Towards a Thomason model structure on the category of strict n-categories
Dimitri Ara, Georges Maltsiniotis

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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Logic
