The Resource An Invitation to General Algebra and Universal Constructions, by George M. Bergman, (electronic resource)
An Invitation to General Algebra and Universal Constructions, by George M. Bergman, (electronic resource)
Resource Information
The item An Invitation to General Algebra and Universal Constructions, by George M. Bergman, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item An Invitation to General Algebra and Universal Constructions, by George M. Bergman, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in noncategorytheoretic terms, of many familiar and notsofamiliar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in categorytheoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book
 Language
 eng
 Edition
 2nd ed. 2015.
 Extent
 X, 572 p. 90 illus.
 Contents

 1 About the course, and these notes
 Part I: Motivation and Examples
 2 Making Some Things Precise
 3 Free Groups
 4 A Cook's Tour
 Part II: Basic Tools and Concepts
 5 Ordered Sets, Induction, and the Axiom of Choice
 6 Lattices, Closure Operators, and Galois Connections
 7 Categories and Functors
 8 Universal Constructions
 9 Varieties of Algebras
 Part III: More on Adjunctions
 10 Algebras, Coalgebras, and Adjunctions
 References
 List of Exercises
 Symbol Index
 Word and Phrase Index
 Isbn
 9783319114781
 Label
 An Invitation to General Algebra and Universal Constructions
 Title
 An Invitation to General Algebra and Universal Constructions
 Statement of responsibility
 by George M. Bergman
 Language
 eng
 Summary
 Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in noncategorytheoretic terms, of many familiar and notsofamiliar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in categorytheoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book
 http://library.link/vocab/creatorName
 Bergman, George M
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink (Online service)
 Series statement
 Universitext,
 http://library.link/vocab/subjectName

 Mathematics
 Associative rings
 Rings (Algebra)
 Category theory (Mathematics)
 Homological algebra
 Algebra
 Label
 An Invitation to General Algebra and Universal Constructions, by George M. Bergman, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 1 About the course, and these notes  Part I: Motivation and Examples  2 Making Some Things Precise  3 Free Groups  4 A Cook's Tour  Part II: Basic Tools and Concepts  5 Ordered Sets, Induction, and the Axiom of Choice  6 Lattices, Closure Operators, and Galois Connections  7 Categories and Functors  8 Universal Constructions  9 Varieties of Algebras  Part III: More on Adjunctions  10 Algebras, Coalgebras, and Adjunctions  References  List of Exercises  Symbol Index  Word and Phrase Index
 Control code
 9783319114781
 Dimensions
 unknown
 Edition
 2nd ed. 2015.
 Extent
 X, 572 p. 90 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319114781
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319114781
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086465232
 Label
 An Invitation to General Algebra and Universal Constructions, by George M. Bergman, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 1 About the course, and these notes  Part I: Motivation and Examples  2 Making Some Things Precise  3 Free Groups  4 A Cook's Tour  Part II: Basic Tools and Concepts  5 Ordered Sets, Induction, and the Axiom of Choice  6 Lattices, Closure Operators, and Galois Connections  7 Categories and Functors  8 Universal Constructions  9 Varieties of Algebras  Part III: More on Adjunctions  10 Algebras, Coalgebras, and Adjunctions  References  List of Exercises  Symbol Index  Word and Phrase Index
 Control code
 9783319114781
 Dimensions
 unknown
 Edition
 2nd ed. 2015.
 Extent
 X, 572 p. 90 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319114781
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319114781
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086465232
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/AnInvitationtoGeneralAlgebraandUniversal/_ljsPOj63AE/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/AnInvitationtoGeneralAlgebraandUniversal/_ljsPOj63AE/">An Invitation to General Algebra and Universal Constructions, by George M. Bergman, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>