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Quasi-categories vs. Segal spaces: Cartesian edition
Journal of Homotopy and Related Structures ( IF 0.7 ) Pub Date : 2021-08-20 , DOI: 10.1007/s40062-021-00288-2 Nima Rasekh 1
中文翻译:
准范畴 vs. Segal 空间:笛卡尔版
更新日期:2021-08-20
Journal of Homotopy and Related Structures ( IF 0.7 ) Pub Date : 2021-08-20 , DOI: 10.1007/s40062-021-00288-2 Nima Rasekh 1
Affiliation
We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent:
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1.
On marked simplicial sets (due to Lurie [31]),
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2.
On bisimplicial spaces (due to deBrito [12]),
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3.
On bisimplicial sets,
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4.
On marked simplicial spaces.
The main way to prove these equivalences is by using the Quillen equivalences between quasi-categories and complete Segal spaces as defined by Joyal–Tierney and the straightening construction due to Lurie.
中文翻译:
准范畴 vs. Segal 空间:笛卡尔版
我们证明定义笛卡尔纤维和笛卡尔模型结构的四种不同方式都是 Quillen 等价的:
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1.
在标记单纯集上(由于 Lurie [31]),
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2.
在双简空间上(由于 deBrito [12]),
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3.
在双简集上,
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4.
在标记的单纯空间上。
证明这些等价的主要方法是使用 Joyal-Tierney 定义的准范畴和完全 Segal 空间之间的 Quillen 等价以及 Lurie 的矫直构造。