Quasi-categories vs. Segal spaces: Cartesian edition

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2021-08-20 DOI:10.1007/s40062-021-00288-2

Nima Rasekh

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引用次数: 7

Abstract

We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent:

1.
On marked simplicial sets (due to Lurie [31]),
2.
On bisimplicial spaces (due to deBrito [12]),
3.
On bisimplicial sets,
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.

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准范畴与西格尔空间:笛卡尔版

我们证明了四种不同的定义笛卡尔振动和笛卡尔模型结构的方法都是Quillen等效的:1。在标记简单集上(由于Lurie[31])， 2。2 .关于双斜空间(由于deBrito [12])，在二项式集上，4。在标记的简单空间上。证明这些等价的主要方法是利用Joyal-Tierney定义的拟范畴与完全Segal空间之间的Quillen等价以及Lurie的拉直构造。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.