论文标题
比较立方体和球形的定向路径
Comparing cubical and globular directed paths
论文作者
论文摘要
流量是同质类型上的有向空间结构。众所周知，预留集作为流的实现的基本同质型类型是同质的，等效于将前提集的实现作为拓扑空间。这种认识取决于Q-成熟剂替代品的非规范选择。我们构建了一个新的实现函数，从预留集到流量，该函数等于前一个，并且不取决于选择任何同伴替代函数的选择。主要工具是劳森（Raussen）引入的天然$ d $ path的概念。我们为给定的预留集获得的流量不再是Q构件的，但仍然是M兼容性。作为一个应用程序，我们证明，预留集作为流的实现的执行路径的空间是同质的，等于前提集合的几何实现中的顶点之间的非稳定$ d $ Paths的空间。
A flow is a directed space structure on a homotopy type. It is already known that the underlying homotopy type of the realization of a precubical set as a flow is homotopy equivalent to the realization of the precubical set as a topological space. This realization depends on the non-canonical choice of a q-cofibrant replacement. We construct a new realization functor from precubical sets to flows which is homotopy equivalent to the previous one and which does not depend on the choice of any cofibrant replacement functor. The main tool is the notion of natural $d$-path introduced by Raussen. The flow we obtain for a given precubical set is not anymore q-cofibrant but is still m-cofibrant. As an application, we prove that the space of execution paths of the realization of a precubical set as a flow is homotopy equivalent to the space of nonconstant $d$-paths between vertices in the geometric realization of the precubical set.
