论文标题
非单明简单集的同喻理论
Homotopy Theory of Non-singular Simplicial Sets
论文作者
论文摘要
如果简单的简单简单嵌入，则据说简单套件是非单一的。令$ SSET $表示简单集的类别。我们证明，其对象是非单明的简单集的完整子类别$ nsset $，承认了一个模型结构，因此$ nsset $变为Quillen等于$ SSET $，该$ SSET $由Quillen引起的标准模型结构。 $ NSSET $上的模型结构是从$ SSET $正确引起的，并且它使$ NSSET $成为适当的合并生成的模型类别。与托马森（Thomason）在小型类别上的模型结构（1980）和posets上的Raptis模型结构（2010）一起形成了Quillen等效模型类别的方形图，其中右伴随的子标准是通勤的。
A simplicial set is said to be non-singular if its non-degenerate simplices are embedded. Let $sSet$ denote the category of simplicial sets. We prove that the full subcategory $nsSet$ whose objects are the non-singular simplicial sets admits a model structure such that $nsSet$ becomes is Quillen equivalent to $sSet$ equipped with the standard model structure due to Quillen. The model structure on $nsSet$ is right-induced from $sSet$ and it makes $nsSet$ a proper cofibrantly generated model category. Together with Thomason's model structure on small categories (1980) and Raptis' model structure on posets (2010) these form a square-shaped diagram of Quillen equivalent model categories in which the subsquare of right adjoints commutes.
