Download or read book Categorical Aspects of Topology and Analysis written by B. Banaschewski and published by Springer. This book was released on 2006-11-14 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topology written by Tai-Danae Bradley and published by MIT Press. This book was released on 2020-08-18 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.

Download or read book Categorical Aspects of Topology and Analysis written by B. Banaschewski and published by . This book was released on 2014-01-15 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Categorical Topology and Its Relation to Analysis Algebra and Combinatorics written by Jiří Adámek (ing.) and published by . This book was released on 1989 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Categorical Perspectives written by Jürgen Koslowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Categorical Perspectives" consists of introductory surveys as well as articles containing original research and complete proofs devoted mainly to the theoretical and foundational developments of category theory and its applications to other fields. A number of articles in the areas of topology, algebra and computer science reflect the varied interests of George Strecker to whom this work is dedicated. Notable also are an exposition of the contributions and importance of George Strecker's research and a survey chapter on general category theory. This work is an excellent reference text for researchers and graduate students in category theory and related areas. Contributors: H.L. Bentley * G. Castellini * R. El Bashir * H. Herrlich * M. Husek * L. Janos * J. Koslowski * V.A. Lemin * A. Melton * G. Preuá * Y.T. Rhineghost * B.S.W. Schroeder * L. Schr"der * G.E. Strecker * A. Zmrzlina

Download or read book Categorical Structure of Closure Operators written by D. Dikranjan and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Categorical Homotopy Theory written by Emily Riehl and published by Cambridge University Press. This book was released on 2014-05-26 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.

Download or read book Categorical Foundations written by Maria Cristina Pedicchio and published by Cambridge University Press. This book was released on 2004 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

Download or read book Categorical Topology written by H. L. Bentley and published by . This book was released on 1984 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of the History of General Topology written by C.E. Aull and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.

Download or read book Domain Specific Languages written by Walid Mohamed Taha and published by Springer. This book was released on 2009-07-06 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dijkstra once wrote that computer science is no more about computers than astronomy is about telescopes. Despite the many incredible advances in c- puter science from times that predate practical mechanical computing, there is still a myriad of fundamental questions in understanding the interface between computers and the rest of the world. Why is it still hard to mechanize many tasks that seem to be fundamentally routine, even as we see ever-increasing - pacity for raw mechanical computing? The disciplined study of domain-speci?c languages (DSLs) is an emerging area in computer science, and is one which has the potential to revolutionize the ?eld, and bring us closer to answering this question. DSLs are formalisms that have four general characteristics. – They relate to a well-de?ned domain of discourse, be it controlling tra?c lights or space ships. – They have well-de?ned notation, such as the ones that exist for prescribing music, dance routines, or strategy in a football game. – The informal or intuitive meaning of the notation is clear. This can easily be overlooked, especially since intuitive meaning can be expressed by many di?erent notations that may be received very di?erently by users. – The formal meaning is clear and mechanizable, as is, hopefully, the case for the instructions we give to our bank or to a merchant online.

Download or read book Interactive Theorem Proving written by Jeremy Avigad and published by Springer. This book was released on 2018-07-03 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 9th International Conference on Interactive Theorem Proving, ITP 2018, held in Oxford, UK, in July 2018. The 32 full papers and 5 short papers presented were carefully reviewed and selected from 65 submissions. The papers feature research in the area of logical frameworks and interactive proof assistants. The topics include theoretical foundations and implementation aspects of the technology, as well as applications to verifying hardware and software systems to ensure their safety and security, and applications to the formal verication of mathematical results. Chapters 2, 10, 26, 29, 30 and 37 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Download or read book Horizons of the Mind A Tribute to Prakash Panangaden written by Franck van Breugel and published by Springer. This book was released on 2014-05-23 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift volume contains papers presented at a conference, Prakash Fest, held in honor of Prakash Panangaden, in Oxford, UK, in May 2014, to celebrate his 60th birthday. Prakash Panangaden has worked on a large variety of topics including probabilistic and concurrent computation, logics and duality and quantum information and computation. Despite the enormous breadth of his research, he has made significant and deep contributions. For example, he introduced logic and a real-valued interpretation of the logic to capture equivalence of probabilistic processes quantitatively. The 25 papers included in this volume were carefully reviewed. They cover a large variety of topics in theoretical computer science.

Download or read book Theory and Applications of Models of Computation written by Jianer Chen and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 6th International Conference on Theory and Applications of Models of Computation, TAMC 2009, held in Changsha, China in May 2009. The 39 full papers presented together with 7 invited papers as well as 3 plenary talks were selected from 86 submissions. The papers address the three main themes of the conference which were Computability, Complexity, and Algorithms. The conference aimed to bring together researchers with interests in theoretical computer science, algorithmic mathematics, and applications to the physical sciences.

Download or read book Algebra and Coalgebra in Computer Science written by José Luis Fiadeiro and published by Springer Science & Business Media. This book was released on 2005 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First International Conference on Algebra and Coalgebra in Computer Science, CALCO 2005, held in Swansea, UK in September 2005. The biennial conference was created by joining the International Workshop on Coalgebraic Methods in Computer Science (CMCS) and the Workshop on Algebraic Development Techniques (WADT). It addresses two basic areas of application for algebras and coalgebras – as mathematical objects as well as their application in computer science. The 25 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 62 submissions. The papers deal with the following subjects: automata and languages; categorical semantics; hybrid, probabilistic, and timed systems; inductive and coinductive methods; modal logics; relational systems and term rewriting; abstract data types; algebraic and coalgebraic specification; calculi and models of concurrent, distributed, mobile, and context-aware computing; formal testing and quality assurance; general systems theory and computational models (chemical, biological, etc); generative programming and model-driven development; models, correctness and (re)configuration of hardware/middleware/architectures; re-engineering techniques (program transformation); semantics of conceptual modelling methods and techniques; semantics of programming languages; validation and verification.

Download or read book Uncertainty in Artificial Intelligence written by Bruce D'Ambrosio and published by Elsevier. This book was released on 2014-06-28 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Proceedings 1991

Download or read book Foundations of Software Science and Computational Structures written by Andrew D. Gordon and published by Springer Science & Business Media. This book was released on 2003-03-14 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 6th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2003, held in Warsaw, Poland in April 2003. The 26 revised full papers presented together with an invited paper were carefully reviewed and selected from 96 submissions. Among the topics covered are algebraic models; automata and language theory; behavioral equivalences; categorical models; computation processes over discrete and continuous data; computation structures; logics of programs; models of concurrent, reactive, distributed, and mobile systems; process algebras and calculi; semantics of programming languages; software specification and refinement; transition systems; and type systems and type theory.