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An introduction to the language of category theory [electronic resource]

An introduction to the language of category theory [electronic resource]

Material type
E-Book(소장)
Personal Author
Roman, Steven.
Title Statement
An introduction to the language of category theory [electronic resource] / Steven Roman.
Publication, Distribution, etc
Cham :   Birkhäuser,   2017.  
Physical Medium
1 online resource (xii, 169 p.) : ill. (some col.).
Series Statement
Compact textbooks in mathematics,2296-4568
ISBN
9783319419169 9783319419176 (eBook)
요약
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 university-level 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, step-by-step 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 hom-set 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.
General Note
Title from e-Book title page.  
Content Notes
Preface -- Categories -- Functors and Natural Transformations -- Universality -- Cones and Limits -- Adjoints -- References -- Index of Symbols -- Index.
Bibliography, Etc. Note
Includes bibliographical references (p. 165) and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Algebra.
Short cut
URL
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020 ▼a 9783319419169
020 ▼a 9783319419176 (eBook)
040 ▼a 211009 ▼c 211009 ▼d 211009
050 4 ▼a QA169
082 0 4 ▼a 512.62 ▼2 23
084 ▼a 512.62 ▼2 DDCK
090 ▼a 512.62
100 1 ▼a Roman, Steven.
245 1 3 ▼a An introduction to the language of category theory ▼h [electronic resource] / ▼c Steven Roman.
260 ▼a Cham : ▼b Birkhäuser, ▼c 2017.
300 ▼a 1 online resource (xii, 169 p.) : ▼b ill. (some col.).
490 1 ▼a Compact textbooks in mathematics, ▼x 2296-4568
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references (p. 165) and index.
505 0 ▼a Preface -- Categories -- Functors and Natural Transformations -- Universality -- Cones and Limits -- Adjoints -- References -- Index of Symbols -- Index.
520 ▼a 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 university-level 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, step-by-step 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 hom-set 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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Algebra.
830 0 ▼a Compact textbooks in mathematics.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=https://doi.org/10.1007/978-3-319-41917-6
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.62 Accession No. E14013850 Availability Loan can not(reference room) Due Date Make a Reservation Service M

Contents information

Author Introduction

스티븐 로만(지은이)

캘리포니아 주립대 플러톤(Fullerton)의 수학과 명예 교수로 현재까지 슈프링거 출판사(Springer-Verlag)가 출간한 수학 관련 책(『Coding and Information』, 『Advanced Linear Algebra』, 『Field Theory』)을 포함하여 32권의 책을 집필했다. 여기에 15권 분량의 소책자 시리즈인 'Modules in Mathematics'와 오라일리가 출간한 『Access Database Design & Programming』,『Learning Word Programming』,『Developing Visual Basic Add-Ins』, 『엑셀 매크로 시작부터 활용까지(Writing Excel Macros)』(한빛미디어, 2000)를 집필했고, 이 외에도 하드웨어와 객체지향 프로그래밍에 관련 책도 두 권 집필했다. 로먼 박사의 주요 관심 분야는 순열 조합론, 대수학, 컴퓨터 과학이다.

Information Provided By: : Aladin

Table of Contents

Preface
Categories
Functors and Natural Transformations
Universality
Cones and Limits
Adjoints
References
Index of Symbols
Index.

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