Compact Textbooks in Mathematics

An Introduction to the Language of Category Theory

Authors: Roman, Steven

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  • 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
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eBook £17.99
£35.99 (listprice)
price for United Kingdom (gross)
valid through June 30, 2019
  • ISBN 978-3-319-41917-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover £22.99
£44.99 (listprice)
price for United Kingdom (gross)
valid through June 30, 2019
  • ISBN 978-3-319-41916-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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 naturaltransformations, 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.

About the authors

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).

Reviews

“This book offers a fast, but very complete, introduction to the basic concepts in category theory, which any reader with a basic knowledge of abstract algebra will follow easily. … The theory is very well complemented by a list of proposed exercises at the end of every chapter… . This book is appropriate, as was said previously, for a fast introduction to category theory, and could be very useful for a short introductory course on categorical methods in advanced algebra.” (Juan Antonio López-Ramos, Mathematical Reviews, July, 2017)

“This book is, as promised in this series, a compact, easy to read and useful for lecturers introduction to the basic concepts of category theory. It is very convenient for self-studying and it can be used as starting point to read more advanced book on category theory. The book includes very nice and helpful diagrams, detailed explanation of the concepts and, in every chapter, a set of exercises that will help the reader to better understanding the text.” (Blas Torrecillas, zbMATH 1360.18001, 2017)


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook £17.99
£35.99 (listprice)
price for United Kingdom (gross)
valid through June 30, 2019
  • ISBN 978-3-319-41917-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover £22.99
£44.99 (listprice)
price for United Kingdom (gross)
valid through June 30, 2019
  • ISBN 978-3-319-41916-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to the Language of Category Theory
Authors
Series Title
Compact Textbooks in Mathematics
Copyright
2017
Publisher
Birkhäuser Basel
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-41917-6
DOI
10.1007/978-3-319-41917-6
Softcover ISBN
978-3-319-41916-9
Series ISSN
2296-4568
Edition Number
1
Number of Pages
XII, 169
Number of Illustrations
171 b/w illustrations, 5 illustrations in colour
Topics