论文标题
同源理论的平坦替代品
Flat replacements of homology theories
论文作者
论文摘要
对于同源性理论，可以将添加剂位点和新的同源函数与该站点上添加式束带类别的值相关联。如果可以证明此类别的滑轮等效于Hopf代数的综合类别，那么我们通过与基础模块函数组成来获得新的同源理论。这种新的同源性理论始终是平坦的，我们称其为原始理论的平坦替代。例如，PstrąGowski表明复杂的恢复是单一同源性的平坦替代。在本文中，我们研究了与同源理论相关的站点的基本属性，我们证明了存在平坦替代的存在定理。
To a homology theory one can associate an additive site and a new homological functor with values in the category of additive sheaves on that site. If this category of sheaves can be shown to be equivalent to a category of comodules of a Hopf algebroid, then we obtain a new homology theory by composing with the underlying module functor. This new homology theory is always flat and we call it a flat replacement of the original theory. For example, Pstrągowski has shown that complex cobordism is a flat replacement of singular homology. In this article we study the basic properties of the sites associated to homology theories and we prove an existence theorem for flat replacements.
