Equivalence of cubical and simplicial approaches to (∞, n)-categories

被引：2
作者：
Doherty, Brandon
Kapulkin, Krzysztof
Maehara, Yuki
机构：
来源：
ADVANCES IN MATHEMATICS | 2023年 / 416卷
关键词：
n)-category; Complicial set; Cubical set; Model structure; Quillen equivalence; SETS;
D O I：
10.1016/j.aim.2023.108902
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that the marked triangulation functor from the category of marked cubical sets equipped with a model structure for (n-trivial, saturated) comical sets to the category of marked simplicial set equipped with a model structure for (n-trivial, saturated) complicial sets is a Quillen equivalence. Our proof is based on the theory of cones, previously developed by the first two authors together with Lindsey and Sattler.(c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页数：81
相关论文
共 19 条
[1]   Varieties of Cubical Sets [J].
Buchholtz, Ulrik ;
Morehouse, Edward .
RELATIONAL AND ALGEBRAIC METHODS IN COMPUTER SCIENCE, RAMICS 2017, 2017, 10226 :77-92
[2]  
Campion T, 2020, Arxiv, DOI arXiv:2005.07603
[3]  
Cisinski DC, 2006, ASTERISQUE, pXI
[4]  
Doherty B, 2022, Arxiv, DOI [arXiv:2005.04853, 10.48550/arXiv.2005.04853, DOI 10.48550/ARXIV.2005.04853]
[5]  
Doherty B, 2022, Arxiv, DOI arXiv:2207.03636
[6]  
Gabriel P., 1967, CALCULUS FRACTIONS H, DOI [10.1007/978-3-642-85844-4, DOI 10.1007/978-3-642-85844-4]
[7]  
Grandis Marco, 2003, THEOR APPL CATEG, V11, P185
[8]   A cubical approach to straightening [J].
Kapulkin, Krzysztof ;
Voevodsky, Vladimir .
JOURNAL OF TOPOLOGY, 2020, 13 (04) :1682-1700
[9]  
Kapulkin K, 2019, NEW YORK J MATH, V25, P627
[10]  
Maehara, 2020, ARXIV200311757
12