Julie Bergner: Models for equivariant (∞, 1)-categories

Recent results of Marc Stephan give conditions under which a cofibrantly generated model category has an equivariant analogue, where the objects have a group action and weak equivalences and fibrations are defined via fixed point objects.  We apply his results to several models for (\infty, 1)-categories.  For discrete groups, all models satisfy the required conditions.  For simplicial or topological groups, we need to consider those models which have the additional structure of a simplicial or topological model category, respectively.