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摘要翻译：
引入并发展了阿贝尔范畴的标量扩张的概念。对于满足适当有限性条件的每一个F-线性阿贝尔范畴a,给出一个F'-线性阿贝尔范畴a'和一个精确的F-线性函子T:A-->a'。该函子在目标为F′-线性阿贝尔范畴的F-线性右精确函子中是普适的。我们讨论了这个概念的各种基本性质，其中包括与多线性内函子如张量积的相容性，以及函子和范畴的有利性质的持久性。我们得到了Tannakian范畴的标量扩张的概念，这使得我们可以推导出Tannakian范畴的代数单群的结果。
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英文标题：
《Scalar Extension of Abelian and Tannakian Categories》
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作者：
Nicolas Stalder
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Category Theory 范畴理论
分类描述：Enriched categories, topoi, abelian categories, monoidal categories, homological algebra
丰富范畴，topoi，abelian范畴，monoidal范畴，同调代数
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We introduce and develop the notion of scalar extension for abelian categories. Given a field extension F'/F, to every F-linear abelian category A satisfying a suitable finiteness condition we associate an F'-linear abelian category A' and an exact F-linear functor t: A --> A'. This functor is universal among F-linear right exact functors with target an F'-linear abelian category. We discuss various basic properties of this concept, among others compatibilities with multilinear endofunctors such as tensor products, and the permanence of favourable properties of the functors and categories involved. We obtain the notion of scalar extension for Tannakian categories, which allows us to deduce consequences for the algebraic monodromy groups of Tannakian categories.
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PDF链接：
https://arxiv.org/pdf/0806.0308
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