Azumaya Categories
Azumaya Categories
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东屋类别
DOI：
10.1023/a:1020570213428
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发表时间：
2002
影响因子：
0.6
通讯作者：
E. Vitale
中科院分区：
文献类型：
--
作者：
F. Borceux;E. Vitale
我们定义的概念Azumaya范畴和Brauer组在范畴论丰富了一些非常一般的基础范畴V。我们证明了各种定义的等价性，特别是在可分范畴或progenerating双模。当V是交换环R上的模范畴时，我们重新获得Azumaya代数和Brauer群的经典概念，并提供了这些理论的另一种纯范畴处理。但我们的理论也适用于拓扑、度量或Banach模的情况，适用于这种结构或分次这种结构的层，以及许多其他例子。
We define the notions of Azumaya category and Brauer group in category theory enriched over some very general base category V. We prove the equivalence of various definitions, in particular in terms of separable categories or progenerating bimodules. When V is the category of modules over a commutative ring R with unit, we recapture the classical notions of Azumaya algebra and Brauer group and provide an alternative, purely categorical treatment of those theories. But our theory applies as well to the cases of topological, metric or Banach modules, to the sheaves of such structures or graded such structures, and many other examples.