Embeddings of derived categories of bornological modules
Embeddings of derived categories of bornological modules
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出生学模块的派生类别的嵌入
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
R. Meyer
中科院分区：
文献类型：
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作者：
R. Meyer
设A是一个具有可数基的代数，B是一个包含A作为稠密子代数的Frechet代数。这种嵌入将函子从B-模的导出范畴诱导到A-模的导出范畴。在许多重要的例子中，这个函子是完全忠实的。我们研究这个属性的一些细节，给出几个等价条件，例子，和应用。
为了准备这一点，我们仔细解释了如何用模代数上的同调代数。我们构造了有界左A-模的导范畴和一些标准导函子，特别强调了张量积和内部Hom函子之间的伴随结合性。我们还讨论了非单位代数上的本质模范畴及其函性。
Let A be an algebra with a countable basis and let B be, say, a Frechet algebra that contains A as a dense subalgebra. This embedding induces a functor from the derived category of B-modules to the derived category of A-modules. In many important examples, this functor is fully faithful. We study this property in some detail, giving several equivalent conditions, examples, and applications.
To prepare for this, we explain carefully how to do homological algebra with modules over bornological algebras. We construct the derived category of bornological left A-modules and some standard derived functors, with special emphasis on the adjoint associativity between the tensor product and the internal Hom functor. We also discuss the category of essential modules over a non-unital algebra and its functoriality.