论文标题
可构造滑轮的同拷贝不变性
The homotopy-invariance of constructible sheaves
论文作者
论文摘要
本文的目的是解释为什么为什么将分层拓扑空间$ s $发送给$ \ infty $ - $ s $ s $的$ \ infty $类别，并在$ s $上带有系数，其中一大型可呈现的$ \ infty $类别是同质的。为此，我们首先在未分层的设置中建立许多结果，即局部恒定（超级）滑轮的设置。例如，如果$ x $是本地易于收缩的拓扑空间，而$ \ nathcal {e} $是一个可呈现的$ \ infty $ - 类别，那么我们为常量的Hypersheaf Foundor $ \ Mathcal {e} \ to提供一个具体的公式\ mathrm {sh}^{\ mathrm {help}}}}（x; \ mathcal {e}）$。该公式使我们表明，不断的Hypersheaf函数是正确的伴随，如果$ x $也很差，则完全忠实。它还使我们证明了局部恒定的高度迁移的一般单构型等效性和分类künneth公式。
The purpose of this paper is to explain why the functor that sends a stratified topological space $S$ to the $\infty$-category of constructible (hyper)sheaves on $S$ with coefficients in a large class of presentable $\infty$categories is homotopy-invariant. To do this, we first establish a number of results in the unstratified setting, i.e., the setting of locally constant (hyper)sheaves. For example, if $X$ is a locally weakly contractible topological space and $\mathcal{E}$ is a presentable $\infty$-category, then we give a concrete formula for the constant hypersheaf functor $\mathcal{E}\to \mathrm{Sh}^{\mathrm{hyp}}(X;\mathcal{E})$. This formula lets us show that the constant hypersheaf functor is a right adjoint, and is fully faithful if $X$ is also weakly contractible. It also lets us prove a general monodromy equivalence and categorical Künneth formula for locally constant hypersheaves.
