Categorical Structures And Their Applications

Author : Werner G„hler,Gerhard Preuss,Horst Herrlich
Publisher : World Scientific
Page : 378 pages
File Size : 50,7 Mb
Release : 2004
Category : Mathematics
ISBN : 9812702415

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Categorical Structures and Their Applications by Werner G„hler,Gerhard Preuss,Horst Herrlich Pdf

The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich OCo one of the leading category theorists of the world OCo to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader will find a complete list of Horst HerrlichOCOs publications. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences."

Author : W Gähler,G Preuss
Publisher : World Scientific
Page : 356 pages
File Size : 40,6 Mb
Release : 2004-09-28
Category : Mathematics
ISBN : 9789814481700

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Categorical Structures and Their Applications by W Gähler,G Preuss Pdf

The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich — one of the leading category theorists of the world — to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader will find a complete list of Horst Herrlich's publications. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:On Boole's Booleanness (B Banaschewski)Homeomorphically Closed Nearness Spaces (H L Bentley & J W Carlson)The Tensor Product of Orthomodular Posets (R Börger)Saturated Collections of Metrics (E Colebunders et al.)Topological Structures in Logics (W Gähler)The Structure of Affine Algebraic Sets (E Giuli)A Characterization of Co-Retracts of Functional Structures (R Kaschek)Introducing Lagois Correspondences (A Melton)On Coalgebras which are Algebras (H-E Porst & C Dzierzon)Fibrewise Sobriety (G Richter & A Vauth)and other papers Readership: Graduate students, researchers, academics and lecturers in mathematics and computer science. Keywords:Category Theory;Algebra;Logic;Topology;Fuzzy Structures;Computer Science

Author : Dikran Dikranjan,Walter Tholen
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 47,8 Mb
Release : 1995-10-31
Category : Mathematics
ISBN : 0792337727

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Categorical Structure of Closure Operators by Dikran Dikranjan,Walter Tholen Pdf

Our motivation for gathering the material for this book over aperiod of seven years has been to unify and simplify ideas wh ich appeared in a sizable number of re search articles during the past two decades. More specifically, it has been our aim to provide the categorical foundations for extensive work that was published on the epimorphism- and cowellpoweredness problem, predominantly for categories of topological spaces. In doing so we found the categorical not ion of closure operators interesting enough to be studied for its own sake, as it unifies and describes other significant mathematical notions and since it leads to a never-ending stream of ex amples and applications in all areas of mathematics. These are somewhat arbitrarily restricted to topology, algebra and (a small part of) discrete mathematics in this book, although other areas, such as functional analysis, would provide an equally rich and interesting supply of examples. We also had to restrict the themes in our theoretical exposition. In spite of the fact that closure operators generalize the uni versal closure operations of abelian category theory and of topos- and sheaf theory, we chose to mention these aspects only en passant, in favour of the presentation of new results more closely related to our original intentions. We also needed to refrain from studying topological concepts, such as compactness, in the setting of an arbitrary closure-equipped category, although this topic appears prominently in the published literature involving closure operators.

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 50,6 Mb
Release : 2004
Category : Categories (Mathematics)
ISBN : OCLC:1090039162

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Categorical Structures and Their Applications by Anonim Pdf

Author : Werner Gähler
Publisher : Unknown
Page : 333 pages
File Size : 41,7 Mb
Release : 2004
Category : Electronic
ISBN : 981256053X

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Proceedings of the North-West European Category Seminar Categorical Structures and Their Applications by Werner Gähler Pdf

Author : Andrea Asperti,Giuseppe Longo
Publisher : MIT Press (MA)
Page : 330 pages
File Size : 42,7 Mb
Release : 1991
Category : Computers
ISBN : UOM:39015022019742

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Categories, Types, and Structures by Andrea Asperti,Giuseppe Longo Pdf

Category theory is a mathematical subject whose importance in several areas of computer science, most notably the semantics of programming languages and the design of programmes using abstract data types, is widely acknowledged. This book introduces category theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design.

Author : Gerhard Preuß
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400928596

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Theory of Topological Structures by Gerhard Preuß Pdf

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : R Costa,Jr., Henrique Guzzo,A. Grichkov,L.A. Peresi
Publisher : CRC Press
Page : 492 pages
File Size : 51,8 Mb
Release : 2019-05-20
Category : Mathematics
ISBN : 9780429529993

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NonasSociative Algebra and Its Applications by R Costa,Jr., Henrique Guzzo,A. Grichkov,L.A. Peresi Pdf

A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.

