Identifying the homotopy fiber of a map of semi-Segal spaces

Abstract: We prove a version of Quillen's theorems for a map of semi-Segal spaces. We construct a bi-semi-simplicial resolution similar to the one associated to a functor of non-unital topological categories. As a consequence we can represent the homotopy fiber of a map of semi-Segal spaces as the geometric realization of a certain semi-simplicial space.