The enriched Thomason model structure on 2-categories

被引:0
|
作者
Pavlov, Dmitri [1 ]
机构
[1] Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA
关键词
HOMOTOPY-THEORY; CATEGORIES; ALGEBRAS; MODULES;
D O I
10.1016/j.jpaa.2023.107496
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove that categories enriched in the Thomason model structure admit a model structure that is Quillen equivalent to the Bergner model structure on simplicial categories, providing a new model for (infinity, 1)-categories. Along the way, we construct model structures on modules and monoids in the Thomason model structure and prove that any model structure on the category of small categories that has the same weak equivalences as the Thomason model structure is not a cartesian model structure. This paper is also available as arXiv :2208 .02954v4.(c) 2023 Published by Elsevier B.V.
引用
收藏
页数:23
相关论文
共 50 条
  • [1] A Quillen model structure for 2-categories
    Lack, S
    K-THEORY, 2002, 26 (02): : 171 - 205
  • [2] SOME STRUCTURE OF CATEGORY OF 2-CATEGORIES
    GRAY, JW
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (02): : A388 - A388
  • [3] The formal ball model for 2-categories
    Kostanek, Mateusz
    Waszkiewicz, Pawel
    MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE, 2011, 21 (01) : 41 - 64
  • [4] A DOUBLE CATEGORICAL MODEL OF WEAK 2-CATEGORIES
    Paoli, Simona
    Pronk, Dorette
    THEORY AND APPLICATIONS OF CATEGORIES, 2013, 28 : 933 - 980
  • [5] Adjunction in 2-categories
    Kaledin, D. B.
    RUSSIAN MATHEMATICAL SURVEYS, 2020, 75 (05) : 883 - 927
  • [6] Homotopy ends and Thomason model categories
    Weibel C.
    Selecta Mathematica, 2001, 7 (4) : 533 - 564
  • [7] Monoidal categories and monoidal 2-categories
    不详
    NON-SEMISIMPLE TOPOLOGICAL QUANTUM FIELD THEORIES FOR 3-MANIFOLDS WITH CORNERS, 2002, 1765 : 217 - 259
  • [8] 2-CATEGORIES OF SHEAVES
    PATNAIK, SN
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 16 (03): : 584 - &
  • [9] DOCTRINES ON 2-CATEGORIES
    ZOBERLEIN, V
    MATHEMATISCHE ZEITSCHRIFT, 1976, 148 (03) : 267 - 279
  • [10] A Thomason model structure on the category of small n-fold categories
    Fiore, Thomas M.
    Paoli, Simona
    ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2010, 10 (04): : 1933 - 2008