拓扑分析与生糙分析中的同调替代对象
Homological surrogates in topological and bornological analysis
浏览论文内容
中文总结 AI 辅助
本文为具有核的强亏格-精确范畴构造同调替代对象，通过三项复形局部化给出显式核余核公式，并为多种完备空间及生糙模范畴建立导出等价阿贝尔模型与极大精确结构。
中文摘要 AI 辅助
我们描述了具有核的强亏格-精确范畴的心，作为同伦意义下三项复形范畴的局部化，无需假设核的可容许性。我们构造了分数运算，并给出了核与余核的显式公式。对于完备局部凸空间——其非拟阿贝尔性由Prosmans（2000）确立——我们的描述及其对偶通过两种精确性概念的选择提供了导出等价的阿贝尔模型。对于拟完备、序列完备及局部（即Mackey）完备空间，我们证明了拓扑精确序列构成极大亏格-精确结构，尽管这些范畴在局部凸Hausdorff空间范畴中并非扩张封闭的。我们的结果仍使它们可通过诱导的精确性概念进入同调代数领域。进一步的应用涉及具有非极大线性分裂精确结构的生糙模的拟阿贝尔范畴。
英文摘要
We describe hearts of strongly deflation-exact categories with kernels as localizations of categories of three-term complexes up to homotopy, without assuming admissibility of kernels. We construct a calculus of fractions and give explicit formulas for kernels and cokernels. For complete locally convex spaces, whose failure to be quasiabelian was established by Prosmans (2000), our description and its dual provide derived equivalent abelian models through two choices of a notion of exactness. For quasi-complete, sequentially complete and locally (a.k.a. Mackey) complete spaces, we show that the topologically exact sequences form the maximal deflation-exact structure, although these categories are not extension-closed in the category of locally convex Hausdorff spaces. Our results make them nevertheless accessible to homological algebra with respect to the induced notion of exactness. Further applications concern the quasiabelian category of bornological modules equipped with the non-maximal linear split exact structure.
发表机构
- University of Hamburg（汉堡大学）
机构由 AI 辅助整理，请以论文原文为准。
