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Author : Fosco Loregian
Publisher : Cambridge University Press
Page : 331 pages
File Size : 43,6 Mb
Release : 2021-07-22
Category : Mathematics
ISBN : 9781108746120
This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.
Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 42,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475747218
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
Author : Orna Kupferman,Pawel Sobocinski
Publisher : Springer Nature
Page : 575 pages
File Size : 45,5 Mb
Release : 2023-04-20
Category : Computers
ISBN : 9783031308291
This open access book constitutes the proceedings of the 26th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2023, which was held during April 22-27, 2023, in Paris, France, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2023. The 26 regular papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems.
Author : Vladimir Dobrev
Publisher : Springer Nature
Page : 526 pages
File Size : 42,7 Mb
Release : 2023-01-29
Category : Mathematics
ISBN : 9789811947513
This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in Physics" held in Sofia, Bulgaria (on-line) in June 2021. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field. The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Author : K Heiner Kamps,Timothy Porter
Publisher : World Scientific
Page : 476 pages
File Size : 46,5 Mb
Release : 1997-04-11
Category : Mathematics
ISBN : 9789814502559
The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many other categories (e.g. spaces over a fixed base, groupoids, chain complexes, module categories). Studying categorical versions of homotopy structure, such as cylinders and path space constructions, enables not only a unified development of many examples of known homotopy theories but also reveals the inner working of the classical spatial theory. This demonstrates the logical interdependence of properties (in particular the existence of certain Kan fillers in associated cubical sets) and results (Puppe sequences, Vogt's Iemma, Dold's theorem on fibre homotopy equivalences, and homotopy coherence theory).
Author : Fabio Gadducci,Timo Kehrer
Publisher : Springer Nature
Page : 311 pages
File Size : 45,8 Mb
Release : 2021-06-17
Category : Computers
ISBN : 9783030789466
This book constitutes the refereed proceedings of the 14th International Conference on Graph Transformation, ICGT 2021, which took place virtually during June 24-25, 2021. The 14 full papers and 2 tool papers presented in this book were carefully reviewed and selected from 26 submissions. They deal with the following topics: theoretical advances; application domains; and tool presentations.
Author : Hideto Asashiba,Shigeto Kawata,Nanqing Ding,Nam Kyun Kim
Publisher : World Scientific
Page : 256 pages
File Size : 44,7 Mb
Release : 2021-01-04
Category : Mathematics
ISBN : 9789811230301
Since 1991, the group of ring theorists from China and Japan, joined by Korea from 1995 onwards, took turns to hold the quadrennial international conferences (sometimes also referred to as symposiums). As the proceedings of the eighth conference held in Nagoya, Japan in 2019, this volume consists of a collection of articles by invited speakers (survey) and general speakers (survey and original), all of which were refereed by world experts.The survey articles show the trends of current research and offer clear, thorough explanations that are ideal for researchers also in other specialized areas of ring theory. The original articles display new results, ideas and tools for research investigations in ring theory.The articles cover major areas in ring theory, such as: structures of rings, module theory, homological algebra, groups, Hopf algebras, Lie theory, representation theory of rings, (non-commutative) algebraic geometry, commutative rings (structures, representations), amongst others.This volume is a useful resource for researchers — both beginners and advanced experts — in ring theory.
Author : Donald Yau
Publisher : CRC Press
Page : 361 pages
File Size : 55,7 Mb
Release : 2023-12-06
Category : Mathematics
ISBN : 9781003807469
This monograph is the first and only book-length reference for this material. Contents of Chapter 2, Chapter 3, Part 2, and Part 3 is new, not having appeared in any of the research literature. The book will appeal to mathematicians interested in topology. Book shelved as a reference title.
Author : Saunders MacLane
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 53,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781461298397
Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint pair of functors. This appears in many substantially equivalent forms: That of universal construction, that of direct and inverse limit, and that of pairs offunctors with a natural isomorphism between corresponding sets of arrows. All these forms, with their interrelations, are examined in Chapters III to V. The slogan is "Adjoint functors arise everywhere". Alternatively, the fundamental notion of category theory is that of a monoid -a set with a binary operation of multiplication which is associative and which has a unit; a category itself can be regarded as a sort of general ized monoid. Chapters VI and VII explore this notion and its generaliza tions. Its close connection to pairs of adjoint functors illuminates the ideas of universal algebra and culminates in Beck's theorem characterizing categories of algebras; on the other hand, categories with a monoidal structure (given by a tensor product) lead inter alia to the study of more convenient categories of topological spaces.
