论文标题
具有线性拓扑的拓扑矢量空间的确切类别
Exact categories of topological vector spaces with linear topology
论文作者
论文摘要
我们解释了为什么在完整的，分离的拓扑矢量空间中，对具有线性拓扑的完整，分离的拓扑矢量空间的天真定义会失败。特别是，与ARXIV相反：0711.2527，这种拓扑矢量空间的类别不是准阿贝尔语。我们提出了对确切类别结构的校正定义，该定义正常。然后，我们解释说，校正后的定义仍然存在缺点，因为它在其中不精确，并讨论了完善确切类别结构的方法，以使张量产品函数精确。
We explain why the naive definition of a natural exact category structure on complete, separated topological vector spaces with linear topology fails. In particular, contrary to arXiv:0711.2527, the category of such topological vector spaces is not quasi-abelian. We present a corrected definition of exact category structure which works OK. Then we explain that the corrected definition still has a shortcoming in that a natural tensor product functor is not exact in it, and discuss ways to refine the exact category structure so as to make the tensor product functors exact.
