Category Theory
Category Theory
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DOI：
10.1093/acprof:oso/9780198568612.001.0001
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
S. Awodey
中科院分区：
文献类型：
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作者：
S. Awodey
范畴论是抽象代数的一个分支，有着令人难以置信的广泛应用。这本教科书和参考书不仅针对数学家，也针对计算机科学、逻辑学、语言学、认知科学、哲学和任何其他应用这些思想的领域的研究人员和学生。包含明确的定义的基本概念，阐明了许多方便的例子，并提供充分的证明所有重要的命题和定理，这本书的目的是使基本思想，定理和方法的范畴论理解这一广泛的读者群。虽然假设很少的数学前提，但数学严谨性的标准并没有妥协。所涵盖的材料包括标准的核心类别;函子;自然变换;等价;限制和colimits;函子类别; representables; Yoneda的引理;伴随;单子。还提供了一个额外的主题carless-closed范畴和微积分-计算机科学家，逻辑学家和语言学家必须！这第二版包含了对原文的许多修订，包括扩大论述，修改和阐述证明，提供额外的图表，纠正印刷错误，最后，增加了一个全新的monoidal范畴部分。还增加了近百个新练习，许多都有解决方案，使这本书作为课程教材和自学更有用。
Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists!This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.