Algebras and Modules in Monoidal Model Categories
Algebras and Modules in Monoidal Model Categories
复制标题
幺半群模型类别中的代数和模
DOI：
--
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
B. Shipley
中科院分区：
文献类型：
--
作者：
S. Schwede;B. Shipley
近年来，结构环谱(以前称为A∞环谱和E∞环谱)的理论由于发现了具有严格结合和交换Smash积的谱范畴而得到简化。现在，环谱可以简单地定义为相对于这些新的谱范畴之一中的Smash积的么半群。本文提供了一种构造环、代数和模谱范畴的模型范畴结构的一般方法。这为获得对称环谱、具有Smash积的函子、伽马环和图环谱的模型范畴提供了必要的输入。我们的方法所应用的代数例子包括有限群的群代数上的稳定模范畴和微分分次代数上的无界链复形。1991年数学科目分类：小学55U35；中学18D10。
In recent years the theory of structured ring spectra (formerly known as A∞‐ and E∞‐ring spectra) has been simplified by the discovery of categories of spectra with strictly associative and commutative smash products. Now a ring spectrum can simply be defined as a monoid with respect to the smash product in one of these new categories of spectra. In this paper we provide a general method for constructing model category structures for categories of ring, algebra, and module spectra. This provides the necessary input for obtaining model categories of symmetric ring spectra, functors with smash product, Gamma‐rings, and diagram ring spectra. Algebraic examples to which our methods apply include the stable module category over the group algebra of a finite group and unbounded chain complexes over a differential graded algebra. 1991 Mathematics Subject Classification: primary 55U35; secondary 18D10.