U. Haifa Topology & Geometry seminar: Wednesday, November 26, 2025. Speaker: Lyne Moser (Regensburg). Title: “Modeling (∞, 1)-categories with Segal spaces”.
Classically, (∞, 1)-categories are modeled by complete Segal spaces. However, many examples first arise as non-complete Segal spaces, which are then completed abstractly to obtain an (∞, 1)-category. With Nuiten, we construct a model of (∞, 1)-categories in which completeness is not required. In this talk, I will present the main features of this model structure and the strategy used to construct it. In particular, we use a theorem, from joint work with Guetta, Sarazola, and Verdugo, that provides general methods for building model structures. Since the fibrant objects of our new model of (∞, 1)-categories are the Segal spaces themselves, this framework allows us to work directly with Segal spaces without passing to their completions. As illustrations, I will explain how the usual nerve of a category provides a model for the inclusion of categories into (∞, 1)-categories, and how the new model allows one to compute pullbacks (or more general limits) of (∞, 1)-categories directly using non-complete Segal spaces.
