A characterization of fibrant Segal categories

Abstract

In this note we prove that Reedy fibrant Segal categories are fibrant objects in the model category structure S C c \mathcal {SC}_c . Combining this result with a previous one, we thus have that the fibrant objects are precisely the Reedy fibrant Segal categories. We also show that the analogous result holds for Segal categories that are fibrant in the projective model structure on simplicial spaces, considered as objects in the model structure S C f \mathcal {SC}_f .