Abstract In this paper, we construct a model structure for ‐categories on the category of simplicial spaces, whose fibrant objects are the Segal spaces. In particular, we show that it is Quillen equivalent to the models of ‐categories given by complete Segal spaces and Segal categories. We furthermore prove that this model structure has desirable properties: it is cartesian closed and left proper. As applications, we get a simple description of the inclusion of categories into ‐categories and of homotopy limits of ‐categories.
Moser et al. (Thu,) studied this question.