Author : D. Dikranjan,Walter Tholen
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 46,8 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9789401584005

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Categorical Structure of Closure Operators by D. Dikranjan,Walter Tholen Pdf

Our motivation for gathering the material for this book over aperiod of seven years has been to unify and simplify ideas wh ich appeared in a sizable number of re search articles during the past two decades. More specifically, it has been our aim to provide the categorical foundations for extensive work that was published on the epimorphism- and cowellpoweredness problem, predominantly for categories of topological spaces. In doing so we found the categorical not ion of closure operators interesting enough to be studied for its own sake, as it unifies and describes other significant mathematical notions and since it leads to a never-ending stream of ex amples and applications in all areas of mathematics. These are somewhat arbitrarily restricted to topology, algebra and (a small part of) discrete mathematics in this book, although other areas, such as functional analysis, would provide an equally rich and interesting supply of examples. We also had to restrict the themes in our theoretical exposition. In spite of the fact that closure operators generalize the uni versal closure operations of abelian category theory and of topos- and sheaf theory, we chose to mention these aspects only en passant, in favour of the presentation of new results more closely related to our original intentions. We also needed to refrain from studying topological concepts, such as compactness, in the setting of an arbitrary closure-equipped category, although this topic appears prominently in the published literature involving closure operators.

Author : Francis Borceux
Publisher : Springer
Page : 375 pages
File Size : 41,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540459859

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Categorical Algebra and its Applications by Francis Borceux Pdf

Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences. The volume contains 28 carefully selected and refereed papers, out of 96 talks delivered, and illustrates the usefulness of category theory today as a powerful tool of investigation in many other areas.

Author : Maria Cristina Pedicchio,Walter Tholen
Publisher : Cambridge University Press
Page : 452 pages
File Size : 52,9 Mb
Release : 2004
Category : Mathematics
ISBN : 0521834147

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Categorical Foundations by Maria Cristina Pedicchio,Walter Tholen Pdf

Publisher Description

Author : Jairo José da Silva
Publisher : Springer
Page : 275 pages
File Size : 54,8 Mb
Release : 2017-08-22
Category : Philosophy
ISBN : 9783319630731

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Mathematics and Its Applications by Jairo José da Silva Pdf

This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what does it mean to exist, mathematical structures: what are they and how do we know them, how different layers of mathematical structuring relate to each other and to perceptual structures, and how to use mathematics to find out how the world is. The book simultaneously develops along two lines, both inspired and enlightened by Edmund Husserl’s phenomenological philosophy. One line leads to the establishment of a particular version of mathematical structuralism, free of “naturalist” and empiricist bias. The other leads to a logical-epistemological explanation and justification of the applicability of mathematics carried out within a unique structuralist perspective. This second line points to the “unreasonable” effectiveness of mathematics in physics as a means of representation, a tool, and a source of not always logically justified but useful and effective heuristic strategies.

Author : Jean-Pierre Magnot
Publisher : American Mathematical Society
Page : 272 pages
File Size : 42,5 Mb
Release : 2024-02-02
Category : Mathematics
ISBN : 9781470472542

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Recent Advances in Diffeologies and Their Applications by Jean-Pierre Magnot Pdf

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic topology and higher homotopy theory to integrable systems and optimization in PDE. The geometric framework proposed by diffeologies is known to be one of the most general approaches to problems arising in several areas of mathematics. It can adapt to many contexts without major technical difficulties and produce examples inaccessible by other means, in particular when studying singularities or geometry in infinite dimension. Thanks to this adaptability, diffeologies appear to have become an interesting and useful language for a growing number of mathematicians working in many different fields. Some articles in the volume also illustrate some recent developments of the theory, which makes it even more deep and useful.

Author : Stuart C. Hackett
Publisher : Wipf and Stock Publishers
Page : 382 pages
File Size : 50,8 Mb
Release : 2009-01-21
Category : Religion
ISBN : 9781725225039

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The Resurrection of Theism by Stuart C. Hackett Pdf

"The Christian world view," contends the author, "both needs and embodies a thoroughgoing, rational apologetic as a manifestation of its relevance to the contemporary mind. . . . Christian faith should be defended in terms of criteria which center in rational objectivity as the norm of truth and evaluation." The author, who stands in the tradition of Aquinas, Butler, Orr, and Tennant, deals first with the problem of epistemological approach (part 1). Then he tackles the apologetic of natural revelation, first setting forth the inadequacy of every major alternate to rational empiricism (part 2), then demonstrating the existence of the God of theism (part 3). Each chapter is well outlined, and these outlines appear together in an "Analytical Table of Contents." This feature, as well as a bibliography and index, makes this a useful textbook for courses in apologetics and philosophy.

Author : Brendan Fong,David I. Spivak
Publisher : Cambridge University Press
Page : 351 pages
File Size : 43,9 Mb
Release : 2019-07-18
Category : Computers
ISBN : 9781108482295

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An Invitation to Applied Category Theory by Brendan Fong,David I. Spivak Pdf

Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.