论文标题
预留套件的定向退化图
Directed degeneracy maps for precubical sets
论文作者
论文摘要
引入了对称横向组，以使平行产物的构造具有同步过程代数函数。事实证明，可以从以下意义上对对称横向组进行定向同拷贝。使用Q-codibrant替换函数引入了来自对称横向集合到流的Q真实函数。通过拓扑旋转图，构建了共晶拓扑立方体。它可以被视为共晶拓扑空间，也可以视为共晶律师公制空间。通过劳森（Raussen）的自然$ d $ Path的概念，由于其律师公制空间的结构而扩展到对称的横向集合，从对称横向组中实现了对称横向组的自然实现函数。事实证明，这两个实现函数是通过使用以下事实，即定义对称横向集合在Shulman的意义上是C-REDY，这两个实现函数是同质的。这将概括为先前在预比例集的先前获得的对称横向集。
Symmetric transverse sets were introduced to make the construction of the parallel product with synchronization for process algebras functorial. It is proved that one can do directed homotopy on symmetric transverse sets in the following sense. A q-realization functor from symmetric transverse sets to flows is introduced using a q-cofibrant replacement functor of flows. By topologizing the cotransverse maps, the cotransverse topological cube is constructed. It can be regarded both as a cotransverse topological space and as a cotransverse Lawvere metric space. A natural realization functor from symmetric transverse sets to flows is introduced using Raussen's notion of natural $d$-path extended to symmetric transverse sets thanks to their structure of Lawvere metric space. It is proved that these two realization functors are homotopy equivalent on cofibrant symmetric transverse sets by using the fact that the small category defining symmetric transverse sets is c-Reedy in Shulman's sense. This generalizes to symmetric transverse sets results previously obtained for precubical sets.
