An Introduction to Homological Algebra
An Introduction to Homological Algebra
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DOI：
10.1007/b98977
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发表时间：
1979-07
期刊：
影响因子：
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通讯作者：
J. Rotman
中科院分区：
文献类型：
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作者：
J. Rotman
《同调代数》自1979年第一本书问世以来，在近三十年的时间里得到了发展。两本书讨论了最近的结果是韦伯，介绍同调代数，1994年，和Gelfand-Manin，方法的同调代数，2003年。在他们的前言中，Gelfand和Manin将同调代数的历史分为三个时期：第一个时期结束于20世纪60年代初，最终将同调代数应用于正则局部环。第二个时期，受A. Grothendieck和J. - P. Serre，持续到1980年代;它涉及阿贝尔范畴和层上同调。第三个时期，即衍生范畴和三角范畴的演变，仍在进行中。这两本较新的书都讨论了所有三个时期（另见Kashiwara Schapira，Categories and Sheaves）。本书的原始版本仅讨论了第一个时期;这个新版本仍然处于相同的介绍级别，但现在也介绍了第二个时期。这种变化在专业上是有意义的，因为自1979年以来，数学界发生了变化;今天，几乎所有的数学研究生都学习了关于函子和范畴的东西，所以我现在可以更认真地对待范畴观点了。当我还是一名研究生时，同调代数是一门冷门学科。普遍的态度是，这是一种怪诞的形式主义，学起来很无聊，一旦学会了就没有多大用处。
Homological Algebra has grown in the nearly three decades since the rst e-tion of this book appeared in 1979. Two books discussing more recent results are Weibel, An Introduction to Homological Algebra, 1994, and Gelfand–Manin, Methods of Homological Algebra, 2003. In their Foreword, Gelfand and Manin divide the history of Homological Algebra into three periods: the rst period ended in the early 1960s, culminating in applications of Ho-logical Algebra to regular local rings. The second period, greatly in uenced by the work of A. Grothendieck and J.-P. Serre, continued through the 1980s; it involves abelian categories and sheaf cohomology. The third period,-volving derived categories and triangulated categories, is still ongoing. Both of these newer books discuss all three periods (see also Kashiwara–Schapira, Categories and Sheaves). The original version of this book discussed the rst period only; this new edition remains at the same introductory level, but it now introduces thesecond period as well. This change makes sense pe-gogically, for there has been a change in the mathematics population since 1979; today, virtually all mathematics graduate students have learned so-thing about functors and categories, and so I can now take the categorical viewpoint more seriously. When I was a graduate student, Homological Algebra was an unpopular subject. The general attitude was that it was a grotesque formalism, boring to learn, and not very useful once one had learned it.