The Resource An Introduction to the Language of Category Theory, by Steven Roman, (electronic resource)
An Introduction to the Language of Category Theory, by Steven Roman, (electronic resource)
Resource Information
The item An Introduction to the Language of Category Theory, by Steven Roman, (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 Introduction to the Language of Category Theory, by Steven Roman, (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
 This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in universitylevel mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, stepbystep manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. 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 homset categories. Chapter 2 is devoted to functors and natural transformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions – products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts.
 Language
 eng
 Extent
 1 online resource (XII, 169 pages)
 Contents

 Preface
 Categories
 Functors and Natural Transformations
 Universality
 Cones and Limits
 Adjoints
 References
 Index of Symbols
 Index
 Isbn
 9783319419176
 Label
 An Introduction to the Language of Category Theory
 Title
 An Introduction to the Language of Category Theory
 Statement of responsibility
 by Steven Roman
 Language
 eng
 Summary
 This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in universitylevel mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, stepbystep manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. 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 homset categories. Chapter 2 is devoted to functors and natural transformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions – products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Roman, Steven
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement

 Springer eBooks
 Compact Textbooks in Mathematics,
 http://library.link/vocab/subjectName

 Mathematics
 Category theory (Mathematics)
 Homological algebra
 Algebra
 Ordered algebraic structures
 Mathematics
 Category Theory, Homological Algebra
 Order, Lattices, Ordered Algebraic Structures
 General Algebraic Systems
 Label
 An Introduction to the Language of Category Theory, by Steven Roman, (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
 Preface  Categories  Functors and Natural Transformations  Universality  Cones and Limits  Adjoints  References  Index of Symbols  Index
 Control code
 9783319419176
 Dimensions
 unknown
 Extent
 1 online resource (XII, 169 pages)
 File format
 multiple file formats
 Form of item

 online
 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
 9783319419176
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319419176
 Other physical details
 176 illustrations, 5 illustrations in color.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)969438432
 Label
 An Introduction to the Language of Category Theory, by Steven Roman, (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
 Preface  Categories  Functors and Natural Transformations  Universality  Cones and Limits  Adjoints  References  Index of Symbols  Index
 Control code
 9783319419176
 Dimensions
 unknown
 Extent
 1 online resource (XII, 169 pages)
 File format
 multiple file formats
 Form of item

 online
 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
 9783319419176
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319419176
 Other physical details
 176 illustrations, 5 illustrations in color.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)969438432
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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/AnIntroductiontotheLanguageofCategory/5MLOKx5wtAU/" 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/AnIntroductiontotheLanguageofCategory/5MLOKx5wtAU/">An Introduction to the Language of Category Theory, by Steven Roman, (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>