Categorical Algebra And Its Applications
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Handbook Of Categorical Algebra Basic Category Theory
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Author : Francis Borceux
language : en
Publisher: Cambridge University Press
Release Date : 1994
Handbook Of Categorical Algebra Basic Category Theory written by Francis Borceux and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
The first of a 3-volume work, this text gives a detailed account of what should be known by all working in, or using category theory. This volume covers basic the concepts.
Categorical Foundations
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Author : Maria Cristina Pedicchio
language : en
Publisher: Cambridge University Press
Release Date : 2004
Categorical Foundations written by Maria Cristina Pedicchio and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Publisher Description
Categorical Algebra And Its Applications
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Author : Francis Borceux
language : en
Publisher: Springer
Release Date : 2006-11-14
Categorical Algebra And Its Applications written by Francis Borceux and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
Categorical Algebra And Its Applications
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Author : Francis Borceux
language : en
Publisher:
Release Date : 2014-01-15
Categorical Algebra And Its Applications written by Francis Borceux and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Handbook Of Categorical Algebra Volume 2 Categories And Structures
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Author : Francis Borceux
language : en
Publisher: Cambridge University Press
Release Date : 2008-04-24
Handbook Of Categorical Algebra Volume 2 Categories And Structures written by Francis Borceux and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-24 with Mathematics categories.
The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibered categories.
Categorical Structures And Their Applications
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Author : Werner Ghler
language : en
Publisher: World Scientific
Release Date : 2004
Categorical Structures And Their Applications written by Werner Ghler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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
Handbook Of Categorical Algebra Volume 3 Sheaf Theory
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Author : Francis Borceux
language : en
Publisher: Cambridge University Press
Release Date : 1994-12-08
Handbook Of Categorical Algebra Volume 3 Sheaf Theory written by Francis Borceux and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-08 with Mathematics categories.
The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen. The book is planned also to serve as a reference book for both specialists in the field and all those using category theory as a tool. Volume 3 begins with the essential aspects of the theory of locales, proceeding to a study in chapter 2 of the sheaves on a locale and on a topological space, in their various equivalent presentations: functors, etale maps or W-sets. Next, this situation is generalized to the case of sheaves on a site and the corresponding notion of Grothendieck topos is introduced. Chapter 4 relates the theory of Grothendieck toposes with that of accessible categories and sketches, by proving the existence of a classifying topos for all coherent theories.
Louvain La Neuve Conference On Categorical Algebra And Its Applications 1
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Author :
language : en
Publisher:
Release Date : 1988
Louvain La Neuve Conference On Categorical Algebra And Its Applications 1 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Topology
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Author : Tai-Danae Bradley
language : en
Publisher: MIT Press
Release Date : 2020-08-18
Topology written by Tai-Danae Bradley and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-18 with Mathematics categories.
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. After presenting the basics of both category theory and topology, the book covers the universal properties of familiar constructions and three main topological properties—connectedness, Hausdorff, and compactness. It presents a fine-grained approach to convergence of sequences and filters; explores categorical limits and colimits, with examples; looks in detail at adjunctions in topology, particularly in mapping spaces; and examines additional adjunctions, presenting ideas from homotopy theory, the fundamental groupoid, and the Seifert van Kampen theorem. End-of-chapter exercises allow students to apply what they have learned. The book expertly guides students of topology through the important transition from undergraduate student with a solid background in analysis or point-set topology to graduate student preparing to work on contemporary problems in mathematics.
Mal Cev Protomodular Homological And Semi Abelian Categories
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Author : Francis Borceux
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-02-29
Mal Cev Protomodular Homological And Semi Abelian Categories written by Francis Borceux and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-29 with Mathematics categories.
The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and synthetic notions of Mal'cev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. The book gives full importance to examples and makes strong connections with Universal Algebra. One of its aims is to allow appreciating how productive the essential categorical constraint is: knowing an object, not from inside via its elements, but from outside via its relations with its environment. The book is intended to be a powerful tool in the hands of researchers in category theory, homology theory and universal algebra, as well as a textbook for graduate courses on these topics.