Cubical structures, homotopy theory

被引:0
|
作者
Antolini R. [1 ]
机构
[1] Dipartimento di Matematica, Seconda Université Degli Studi di Roma Tor Vergata, 00133 Roma, Via della Ricerca Scientifica
关键词
Topological Space; Homotopy Type; Homotopy Group; Homotopy Theory; Forgetful Functor;
D O I
10.1007/BF02505901
中图分类号
学科分类号
摘要
We investigate the categories of semi-cubical complexes with or loithout degeneracies. We prove that the Kan condition does not imply that a semi-cubical complex admits degeneracies and that, unlike the simplicial case, there is no cubical approximation theorem while we prove such a theorem for semi-cubical complexes with degeracies.
引用
收藏
页码:317 / 324
页数:7
相关论文
共 50 条
  • [1] Cubical Synthetic Homotopy Theory
    Mortberg, Anders
    Pujet, Loic
    CPP '20: PROCEEDINGS OF THE 9TH ACM SIGPLAN INTERNATIONAL CONFERENCE ON CERTIFIED PROGRAMS AND PROOFS, 2020, : 158 - 171
  • [2] A Cubical Approach to Synthetic Homotopy Theory
    Licata, Daniel R.
    Brunerie, Guillaume
    2015 30TH ANNUAL ACM/IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS), 2015, : 92 - 103
  • [3] A cubical model of homotopy type theory
    Awodey, Steve
    ANNALS OF PURE AND APPLIED LOGIC, 2018, 169 (12) : 1270 - 1294
  • [4] CANONICITY AND HOMOTOPY CANONICITY FOR CUBICAL TYPE THEORY
    Coquand, Thierry
    Huber, Simon
    Sattler, Christian
    LOGICAL METHODS IN COMPUTER SCIENCE, 2022, 18 (01)
  • [5] Cubical setting for discrete homotopy theory, revisited
    Carranza, D.
    Kapulkin, K.
    COMPOSITIO MATHEMATICA, 2025, 160 (12)
  • [6] Cubical methods in homotopy type theory and univalent foundations
    Mortberg, Anders
    MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE, 2021, : 1 - 38
  • [7] CUBICAL POLYHEDRA AND HOMOTOPY
    HOLSZTYN.W
    BLASS, J
    ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1973, 54 (03): : 416 - 425
  • [8] CUBICAL POLYHEDRA AND HOMOTOPY
    BLASS, J
    HOLSZTYNSKI, W
    ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1971, 50 (02): : 131 - +
  • [9] Homotopy groups of cubical sets
    Carranza, Daniel
    Kapulkin, Krzysztof
    EXPOSITIONES MATHEMATICAE, 2023, 41 (04)
  • [10] CUBICAL POLYHEDRA AND HOMOTOPY .3.
    BLASS, J
    HOLSZTYN.W
    ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1972, 53 (3-4): : 275 - 279