EAN: 9783319419169

COMPACT TEXTBOOKS IN MATHEMATICS AN INTRODUCT...

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.

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