Author : Katrina Barron,Elizabeth Jurisich,Antun Milas,Kailash Misr
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 54,5 Mb
Release : 2017-08-15
Category : Lie algebras
ISBN : 9781470426668
This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.
Author : Richard J. Boulton,Paul B. Jackson
Publisher : Springer
Page : 402 pages
File Size : 48,8 Mb
Release : 2003-06-30
Category : Computers
ISBN : 9783540447559
This volume constitutes the proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2001) held 3–6 September 2001 in Edinburgh, Scotland. TPHOLs covers all aspects of theorem proving in higher order logics, as well as related topics in theorem proving and veri?cation. TPHOLs 2001 was collocated with the 11th Advanced Research Working Conference on Correct Hardware Design and Veri?cation Methods (CHARME 2001). This was held 4–7 September 2001 in nearby Livingston, Scotland at the Institute for System Level Integration, and a joint half-day session of talks was arranged for the 5th September in Edinburgh. An excursion to Traquair House and a banquet in the Playfair Library of Old College, University of Edinburgh were also jointly organized. The proceedings of CHARME 2001 have been p- lished as volume 2144 of Springer-Verlag’s Lecture Notes in Computer Science series, with Tiziana Margaria and Tom Melham as editors. Each of the 47 papers submitted in the full research category was refereed by at least 3 reviewers who were selected by the Program Committee. Of these submissions, 23 were accepted for presentation at the conference and publication in this volume. In keeping with tradition, TPHOLs 2001 also o?ered a venue for the presentation of work in progress, where researchers invite discussion by means of a brief preliminary talk and then discuss their work at a poster session. A supplementary proceedings containing associated papers for work in progress was published by the Division of Informatics at the University of Edinburgh.
Author : Helene Kirchner,Christophe Ringeissen
Publisher : Springer
Page : 508 pages
File Size : 55,7 Mb
Release : 2003-08-02
Category : Computers
ISBN : 9783540457190
This volume contains the proceedings of AMAST 2002, the 9th International Conference on Algebraic Methodology and Software Technology, held during September 9–13, 2002, in Saint-Gilles-les-Bains, R ́eunion Island, France. The major goal of the AMAST conferences is to promote research that may lead to setting software technology on a ?rm mathematical basis. This goal is achieved through a large international cooperation with contributions from both academia and industry. Developing a software technology on a mathematical basis p- duces software that is: (a) correct, and the correctness can be proved mathem- ically, (b) safe, so that it can be used in the implementation of critical systems, (c) portable, i. e. , independent of computing platforms and language generations, (d) evolutionary, i. e. , it is self-adaptable and evolves with the problem domain. All previous AMAST conferences, which were held in Iowa City (1989, 1991), Twente (1993), Montreal (1995), Munich (1996), Sydney (1997), Manaus (1999), and Iowa City (2000), made contributions to the AMAST goals by reporting and disseminating academic and industrial achievements within the AMAST area of interest. During these meetings, AMAST attracted an international following among researchers and practitioners interested in software technology, progr- ming methodology, and their algebraic, and logical foundations.
Author : Gregory Maxwell Kelly
Publisher : CUP Archive
Page : 260 pages
File Size : 41,9 Mb
Release : 1982-02-18
Category : Mathematics
ISBN : 0521287022
Author : Vladimir G. Ivancevic
Publisher : World Scientific
Page : 1346 pages
File Size : 44,7 Mb
Release : 2007
Category : Geometry
ISBN : 9789812770721
Introduction -- Technical preliminaries: tensors, actions and functors -- Applied manifold geometry -- Applied bundle geometry -- Applied jet geometry -- Geometrical path integrals and their applications
Author : Nicolás Andruskiewitsch,Gongxiang Liu,Susan Montgomery,Yinhuo Zhang
Publisher : American Mathematical Soc.
Page : 359 pages
File Size : 50,8 Mb
Release : 2021-07-06
Category : Education
ISBN : 9781470456245
The articles highlight the latest advances and further research directions in a variety of subjects related to tensor categories and Hopf algebras. Primary topics discussed in the text include the classification of Hopf algebras, structures and actions of Hopf algebras, algebraic supergroups, representations of quantum groups, quasi-quantum groups, algebras in tensor categories, and the construction method of fusion categories.