Higher quasi-categories vs higher Rezk spaces
Higher quasi-categories vs higher Rezk spaces
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更高的准类别与更高的 Rezk 空间
DOI：
10.1017/s1865243315000021
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Dimitri Ara
中科院分区：
文献类型：
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作者：
Dimitri Ara
我们引入了n-拟范畴的概念，作为Joyal的n-胞室范畴\Theta_n上的预层上的模型范畴结构的映射对象.我们的定义来自于Cisinski和Joyal的一个想法。然而，我们表明，这个想法必须稍微修改，以获得一个合理的概念。我们构造了n-拟范畴的模型范畴与Rezk \Theta_n-空间的模型范畴之间的两个Quillen等价，证明了n-拟范畴是（\infty，n）-范畴的模型.当n = 1时，我们恢复了Joyal和Tierney在拟范畴和完备Segal空间之间定义的两个Quillen等价.
We introduce a notion of n-quasi-categories as fibrant objects of a model category structure on presheaves on Joyal's n-cell category \Theta_n. Our definition comes from an idea of Cisinski and Joyal. However, we show that this idea has to be slightly modified to get a reasonable notion. We construct two Quillen equivalences between the model category of n-quasi-categories and the model category of Rezk \Theta_n-spaces showing that n-quasi-categories are a model for (\infty, n)-categories. For n = 1, we recover the two Quillen equivalences defined by Joyal and Tierney between quasi-categories and complete Segal spaces.