  In this paper we give a summary of the comparisons between different
definitions of so-called (\infty,1)-categories, which are considered to be
models for \infty-categories whose n-morphisms are all invertible for n>1. They
are also, from the viewpoint of homotopy theory, models for the homotopy theory
of homotopy theories. The four different structures, all of which are
equivalent, are simplicial categories, Segal categories, complete Segal spaces,
and quasi-categories.
