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An Introduction to the Language of Category Theory / by Steven Roman
(Compact Textbooks in Mathematics. ISSN:2296455X)
版 | 1st ed. 2017. |
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出版者 | (Cham : Springer International Publishing : Imprint: Birkhäuser) |
出版年 | 2017 |
大きさ | XII, 169 p. 176 illus., 5 illus. in color : online resource |
著者標目 | *Roman, Steven author SpringerLink (Online service) |
件 名 | LCSH:Algebra, Homological LCSH:Algebra LCSH:Universal algebra FREE:Category Theory, Homological Algebra FREE:Order, Lattices, Ordered Algebraic Structures FREE:General Algebraic Systems |
一般注記 | Preface -- Categories -- Functors and Natural Transformations -- Universality -- Cones and Limits -- Adjoints -- References -- Index of Symbols -- Index 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 HTTP:URL=https://doi.org/10.1007/978-3-319-41917-6 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319419176 |
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電子リソース |
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EB00204406 |
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※2017年9月4日以降