Methods of Homological Algebra
Methods of Homological Algebra
复制标题
DOI：
10.1007/978-3-662-12492-5
复制
发表时间：
1996-01
期刊：
影响因子：
--
通讯作者：
S. Gelfand;Y. Manin
中科院分区：
文献类型：
--
作者：
S. Gelfand;Y. Manin
同调代数最初是作为描述几何对象的拓扑前景的语言而出现的。与每一种成功的语言一样，它迅速扩展了它的覆盖范围和语义，它的当代应用非常广泛。这种现代方法同调代数，由两个领先的作家在该领域，是基于系统使用的语言和思想的派生类别和派生函子。与标准上同调理论的关系（层上同调，谱序列等）描述了在大多数情况下，完整的证明。给出了同伦代数的基本概念和结果。这本书解决的人谁想要学习现代方法同调代数和使用它在他们的工作。对于第二版，作者做了许多修改。
Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections.