Categories for the Working Mathematician
Categories for the Working Mathematician
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DOI：
10.1007/978-1-4612-9839-7
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发表时间：
1971
期刊：
影响因子：
--
通讯作者：
S. Lane
中科院分区：
文献类型：
--
作者：
S. Lane
面向在职数学家的类别提供了一系列在各种领域中有用的一般想法。从基础出发，这本书阐明了范畴、函子、自然变换和对偶的概念。这本书然后转向伴随函子，它提供了对普遍结构的描述，分析了函子的态射集合的表示，以及操纵正向和逆极限的方法。这些范畴概念在后面的章节中得到了广泛的说明，包括伴随函子的基本存在定理的许多应用。代数系统范畴是由某些伴随类数据构造的，并用Beck定理刻画。在考虑了各种应用之后，本书继续构建和利用Kan扩展。第二版包括一些修订和补充，包括两个关于积极感兴趣的主题的新章节。一是关于对称么半群范畴和辫子么半群范畴以及它们的凝聚定理。第二类描述了最近兴起的2-范畴和高维范畴。参考书目也已扩大，涵盖了最近有关类别的许多其他进展。
Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.