  This paper is a study of Bousfield-Segal spaces, a notion introduced by Julie
Bergner drawing on ideas about Eilenberg-Mac Lane objects due to Bousfield. In
analogy to Rezk's Segal spaces, they are defined in such a way that
Bousfield-Segal spaces naturally come equipped with a homotopy-coherent
fraction operation in place of a composition.
  In this paper we show that Bergner's model structure for Bousfield-Segal
spaces in fact can be obtained from the model structure for Segal spaces both
as a localization and a colocalization. We thereby prove that Bousfield-Segal
spaces really are Segal spaces, and that they characterize exactly those with
invertible arrows. We note that the complete Bousfield-Segal spaces are
precisely the homotopically constant Segal spaces, and deduce that the
associated model structure yields a model for both $\infty$-groupoids and
Homotopy Type Theory.
