issues pertinent to the SGNCs that have appeared in the monitoring so far. The general finding is that, while the institutional position and the formal role of the SGNCs have been acknowledged, their concrete contribution and impact on the implementation of minority rights as indirectly stipulated in the FCNM have been addressed in a rather superficial way. Nevertheless, the monitoring documents offer a valuable insight into the issues pertinent to the functioning of the SGNCs that have attracted attention in almost 25 years of monitoring practice. This paper offers a brief overview of the most striking issues relevant to the functioning of the SGNCs and the implementation of minority rights, as documented in the FCNM monitoring.
Conference papers on the topic "Formal category theory"
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Guyot, Alexis, Annabelle Gillet, Eric Leclercq, and Nadine Cullot. "A Formal Framework for Data Lakes Based on Category Theory." In IDEAS'22: International Database Engineered Applications Symposium. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3548785.3548797.
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Gebreyohannes, Solomon, William Edmonson, and Albert Esterline. "Formalization of the responsive and formal design process using category theory." In 2018 Annual IEEE International Systems Conference (SysCon). IEEE, 2018. http://dx.doi.org/10.1109/syscon.2018.8369508.
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Borsatti, Davide, Walter Cerroni, and Stuart Clayman. "From Category Theory to Functional Programming: A Formal Representation of Intent." In 2022 IEEE 8th International Conference on Network Softwarization (NetSoft). IEEE, 2022. http://dx.doi.org/10.1109/netsoft54395.2022.9844061.
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Boudjidj, Abdelghani, and Mohammed El Habib Souidi. "A Formal Composition of Multi-Agent Organization based on Category Theory." In 9th International Conference on Foundations of Computer Science & Technology (CST 2022). Academy and Industry Research Collaboration Center (AIRCC), 2022. http://dx.doi.org/10.5121/csit.2022.121909.
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The application of organizational multi-agent systems (MAS) provides the possibility of solving complex distributed problems such as, task grouping mechanisms, supply chain management, and air traffic control. The composition of MAS organizational models can be considered as an effective solution to group different organizational multi-agent systems into a single organizational multi-agent system. The main objective of this paper is to provide a MAS organizational model based on the composition of two organizational models, Agent Group Role (AGR), and Yet Another Multi Agent Model (YAMAM), with the aim of providing a new MAS model combining the concepts of the composed organizational models. Category theory represents the mathematical formalism for studying and modeling different organizations in a categorical way. This paper is mainly based on the idea of modeling the multi-agent organization AGR and YAMAM in a categorical way in order to obtain formal semantic models describing these organizations of MAS, then compose them using also the theory of categories which represents a very sophisticated mathematical toolbox based on composition.
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Ait-Ameur, Yamine, Alexandre Cortier, Rmi Delmas, and Virginie Wiels. "Formal Modelling of Avionics Systems. An Approach Based on Category Theory and the EXPRESS Modelling Language." In Second International Symposium on Leveraging Applications of Formal Methods, Verification and Validation (isola 2006). IEEE, 2006. http://dx.doi.org/10.1109/isola.2006.11.
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Yakimov, N. I., V. V. Nosnikov, and A. V. Yurenya. "RATIONAL USE OF LAND DERIVED FROM AGRICULTURAL USE." In STATE AND DEVELOPMENT PROSPECTS OF AGRIBUSINESS Volume 2. DSTU-Print, 2020. http://dx.doi.org/10.23947/interagro.2020.2.310-313.
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The article discusses the use of former agricultural lands for afforestation. The fertility of these lands is reduced, low biological activity of soils is noted, the content of substances inhibiting the growth of woody plants is observed. The presence of a compacted subsurface layer contributes to the fact that the root systems of trees are formed by surface and do not reach groundwater. Created forest plantations usually experience a water supply crisis, they die off in dry years, they are easily exposed to diseases and pests. Possible ways of solving problems associated with afforestation in this category of land are suggested.
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Hereth, Mark, Keith Leewis, and Rick Gailing. "The Role of Technology in Preventing/Detecting Mechanical Damage." In 2006 International Pipeline Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/ipc2006-10426.
