عنوان
پدید آورنده
موضوع
رده
QA181
QA181
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
1315232944
(Number (ISBN
1351869558
(Number (ISBN
1351869566
(Number (ISBN
1351869574
(Number (ISBN
9781315232942
(Number (ISBN
9781351869553
(Number (ISBN
9781351869560
(Number (ISBN
9781351869577
Erroneous ISBN
9781138035867
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
An Introduction to Groups, Groupoids and Their Representations /
General Material Designation
[Book]
First Statement of Responsibility
by Alberto Ibort, Miguel A. Rodriguez
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Milton :
Name of Publisher, Distributor, etc.
CRC Press LLC,
Date of Publication, Distribution, etc.
2019.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource (362 pages)
GENERAL NOTES
Text of Note
6.3 The structure of groupoids: Second structure theorem
CONTENTS NOTE
Text of Note
Cover; Title Page; Copyright Page; Dedication; Preface; Acknowledgements; Table of Contents; Introduction; PART I: WORKING WITH CATEGORIES AND GROUPOIDS; 1: Categories: Basic Notions and Examples; 1.1 Introducing the main characters; 1.1.1 Connecting dots, graphs and quivers; 1.1.2 Drawing simple quivers and categories; 1.1.3 Relations, inverses, and some interesting problems; 1.2 Categories: Formal definitions; 1.2.1 Finite categories; 1.2.2 Abstract categories; 1.3 A categorical definition of groupoids and groups; 1.4 Historical notes and additional comments
Text of Note
1.4.1 Groupoids: A short history1.4.2 Categories; 1.4.3 Groupoids and physics; 1.4.4 Groupoids and other points of view; 2: Groups; 2.1 Groups, subgroups and normal subgroups: Basic notions; 2.1.1 Groups: Definitions and examples; 2.1.2 Subgroups and cosets; 2.1.3 Normal subgroups; 2.2 A family of board games: The symmetric group; 2.3 Group homomorphisms and Cayley's theorem; 2.3.1 Group homomorphisms: First properties; 2.3.2 Cayley's theorem for groups; 2.4 The alternating group; 2.4.1 Conjugacy classes: Young diagrams; 2.4.2 Homomorphisms and exact sequences
Text of Note
2.4.3 The group of automorphisms of a group2.5 Products of groups; 2.5.1 Direct product of groups; 2.5.2 Classification of finite Abelian groups; 2.5.3 Semidirect product of groups; 2.6 Historical notes and additional comments; 3: Groupoids; 3.1 Groupoids: Basic concepts; 3.1.1 Groupoids and subgroupoids; 3.1.2 Disjoint union of groupoids; 3.1.3 The groupoid of pairs revisited: Equivalence relations and subgroupoids; 3.1.4 Product of groupoids; 3.2 Puzzles and groupoids; 3.2.1 The "15 puzzle"; 3.2.2 The four squares puzzle: The groupoid 2; 3.2.3 Cyclic puzzles and cyclic groupoids
Text of Note
3.2.4 Rubik's 'pocket cube'4: Actions of Groups and Groupoids; 4.1 Symmetries, groups and groupoids; 4.1.1 Groups and symmetries; 4.1.2 Actions of groups; 4.2 The action groupoid; 4.3 Symmetries and groupoids; 4.3.1 Groupoids and generalised actions; 4.3.2 Groupoids and symmetries: The restriction of an action groupoid; 4.4 Weinstein's tilings; 4.4.1 Tilings and groupoids; 4.4.2 Local symmetries; 4.5 Cayley's theorem for groupoids; 5: Functors and Transformations; 5.1 Functors; 5.1.1 Functors: Definitions and first examples; 5.1.2 Functors and realisations of categories
Text of Note
5.2 An interlude: Categories and databases5.2.1 A simple database: Classes and courses; 5.2.2 Databases and functors; 5.3 Homomorphisms of groupoids; 5.3.1 Homomorphisms of groupoids: Basic notions; 5.3.2 Exact sequences of homomorphisms of groupoids; 5.3.3 Homomorphisms of groupoids, direct unions and products of groupoids; 5.3.4 Groupoids of automorphisms; 5.4 Equivalence: Natural transformations; 5.4.1 Equivalence of categories; 5.4.2 The notion of natural transformation; 6. The Structure of Groupoids; 6.1 Normal subgroupoids; 6.2 Simple groupoids
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SUMMARY OR ABSTRACT
Text of Note
This book offers an introduction to the theory of groupoids and their representations encompassing the standard theory of groups. Using a categorical language, developed from simple examples, the theory of finite groupoids is shown to knit neatly with that of groups and their structure as well as that of their representations is described. The book comprises numerous examples and applications, including well-known games and puzzles, databases and physics applications. Key concepts have been presented using only basic notions so that it can be used both by students and researchers interested in the subject.
ACQUISITION INFORMATION NOTE
Source for Acquisition/Subscription Address
Taylor & Francis
Stock Number
9781315232942
OTHER EDITION IN ANOTHER MEDIUM
Title
An Introduction to Groups, Groupoids and Their Representations.
International Standard Book Number
9781138035867
TOPICAL NAME USED AS SUBJECT
Groupoids.
Groupoids.
MATHEMATICS-- Algebra-- General.
MATHEMATICS-- Combinatorics.
MATHEMATICS-- Geometry-- General.
(SUBJECT CATEGORY (Provisional
MAT-- 002000
MAT-- 012000
MAT-- 036000
PBF
DEWEY DECIMAL CLASSIFICATION
Number
512/
.
28
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA181
PERSONAL NAME - PRIMARY RESPONSIBILITY
Ibort, Alberto.
PERSONAL NAME - ALTERNATIVE RESPONSIBILITY
Rodriguez, Miguel A.
ORIGINATING SOURCE
Date of Transaction
20200822171522.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
