We put a model structure on the category of categories internal to simplicial sets. The weak equivalences in this model structure are preserved and reflected by the nerve functor to bisimplicial sets with the complete Segal space model structure. This model structure is shown to be a model for the homotopy theory of infinity categories. We also study the homotopy theory of internal presheaves over an internal category.
Keywords: internal categories, complete Segal spaces, infinity categories
2010 MSC: 55U40, 18C35, 18D99
Theory and Applications of Categories, Vol. 30, 2015, No. 20, pp 704-750.