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

TL;DR

This paper explores the possibility of establishing a Thomason model structure on the category of strict n-categories, extending classical results from ordinary categories to higher categorical levels.

Contribution

It introduces an abstract Thomason theorem framework for strict n-categories, generalizing known results and setting the stage for future developments in higher category theory.

Findings

Established an abstract Thomason theorem for strict n-categories

Derived a 2-categorical Thomason theorem with a corrected proof

Outlined conditions for n > 2 to achieve an n-categorical Thomason theorem

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.