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Viser: An Introduction to the Language of Category Theory
An Introduction to the Language of Category Theory Vital Source e-bog
Steven Roman
(2017)
An Introduction to the Language of Category Theory Vital Source e-bog
Steven Roman
(2017)
An Introduction to the Language of Category Theory Vital Source e-bog
Steven Roman
(2017)
An Introduction to the Language of Category Theory
Steven Roman
(2017)
Sprog: Engelsk
Detaljer om varen
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: Springer Nature (Januar 2017)
- ISBN: 9783319419176
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- Vital Source 180 day rentals (dynamic pages)
- Udgiver: Springer Nature (Januar 2017)
- ISBN: 9783319419176R180
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- Udgiver: Springer Nature (Januar 2017)
- ISBN: 9783319419176R90
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Detaljer om varen
- Paperback: 117 sider
- Udgiver: Springer International Publishing AG (Januar 2017)
- ISBN: 9783319419169
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.