论文标题
结构化空间的两种辅助理论
Two cohomology theories for structured spaces
论文作者
论文摘要
在[1]中，我们定义了一种称为“结构化空间”的新型空间，该空间在其每个点附近的局部类似于某些代数结构。我们在引用论文的结论中指出，地图$ f_s $和$ h $在结构化空间的理论中非常重要，它与预期的概念（因此也是托管）和矢量捆绑包具有一定的联系。有涉及此类物体的众所周知的共同体理论。这表明存在（CO）同源性理论的结构化空间的可能性，这与$ f_s $和$ h $相关。在本文中，我们确实为结构化空间开发了两种共同体理论：其中一个来自$ f_s $，而另一个来自$ h $。为了做到这一点，我们首先开发了一种更一般的共同体学理论（在有限情况下称为矩形的同胞学，在无限情况下称为方形的提升理论），实际上也可以在许多其他情况下应用，然后在许多其他情况下都可以使用该理论的结构性空间作为简单的后果。
In [1] we defined a new kind of space called 'structured space' which locally resembles, near each of its points, some algebraic structure. We noted in the conclusion of the cited paper that the maps $f_s$ and $h$, which are of great importance in the theory of structured spaces, have some connections with the notions of presheaves (and hence also sheaves) and vector bundles. There are well known cohomology theories involving such objects; this suggests the possibility of the existence of (co)homology theories for structured spaces which are somehow related to $f_s$ and $h$. In this paper we indeed develop two cohomology theories for structured spaces: one of them arises from $f_s$, while the other one arises from $h$. In order to do this, we first develop a more general cohomology theory (called rectangular cohomology in the finite case, and square cohomology in the infinite case), which can actually be applied also in many other situations, and then we obtain the cohomology theories for structured spaces as simple consequences of this theory.
