English

Towards a Thomason model structure on the category of strict n-categories

Algebraic Topology 2020-09-07 v3 Category Theory

Abstract

The purpose of this article is to present ideas towards obtaining a model category structure on the category of small strict n-categories, generalizing the one obtained by Thomason on ordinary categories. Following ideas of Grothendieck and Cisinski, we obtain an "abstract Thomason theorem", which easily implies the classical Thomason theorem. We deduce a 2-categorical Thomason theorem, an incorrect proof of which has been published by K. Worytkiewicz, K. Hess, P. Parent and A. Tonks. For n > 2, we isolate sufficient conditions to obtain an n-categorical Thomason theorem. These conditions will be investigated in further work.

Keywords

Cite

@article{arxiv.1305.5086,
  title  = {Towards a Thomason model structure on the category of strict n-categories},
  author = {Dimitri Ara and Georges Maltsiniotis},
  journal= {arXiv preprint arXiv:1305.5086},
  year   = {2020}
}

Comments

92 pages, in French, v2: Section 7 partially rewritten to prove a more precise version of Proposition 6.20, new section on cofibrant objects added, v3: typos corrected, references added