Classically, (\u221e, 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 (\u221e, 1)-category. With Nuiten, we construct a model of (\u221e, 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 (\u221e, 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 (\u221e, 1)-categories, and how the new model allows one to compute pullbacks (or more general limits) of (\u221e, 1)-categories directly using non-complete Segal spaces.
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Recording: Classically, (\u221e, 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 (\u221e, 1)-category. With Nuiten, we construct a model of (\u221e, 1)-categories in which completeness…
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