An Introduction to the Language of Categor...

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Beschreibung

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.

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

Über den Autor

Steven Roman is Professor Emeritus of Mathematics at California State University Fullerton. He is the author of numerous other mathematics textbooks, including Field Theory (2006), Advanced Linear Algebra (2008), Fundamentals of Group Theory (2012), Introduction to the Mathematics of Finance (2012), and An Introduction to Catalan Numbers (2015).

Zusammenfassung

Presents all the basic concepts of category theory without requiring any preliminary knowledge

Employs friendly, less-formal language and notation to allow reader to focus more on the main concepts, which can be overwhelming for beginners

Appropriate for advanced students in mathematics, computer science, physics, and related fields looking for an introduction to category theory

Includes an example of the application of Yoneda's lemma, not usually included in introductory texts

Provides a good preparation for more advanced books on category theory

Includes supplementary material: [...]

Inhaltsverzeichnis

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

Details

Erscheinungsjahr:	2017
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Compact Textbooks in Mathematics
Inhalt:	xii 169 S. 171 s/w Illustr. 5 farbige Illustr. 169 p. 176 illus. 5 illus. in color.
ISBN-13:	9783319419169
ISBN-10:	3319419161
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Roman, Steven
Auflage:	1st ed. 2017
Hersteller:	Springer International Publishing Springer International Publishing AG Compact Textbooks in Mathematics
Maße:	235 x 155 x 11 mm
Von/Mit:	Steven Roman
Erscheinungsdatum:	13.01.2017
Gewicht:	0,289 kg

Artikel-ID: 108270701