An Introduction To The Language Of Category Theory - Roman Steven | Libro Birkhäuser 01/2017 - HOEPLI.it


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roman steven - an introduction to the language of category theory

An Introduction to the Language of Category Theory




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Birkhäuser

Pubblicazione: 01/2017
Edizione: 1st ed. 2017





Trama

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.





Sommario

Preface.- Categories.- Functors and Natural Transformations.- Universality.- Cones and Limits.- Adjoints.- References.- Index of Symbols.- Index.




Autore

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).







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Altre Informazioni

ISBN:

9783319419169

Condizione: Nuovo
Collana: Compact Textbooks in Mathematics
Dimensioni: 235 x 155 mm Ø 2876 gr
Formato: Brossura
Illustration Notes:171 Illustrations, black and white
Pagine Arabe: 169
Pagine Romane: xii






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