An Introduction to the Language of Category Theory

Nonfiction, Science & Nature, Mathematics, Algebra, History
Cover of the book An Introduction to the Language of Category Theory by Steven Roman, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Steven Roman ISBN: 9783319419176
Publisher: Springer International Publishing Publication: January 5, 2017
Imprint: Birkhäuser Language: English
Author: Steven Roman
ISBN: 9783319419176
Publisher: Springer International Publishing
Publication: January 5, 2017
Imprint: Birkhäuser
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Finding Her in History by Steven Roman
Cover of the book Enhancing Reflection within Situated Learning by Steven Roman
Cover of the book Robotics in Education by Steven Roman
Cover of the book Mineral and Thermal Waters of Southeastern Europe by Steven Roman
Cover of the book Musculoskeletal Ultrasound in Rheumatology Review by Steven Roman
Cover of the book Geosciences of Azerbaijan by Steven Roman
Cover of the book Algorithms for Data Science by Steven Roman
Cover of the book Random Sets and Random Fuzzy Sets as Ill-Perceived Random Variables by Steven Roman
Cover of the book The Urban Transport Crisis in Emerging Economies by Steven Roman
Cover of the book Radio Frequency Propagation Made Easy by Steven Roman
Cover of the book Graftless Solutions for the Edentulous Patient by Steven Roman
Cover of the book Outlook and Challenges of Nano Devices, Sensors, and MEMS by Steven Roman
Cover of the book Glaciers of Georgia by Steven Roman
Cover of the book Fetal and Hybrid Procedures in Congenital Heart Diseases by Steven Roman
Cover of the book Uncertainty Modeling by Steven Roman
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy