Equivariant complete Segal spaces (Q5963056)

This paper is concerned with equivariant Segal spaces as models for equivariant \((\infty,1)\)-categories. For a discrete group \(G\) it is shown that the category of simplicial \(G\)-spaces has a topological model structure in which the fibrant objects are the Segal \(G\)-spaces. For a discrete group or compact Lie group \(G\) it is shown that the category of simplicial \(G\)-spaces has a topological model structure in which the fibrant objects are the complete Segal \(G\)-spaces. For a discrete group \(G\) it is shown that a small \(G\)-category has a \(G\)-classifying diagram which is a complete Segal \(G\)-space.