Overview
- 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: sn.pub/extras
Part of the book series: Compact Textbooks in Mathematics (CTM)
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Table of contents (5 chapters)
Keywords
About this book
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.
Reviews
“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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: An Introduction to the Language of Category Theory
Authors: Steven Roman
Series Title: Compact Textbooks in Mathematics
DOI: https://doi.org/10.1007/978-3-319-41917-6
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2017
Softcover ISBN: 978-3-319-41916-9Published: 13 January 2017
eBook ISBN: 978-3-319-41917-6Published: 05 January 2017
Series ISSN: 2296-4568
Series E-ISSN: 2296-455X
Edition Number: 1
Number of Pages: XII, 169
Number of Illustrations: 171 b/w illustrations, 5 illustrations in colour
Topics: Category Theory, Homological Algebra, Order, Lattices, Ordered Algebraic Structures, General Algebraic Systems