Modeling (∞,1)‐categories with Segal spaces
Abstract
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.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Logic
programming
and type systems
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN