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Author: K I Rosenthal
Publisher: CRC Press
ISBN: 1498710409
Category : Mathematics
Languages : en
Pages : 160
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Book Description
This book presents a detailed account of the theory of quantaloids, a natural generalization of quantales. The basic theory, examples and construction are given and particular emphasis is placed on the free quantaloid construction, as well as on the perspective provided by enriched categories.
Author: K I Rosenthal
Publisher: CRC Press
ISBN: 1498710409
Category : Mathematics
Languages : en
Pages : 160
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Book Description
This book presents a detailed account of the theory of quantaloids, a natural generalization of quantales. The basic theory, examples and construction are given and particular emphasis is placed on the free quantaloid construction, as well as on the perspective provided by enriched categories.
Author: Marco Grandis
Publisher: World Scientific
ISBN: 9811236100
Category : Mathematics
Languages : en
Pages : 390
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Book Description
Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.
Author: Marco Grandis
Publisher: World Scientific
ISBN: 9811234019
Category : Mathematics
Languages : en
Pages : 374
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Book Description
Local structures, like differentiable manifolds, fibre bundles, vector bundles and foliations, can be obtained by gluing together a family of suitable 'elementary spaces', by means of partial homeomorphisms that fix the gluing conditions and form a sort of 'intrinsic atlas', instead of the more usual system of charts living in an external framework.An 'intrinsic manifold' is defined here as such an atlas, in a suitable category of elementary spaces: open euclidean spaces, or trivial bundles, or trivial vector bundles, and so on.This uniform approach allows us to move from one basis to another: for instance, the elementary tangent bundle of an open Euclidean space is automatically extended to the tangent bundle of any differentiable manifold. The same holds for tensor calculus.Technically, the goal of this book is to treat these structures as 'symmetric enriched categories' over a suitable basis, generally an ordered category of partial mappings.This approach to gluing structures is related to Ehresmann's one, based on inductive pseudogroups and inductive categories. A second source was the theory of enriched categories and Lawvere's unusual view of interesting mathematical structures as categories enriched over a suitable basis.
Author: Lubos Brim
Publisher: Springer
ISBN: 3540456945
Category : Computers
Languages : en
Pages : 628
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Book Description
This book constitutes the refereed proceedings of the 13th International Conference on Concurrency Theory, CONCUR 2002, held in Brno, Czech Republic in August 2002.The 32 revised full papers presented together with abstracts of seven invited contributions were carefully reviewed and selected from 101 submissions. The papers are organized in topical sections on verification and model checking, logic, mobility, probabilistic systems, models of computation and process algebra, security, Petri nets, and bisimulation.
Author: Guojun Wang
Publisher: World Scientific
ISBN: 9814401528
Category : Computers
Languages : en
Pages : 724
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Book Description
The QL&SC 2012 is a major symposium for scientists, and practitioners all around the world to present their latest reseaches, results, ideas, developments and applications in such areas as quantitative logic, many-valued logic, fuzzy logic, quantification of software, artificial intelligence, fuzzy sets and systems and soft computing. This invaluable book provides a broad introduction to the fuzzy reasoning and soft computing. It is certain one should not go too far in approximation and optimization, and a certain degree must be kept in mind. This is the essential idea of quantitative logic and soft computing. The explanations in the book are complete to provide the necessary background material needed to go further into the subject and explore the research literature. It is suitable reading for graduate students. It provides a platform for mutual exchanges from top experts and scholars around the world in this field.
Author: Yongming Li
Publisher: World Scientific
ISBN: 9814401536
Category : Computers
Languages : en
Pages : 724
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Book Description
The QL&SC 2012 is a major symposium for scientists, and practitioners all around the world to present their latest researches, results, ideas, developments and applications in such areas as quantitative logic, many-valued logic, fuzzy logic, quantification of software, artificial intelligence, fuzzy sets and systems and soft computing. This invaluable book provides a broad introduction to the fuzzy reasoning and soft computing. It is certain one should not go too far in approximation and optimization, and a certain degree must be kept in mind. This is the essential idea of quantitative logic and soft computing. The explanations in the book are complete to provide the necessary background material needed to go further into the subject and explore the research literature. It is suitable reading for graduate students. It provides a platform for mutual exchanges from top experts and scholars around the world in this field.
Author: Dirk Hofmann
Publisher: Cambridge University Press
ISBN: 1139993283
Category : Mathematics
Languages : en
Pages : 523
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Book Description
Monoidal Topology describes an active research area that, after various past proposals on how to axiomatize 'spaces' in terms of convergence, began to emerge at the beginning of the millennium. It combines Barr's relational presentation of topological spaces in terms of ultrafilter convergence with Lawvere's interpretation of metric spaces as small categories enriched over the extended real half-line. Hence, equipped with a quantale V (replacing the reals) and a monad T (replacing the ultrafilter monad) laxly extended from set maps to V-valued relations, the book develops a categorical theory of (T,V)-algebras that is inspired simultaneously by its metric and topological roots. The book highlights in particular the distinguished role of equationally defined structures within the given lax-algebraic context and presents numerous new results ranging from topology and approach theory to domain theory. All the necessary pre-requisites in order and category theory are presented in the book.
Author: Grigoriĭ Lazarevich Litvinov
Publisher: American Mathematical Soc.
ISBN: 0821835386
Category : Mathematics
Languages : en
Pages : 378
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Book Description
Idempotent mathematics is a rapidly developing new branch of the mathematical sciences that is closely related to mathematical physics. The existing literature on the subject is vast and includes numerous books and journal papers. A workshop was organized at the Erwin Schrodinger Institute for Mathematical Physics (Vienna) to give a snapshot of modern idempotent mathematics. This volume contains articles stemming from that event. Also included is an introductory paper by G. Litvinov and additional invited contributions. The resulting volume presents a comprehensive overview of the state of the art. It is suitable for graduate students and researchers interested in idempotent mathematics and tropical mathematics.
Author: M. Hazewinkel
Publisher: Elsevier
ISBN: 0080569412
Category : Mathematics
Languages : en
Pages : 577
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Book Description
Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes
Author: K. Glazek
Publisher: Springer Science & Business Media
ISBN: 9401599645
Category : Mathematics
Languages : en
Pages : 394
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Book Description
This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).
