Introduction To The Language Of Category Theory paperback english - 13 Jan 2017
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| Publisher | Birkhauser |
| ISBN 13 | 9783319419169 |
| ISBN 10 | 3319419161 |
| Book Description | 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. |
| Editorial Review | 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. |
| About the Author | 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). |
| Language | English |
| Author | Steven Roman |
| Publication Date | 13 Jan 2017 |
| Number of Pages | 169 |
Introduction To The Language Of Category Theory paperback english - 13 Jan 2017
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