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This paper is a state of the art review of technologies for preventing mechanical damage to pipelines. Technologies are presented in three categories, above ground, surface and below ground. There is a primer on each of the categories describing the fundamentals of the technology and the tools that can be applied by an operator. The primer for each category begins with a summary of the more familiar tools and progressing to emerging technologies. A standard format was chosen simplify presentation of information for each technology offering. The format included the following elements: • Description of the tool for prevention / detection, & mitigation, • Description of the sensor(s), • Reliability expectations, • Discrimination capabilities, • Sensor Range, • Stage of development in the R&D phases, • Cost filter as a beginning of the estimated cost/benefit value, and • Contact details with current government funding when available. There is a summary table with the same format to help in the selection of technologies.
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Simonov, Kirill. "Two-sided market as technological template for exhibition business model." In 11th International Scientific Conference „Business and Management 2020“. VGTU Technika, 2020. http://dx.doi.org/10.3846/bm.2020.503.
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Purpose of the study – to form two-sided network market on discrete sequence of thematically identical short-term periodic trade shows. Methods of the investigation are based on the theory of two-sided markets, the theory of industry markets and entrepreneurship, management theory, logistics theory, the theory of systems. Results of the investigation: process model was developed for transforming plat-form's resources and its parties into intermediary services of exhibition organizer; exhibition market was proved to belong to the category of Rochet & Tirole markets; toolkit of two-sided markets theory was used to develop the concept of value creation management in exhibition market network; features of logistics support for exhibition business were analyzed. All these findings lay foundations of exhibition two-sided network markets theory, created to provide methodological support for exhibition business.
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Babeshko, Eugene, Vyacheslav Kharchenko, Kostiantyn Leontiiev, Oleg Odarushchenko, and Oleksiy Strjuk. "NPP I&C Safety Assessment by Aggregation of Formal Techniques." In 2018 26th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/icone26-82270.
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Safety assessment of nuclear power plant instrumentation and control systems (NPP I&Cs) is a complicated and resource consuming process that is required be done so as to ensure the required safety level and comply to normative regulations. A lot of work have been performed in the field of application of different assessment methods and techniques, modifying them and using their combinations so as to provide unified approach in comprehensive safety assessment. Anyway, performed research have shown there are still challenges to overcome, including rationale and choice of the safety assessment method, verification of assessment results, choosing and applying techniques that support safety assessment process, especially in the nuclear field. In our work we present developed framework that aggregates the most appropriate safety assessment methods typically used for NPP I&Cs. Key features that this framework provides are the formal descriptions of all required input information for every safety assessment method, possible data flows between methods, possible output information for every method. Such representation allows to obtain possible paths required to get necessary indicators, analyze the possibility to verify them by application of different methods that provide same indicators etc. During safety assessment of NPP I&Cs it is very important to address software due to its crucial role in I&C safety assurance. Relevant standards like IEC 60880 [1] and IEC 62138 [2] provide requirements for software related activities and supporting processes in the software safety lifecycle of computer-based I&C systems of nuclear power plants performing functions of safety category A, B and C, as defined by IEC 61226 [3]. Requirements and frameworks provided by IEC 60880 and IEC 62138 for the nuclear application sector correspond to IEC 61508, part 3 [4]. These standards define several types of safety related software and specify particular requirements for each software type. So as to verify software and confirm correspondence to required safety level, different techniques are suggested in normative documents. We share our experience obtained during software failure modes and effect analysis (software FMEA) and software fault insertion (software FIT) processes into FPGA-based platform, NPP I&C systems based on that platform, and RPCT, integrated development environment used by RPC Radiy and end users to design user application logic, specify hardware configuration etc. We apply software FIT to outputs of RPCT, considering source code, configuration files and firmware files. Finally, we provide a case study of application the developed safety assessment framework and software FMEA/FIT practices during practical assessment of FPGA-based NPP I&C system.
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Nór, Soraya, Elizabeth de Siervi, Camila Abad, and Julia Mayer. "Paisagem cultural dos jardins domesticos com plantas medicinais e aromáticas: Grande Florianópolis." In Seminario Internacional de Investigación en Urbanismo. Barcelona: Curso de Arquitetura e Urbanismo. Universidade do Vale do Itajaí, 2016. http://dx.doi.org/10.5821/siiu.6345.
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O estudo procura compreender a interação entre sociedade e natureza, representada pela paisagem cultural
dos jardins domésticos com plantas medicinais e aromáticas. A preservação do conhecimento popular sobre a
natureza, o cultivo, as crenças e usos das plantas medicinais e aromáticas, estudadas com enfoque da
paisagem cultural, pode evocar o passado de forma reflexiva, valorizar a memória local, como forma de
manutenção de uma identidade social presente e viva. A análise da paisagem cultural, categoria espacial
reveladora dos modos de viver e conceber a vida, consiste numa nova perspectiva, que se fundamenta nas
interações entre os aspectos natural e cultural, material e imaterial. O estudo tem realizado entrevistas
filmadas, para elaboração de um vídeo que ilustre a prática cultural dos jardins domésticos, com destaque
para a relação das pessoas com suas plantas, das plantas com sua moradia, do cultivo com sua comunidade
– numa espiral escalar do corpo à cidade. The study seeks to understand the interaction between society and nature, represented by the cultural
landscape of home gardens with medicinal and aromatic plants. The preservation of the popular knowlegde
about the nature, cultivation, the beliefs and the uses of the medicianal and aromatic plants, studied focusing
on the cultural lanscape which can evoke the past, valorize the local memory as a way to maintaining a social
identity alive. The analysis of the cultural landscape, a spatial category that reveal ways of living and
conceiving life, is a new perspective, which is based on the interactions between the natural and cultural
aspects, material and immaterial. The study has made filmed interviews, for the elaboration of a video that
illustrates the cultural practice of home gardens, focusing on the relationship between people and their plants,
plants with their housing, cultivation with his community – a spiral climb of the body to City.
Reports on the topic "Formal category theory"
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Kucherova, Hanna, Anastasiia Didenko, Olena Kravets, Yuliia Honcharenko, and Aleksandr Uchitel. Scenario forecasting information transparency of subjects' under uncertainty and development of the knowledge economy. [б. в.], October 2020. http://dx.doi.org/10.31812/123456789/4469.
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Topicality of modeling information transparency is determined by the influence it has on the effectiveness of management decisions made by an economic entity in the context of uncertainty and information asymmetry. It has been found that information transparency is a poorly structured category which acts as a qualitative characteristic of information and at certain levels forms an additional spectrum of properties of the information that has been adequately perceived or processed. As a result of structuring knowledge about the factor environment, a fuzzy cognitive model of information transparency was constructed in the form of a weighted digraph. Structural analysis and scenario forecasting of optimal alternatives of the fuzzy cognitive model made it possible to evaluate the classes of factors, identify their limited relations, establish the centrality of the roles of information transparency and information and communication security in the system built and evaluate their importance when modeling the situation self-development. Information visibility, reliability and availability have been found to have the strongest impact on the system. Taking into account different initial weights of the key factors — information transparency and information and communication security — the study substantiates the strategic ways for economic entities to achieve their goals in the context of uncertainty and information asymmetry, which allows us to use this approach as a tool for strategic management in the information environment.
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Kwesiga, Victoria, Zita Ekeocha, Stephen Robert Byrn, and Kari L. Clase. Compliance to GMP guidelines for Herbal Manufacturers in East Africa: A Position Paper. Purdue University, November 2021. http://dx.doi.org/10.5703/1288284317428.
