東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

An introduction to the language of c...

Roman, Steven.

Linked to FindBook

Google Book

Amazon

博客來

An introduction to the language of category theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	An introduction to the language of category theory/ by Steven Roman.
Author:	Roman, Steven.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	xii, 169 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Preface -- Categories -- Functors and Natural Transformations -- Universality -- Cones and Limits -- Adjoints -- References -- Index of Symbols -- Index.
Contained By:	Springer eBooks
Subject:	Categories (Mathematics) -
Online resource:	http://dx.doi.org/10.1007/978-3-319-41917-6
ISBN:	9783319419176

An introduction to the language of category theory
Roman, Steven.

An introduction to the language of category theory[electronic resource] /by Steven Roman. - Cham :Springer International Publishing :2017. - xii, 169 p. :ill. (some col.), digital ;24 cm. - Compact textbooks in mathematics,2296-4568. - Compact textbooks in mathematics..

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

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.

ISBN: 9783319419176

Standard No.: 10.1007/978-3-319-41917-6doiSubjects--Topical Terms:

525955
Categories (Mathematics)

LC Class. No.: QA169

Dewey Class. No.: 512.62

An introduction to the language of category theory
LDR:03037nmm a2200337 a 4500 001 2089793
003 DE-He213
005 20170815134418.0
006 m d
007 cr nn 008maaau
008 171013s2017 gw s 0 eng d
020 $a 9783319419176 $q (electronic bk.)
020 $a 9783319419169 $q (paper)
024 7 $a 10.1007/978-3-319-41917-6 $2 doi
035 $a 978-3-319-41917-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA169
072 7 $a PBC $2 bicssc
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 512.62 $2 23
090 $a QA169 $b .R758 2017
100 1 $a Roman, Steven. $3 549558
245 1 3 $a An introduction to the language of category theory $h [electronic resource] / $c by Steven Roman.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2017.
300 $a xii, 169 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Compact textbooks in mathematics, $x 2296-4568
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.
650 0 $a Categories (Mathematics) $3 525955
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Category Theory, Homological Algebra. $3 899944
650 2 4 $a Order, Lattices, Ordered Algebraic Structures. $3 896039
650 2 4 $a General Algebraic Systems. $3 897364
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Compact textbooks in mathematics. $3 2107015
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-41917-6
950 $a Mathematics and Statistics (Springer-11649)