A folk model structure on omega-cat

TL;DR

This paper constructs a model structure on the category of strict omega-categories, enabling a better understanding of their homotopical properties and extending known results to higher dimensions.

Contribution

It introduces a new model structure on omega-categories expressed entirely within their framework, generalizing to n-categories for all n.

Findings

All objects are fibrant.

Cofibrant objects are exactly the free ones.

The model structure transfers to n-categories for all n.

Abstract

We establish a model structure on the category of strict omega-categories. The constructions leading to the model structure in question are expressed entirely within the scope of omega-categories, building on a set of generating cofibrations and a class of weak equivalences as basic items. All object are fibrant while cofibrant objects are exactly the free ones. Our model structure transfers to n-categories along right-adjoints, for each n, thus recovering the known cases n = 1 and n = 2.