Categorical models of unstable G-global homotopy theory

Abstract

We prove that the category G-Cat of small categories with G-action forms a model of unstable G-global homotopy theory for every discrete group G, generalizing Schwede’s global model structure on Cat. As a consequence, we prove that G-Cat models proper G-equivariant homotopy theory not only when we test weak equivalences on fixed points, but also when we test them on categorical homotopy fixed points.