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Category Theory And Applications: A Textbook For Beginners (Second Edition), Marco Grandis


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Автор: Marco Grandis
Название:  Category Theory And Applications: A Textbook For Beginners (Second Edition)
ISBN: 9789811236082
Издательство: World Scientific Publishing
Классификация:
ISBN-10: 9811236089
Обложка/Формат: Hardback
Страницы: 392
Вес: 0.69 кг.
Дата издания: 19.03.2021
Серия: Mathematics
Язык: English
Издание: Second edition
Размер: 229 x 152 x 18
Читательская аудитория: Tertiary education (us: college)
Ключевые слова: Algebra, COMPUTERS / Computer Science,MATHEMATICS / Algebra / General,SCIENCE / Physics / Mathematical & Computational
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Поставляется из: Англии
Описание: 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.


Basic Category Theory

Автор: Leinster
Название: Basic Category Theory
ISBN: 1107044243 ISBN-13(EAN): 9781107044241
Издательство: Cambridge Academ
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Цена: 8237.00 р.
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Описание: Assuming little mathematical background, this short introduction to category theory is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time. Suitable for independent study or as a course book, it gives extensive explanations of the key concepts along with hundreds of examples and exercises.

Geometric and Topological Aspects of the Representation Theory of Finite Groups

Автор: Jon F. Carlson; Srikanth B. Iyengar; Julia Pevtsov
Название: Geometric and Topological Aspects of the Representation Theory of Finite Groups
ISBN: 3319940325 ISBN-13(EAN): 9783319940328
Издательство: Springer
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Цена: 20962.00 р.
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Описание: These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled 'Groups, Representations, and Cohomology' and held from June 22 to June 27, 2015 at Sabhal M?r Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of 'Geometric Methods in the Representation Theory of Finite Groups' and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016.

The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.
Abstract Algebra: Introduction to Groups, Rings and Fields with Applications (Second Edition)

Автор: Reis Clive, Rankin Stuart A.
Название: Abstract Algebra: Introduction to Groups, Rings and Fields with Applications (Second Edition)
ISBN: 9814730548 ISBN-13(EAN): 9789814730549
Издательство: World Scientific Publishing
Цена: 8870.00 р.
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Описание:

This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.

This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.

Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced -- via congruence classes -- to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.

In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.

Abstract Algebra: Introduction to Groups, Rings and Fields with Applications (Second Edition)

Автор: Reis Clive, Rankin Stuart A.
Название: Abstract Algebra: Introduction to Groups, Rings and Fields with Applications (Second Edition)
ISBN: 981473053X ISBN-13(EAN): 9789814730532
Издательство: World Scientific Publishing
Цена: 19483.00 р.
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Описание:

This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.

This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.

Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced -- via congruence classes -- to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.

In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.

Category theory and applications: a textbook for beginners

Автор: Grandis, Marco (univ Di Genova, Italy)
Название: Category theory and applications: a textbook for beginners
ISBN: 9813231068 ISBN-13(EAN): 9789813231061
Издательство: World Scientific Publishing
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Цена: 14256.00 р.
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Описание:

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 deeper 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 its 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.

Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications and a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.

Compressed Sensing and Its Applications: Second International Matheon Conference 2015

Автор: Boche Holger, Caire Giuseppe, Calderbank Robert
Название: Compressed Sensing and Its Applications: Second International Matheon Conference 2015
ISBN: 3319888455 ISBN-13(EAN): 9783319888453
Издательство: Springer
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Цена: 13974.00 р.
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Описание: This contributed volume contains articles written by the plenary and invited speakers from the second international MATHEON Workshop 2015 that focus on applications of compressed sensing.

Applications of Category Theory to Fuzzy Subsets

Автор: S.E. Rodabaugh; Erich Peter Klement; Ulrich H?hle
Название: Applications of Category Theory to Fuzzy Subsets
ISBN: 9401051569 ISBN-13(EAN): 9789401051569
Издательство: Springer
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Цена: 27950.00 р.
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Описание: This book has a fundamental relationship to the International Seminar on Fuzzy Set Theory held each September in Linz, Austria. Beginning with the tenth Seminar, the intimate setting was retained, but each Seminar narrowed in theme;

Reports of the Midwest Category Seminar II

Автор: S. MacLane; M. Andre; D. A. Buchsbaum; E. Dubuc; R
Название: Reports of the Midwest Category Seminar II
ISBN: 3540042318 ISBN-13(EAN): 9783540042310
Издательство: Springer
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Цена: 3487.00 р.
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An Introduction to the Language of Category Theory

Автор: Steven Roman
Название: An Introduction to the Language of Category Theory
ISBN: 3319419161 ISBN-13(EAN): 9783319419169
Издательство: Springer
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Цена: 7685.00 р.
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Описание: The first chapter of the book introduces the definitions of category and functor and discusses diagrams,duality, initial and terminal objects, special types of morphisms, and some special types of categories,particularly comma categories and hom-set categories.

Hopf algebras and their generalizations from a category theoretical point of view

Автор: Boehm, Gabriella
Название: Hopf algebras and their generalizations from a category theoretical point of view
ISBN: 3319981366 ISBN-13(EAN): 9783319981369
Издательство: Springer
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Цена: 6288.00 р.
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Описание: These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications.Since Sweedler's work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg–Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, semi-Hopf group algebras, small categories, and categories enriched in coalgebras.Graduate students and researchers in algebra and category theory will find this book particularly useful. Including a wide range of illustrative examples, numerous exercises, and completely worked solutions, it is suitable for self-study.


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