Cyclic Segal Spaces

In this survey article, we review some conceptual approaches to the cyclic category $\mathrm{\Lambda }$, as well as its description as a crossed simplicial group. We then give a new proof of the model structure on cyclic sets, work through the details of the generalized Reedy structure on cyclic spaces, and introduce model structures for cyclic Segal spaces and cyclic 2-Segal spaces.