论文标题
Culf地图和边缘分区
Culf maps and edgewise subdivision
论文作者
论文摘要
我们表明，对于任何简单的空间$ x $，$ x $上的Culf Maps的$ \ infty $ - 类别相当于$ \ infty $ - $ \ opperatorname {sd}（sd}（x）$，$ x $的ed right bibrations（sd} $）。 （当$ x $是rezk完整的segal或2个segal空间时，$ \ operatatorName {sd}（x）$是$ x $的扭曲箭头类别。）我们给出了两个独立利益的证明；一种利用综合分解和从边缘细分到元素类别神经的自然转化，另一个利用了Ambifinal和Culf Maps的新分解系统，以及右侧细分的正确伴随。使用此主要定理，我们表明分解空间和Culf Maps的$ \ infty $ - 类别是本地的$ \ infty $ -TOPOS。
We show that, for any simplicial space $X$, the $\infty$-category of culf maps over $X$ is equivalent to the $\infty$-category of right fibrations over $\operatorname{sd}(X)$, the edgewise subdivision of $X$. (When $X$ is a Rezk complete Segal or 2-Segal space, $\operatorname{sd}(X)$ is the twisted arrow category of $X$.) We give two proofs of independent interest; one exploiting comprehensive factorization and the natural transformation from the edgewise subdivision to the nerve of the category of elements, and another exploiting a new factorization system of ambifinal and culf maps, together with the right adjoint to edgewise subdivision. Using this main theorem, we show that the $\infty$-category of decomposition spaces and culf maps is locally an $\infty$-topos.
