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