English

Orientals as free weak $\omega$-categories

Category Theory 2023-02-17 v2

Abstract

The orientals are the free strict ω\omega-categories on the simplices introduced by Street. The aim of this paper is to show that they are also the free weak ω\omega-categories on the same generating data. More precisely, we exhibit the Street nerves of the orientals as fibrant replacements of the simplices in Verity's model structure for complicial sets.

Cite

@article{arxiv.2102.09736,
  title  = {Orientals as free weak $\omega$-categories},
  author = {Yuki Maehara},
  journal= {arXiv preprint arXiv:2102.09736},
  year   = {2023}
}

Comments

v2: 24 pages. Major revision. Published version

R2 v1 2026-06-23T23:18:51.935Z