The enriched Thomason model structure on 2-categories

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. This paper is also available as arXiv :2208 .02954v4.(c) 2023 Published by Elsevier B.V.

Automated summary

We prove that categories enriched in the Thomason model structure have a model structure that is Quillen equivalent to the Bergner model structure on simplicial categories, providing a new model for (infinity, 1)-categories. In addition, 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.