The enriched Thomason model structure on 2-categories

TL;DR

This paper establishes a new model structure on 2-categories enriched in the Thomason model, which is Quillen equivalent to the Bergner model, offering a novel approach to (infinity,1)-categories.

Contribution

It introduces a model structure on enriched 2-categories compatible with Thomason's and proves its equivalence to Bergner's model, also exploring model structures on modules and monoids.

Findings

Model structure on enriched 2-categories is Quillen equivalent to Bergner's.

Constructed model structures on modules and monoids in Thomason's setting.

Demonstrated that certain model structures on small categories are not cartesian.

Abstract

We prove that categories enriched in the Thomason model structure admit a model structure that is Quillen equivalent to the Bergner model structure on simplicial categories, providing a new model for (infinity,1)-categories. Along the way, we construct model structures on modules and monoids in the Thomason model structure and prove that any model structure on the category of small categories that has the same weak equivalences as the Thomason model structure is not a cartesian model structure.