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With the global increase in the use of traditional and complementary remedies for the prevention and treatment of illness, the quality and safety of these medicines have become a significant concern for all regulatory authorities. Herbal medicines are the most commonly used form of traditional and complementary medicines in the world and the efficacy and safety of herbal medicines, like conventional medicines, largely depends on their quality from planting to harvesting, preprocessing and final processing. Due to the inherent complexity of herbal medicines, often containing an array of active compounds, the primary processing of herbal medicines has a direct influence on their quality. Quality concerns are the reason why the medicines regulatory agencies insist that manufacturers of medicines strictly follow Good Manufacturing Practices since it is an essential tool to prevent instances of contamination, mix-ups, deviations, failures and errors. However, a strict application of GMP requirements is expensive and would drive the prices of the manufactured products up. As a result, a maturity level grading of facilities is proposed as a way of justifying the costs incurred for manufacturers desiring to reach a broader market and investing in continuous improvement. 36 Good Manufacturing Practice (GMP) inspection reports of local herbal manufacturers conducted by National Drug Authority were analyzed to establish the type and extent of deficiencies to GMP requirements for local herbal manufacturers in Uganda. The different GMP chapters and related sub-parameters constituted the variables used for the analysis of conformity to requirements. The primary outcome variable was the conclusion regarding compliance or noncompliance of the inspected local herbal manufacturing facility. GMP parameters that were frequently defaulted by local herbal manufacturers and the corresponding frequencies were identified. The Pearson Chi-square test was applied independently on each category to find the association that existed between conformity and the questions in each category. Only 22% (8) of the 30 inspected facilities were found to comply with GMP requirements, as per National Drug Authority (NDA) guidelines; while the majority of the facilities, 28 (78%), were found not to comply. Of the facilities inspected, 25 were undergoing GMP inspection for the first time. A total of 1,236 deficiency observations were made in the 36 inspection reports reviewed for the study. The mean for all deficiencies was 34.3, and the standard deviation was 15.829. 91.5% of the facilities did not have mechanisms for a record of market complaints; 80.9% did not meet documentation requirements; 78.9% did not have quality control measures in place, and 65.7% did not meet stores requirements. By encouraging a culture of self/voluntary improvement through the introduction of listing of manufacturers based on a maturity level grading, the National Drug Authority will improve the Herbal Medicines sector as per the mandate of improving the herbal medicine industry. Also, increased sensitization of all relevant stakeholders regarding the requirements for GMP should be intensified.
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Crisosto, Carlos, Susan Lurie, Haya Friedman, Ebenezer Ogundiwin, Cameron Peace, and George Manganaris. Biological Systems Approach to Developing Mealiness-free Peach and Nectarine Fruit. United States Department of Agriculture, 2007. http://dx.doi.org/10.32747/2007.7592650.bard.
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Peach and nectarine production worldwide is increasing; however consumption is flat or declining because of the inconsistent eating quality experienced by consumers. The main factor for this inconsistent quality is mealiness or woolliness, a form of chilling injury that develops following shipping periods in the global fruit market today. Our research groups have devised various postharvest methods to prolong storage life, including controlled atmosphere and delayed storage; however, these treatments only delay mealiness. Mealiness texture results from disruption of the normal ripening process involving disassembly of cell wall material, and creates a soft fruit texture that is dry and grainy instead of juicy and smooth. Solving this problem is a prerequisite for increasing the demand for fresh peach and nectarine. Two approaches were used to reveal genes and their associated biochemical processes that can confer resistance to mealiness or wooliness. At the Volcani Center, Israel, a nectarine cultivar and the peach cultivar (isogenetic materials) from which the nectarine cultivar spontaneously arose, and at the Kearney Agricultural Center of UC Davis, USA, a peach population that segregates for quantitative resistance to mealiness was used for dissecting the genetic components of mealiness development. During our project we have conducted research integrating the information from phenotypic, biochemical and gene expression studies, proposed possible candidate genes and SNPs-QTLs mapping that are involved in reducing peach mealiness susceptibility. Numerous genes related to ethylene biosynthesis and its signal transduction, cell wall structure and metabolism, stress response, different transcription factor families were detected as being differentially accumulated in the cold-treated samples of these sensitive and less sensitive genotypes. The ability to produce ethylene and keep active genes involved in ethylene signaling, GTP-binding protein, EIN-3 binding protein and an ethylene receptor and activation of ethyleneresponsive fruit ripening genes during cold storage provided greater resistance to CI. Interestingly, in the functional category of genes differentially expressed at harvest, less chilling sensitive cultivar had more genes in categories related to antioxidant and heat sock proteins/chaperones that may help fruit to adapt to low temperature stress. The specific objectives of the proposed research were to: characterize the phenotypes and cell wall components of the two resistant systems in response to mealiness- inducing conditions; identify commonalities and specific differences in cell wall proteins and the transcriptome that are associated with low mealiness incidence; integrate the information from phenotypic, biochemical, and gene expression studies to identify candidate genes that are involved in reducing mealiness susceptibility; locate these genes in the Prunus genome; and associate the genes with genomic regions conferring quantitative genetic variation for mealiness resistance. By doing this we will locate genetic markers for mealiness development, essential tools for selection of mealiness resistant peach lines with improved fruit storability and quality. In our research, QTLs have been located in our peach SNPs map, and proposed candidate genes obtained from the integrated result of phenotypic, biochemical and gene expression analysis are being identified in our QTLs as an approach searching for consistent assistant markers for peach breeding programs.
