论文标题
差异原理束和主要无穷捆绑包
Diffeological Principal Bundles and Principal Infinity Bundles
论文作者
论文摘要
在本文中，我们研究差异空间是笛卡尔空间所在的某些离散的简单预示，并覆盖了良好的开放式盖子。简单的预示例上的čech模型结构为我们提供了$ \ infty $ - 堆栈的差异共同体，具有差异学空间，具有差异学的阿贝里安集团$ a $。我们将差异空间的$ \ infty $ stack共同学与文献中的差异空间的两个现有概念进行了比较。最后，我们证明，对于一个差异群体$ g $，差异原理$ g $捆绑的类别的神经是薄弱的同质副本，等同于$ g $ $ g $ - principal $ \ inccipal $ \ infty $ \ infty $ bundty $ bundy $ x $ x $上的bunde bunde bunde bunde bunde bunde bunge of Diffefeological and Epos topos and topos理论。
In this paper, we study diffeological spaces as certain kinds of discrete simplicial presheaves on the site of cartesian spaces with the coverage of good open covers. The Čech model structure on simplicial presheaves provides us with a notion of $\infty$-stack cohomology of a diffeological space with values in a diffeological abelian group $A$. We compare $\infty$-stack cohomology of diffeological spaces with two existing notions of Čech cohomology for diffeological spaces in the literature. Finally, we prove that for a diffeological group $G$, that the nerve of the category of diffeological principal $G$-bundles is weak homotopy equivalent to the nerve of the category of $G$-principal $\infty$-bundles on $X$, bridging the bundle theory of diffeology and higher topos theory.