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Allik, Mirjam, Dandara Ramos, Marilyn Agranonik, Elzo Pereira Pinto Junior, Maria Yury Ichihara, Mauricio Barreto, Alastair Leyland, and Ruth Dundas. Developing a Small-Area Deprivation Measure for Brazil. University of Glasgow, May 2020. http://dx.doi.org/10.36399/gla.pubs.215898.
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This report describes the development of the BrazDep small-area deprivation measure for the whole of Brazil. The measure uses the 2010 Brazilian Population Census data and is calculated for the smallest possible geographical area level, the census sectors. It combines three variables – (1) percent of households with per capita income ≤ 1/2 minimum wage; (2) percent of people not literate, aged 7+; and (3) average of percent of people with inadequate access to sewage, water, garbage collection and no toilet and bath/shower – into a single measure. Similar measures have previously been developed at the census sector level for some states or municipalities, but the deprivation measure described in this report is the first one to be provided for census sectors for the whole of Brazil. BrazDep is a measure of relative deprivation, placing the census sectors on a scale of material well-being from the least to the most deprived. It is useful in comparing areas within Brazil in 2010, but cannot be used to make comparisons across countries or time. Categorical versions of the measure are also provided, placing census sectors into groups of similar levels of deprivation. Deprivation measures, such as the one developed here, have been developed for many countries and are popular tools in public health research for describing the social patterning of health outcomes and supporting the targeting and delivery of services to areas of higher need. The deprivation measure is exponentially distributed, with a large proportion of areas having a low deprivation score and a smaller number of areas experiencing very high deprivation. There is significant regional variation in deprivation; areas in the North and Northeast of Brazil have on average much higher deprivation compared to the South and Southeast. Deprivation levels in the Central-West region fall between those for the North and South. Differences are also great between urban and rural areas, with the former having lower levels of deprivation compared to the latter. The measure was validated by comparing it to other similar indices measuring health and social vulnerability at the census sector level in states and municipalities where it was possible, and at the municipal level for across the whole of Brazil. At the municipal level the deprivation measure was also compared to health outcomes. The different validation exercises showed that the developed measure produced expected results and could be considered validated. As the measure is an estimate of the “true” deprivation in Brazil, uncertainty exists about the exact level of deprivation for all of the areas. For the majority of census sectors the uncertainty is small enough that we can reliably place the area into a deprivation category. However, for some areas uncertainty is very high and the provided estimate is unreliable. These considerations should always be kept in mind when using the BrazDep measure in research or policy. The measure should be used as part of a toolkit, rather than a single basis for decision-making. The data together with documentation is available from the University of Glasgow http: //dx.doi.org/10.5525/gla.researchdata.980. The data and this report are distributed under Creative Commons Share-Alike license (CC BY-SA 4.0) and can be freely used by researchers, policy makers or members of public.