Categorical models of unstable G-global homotopy theory

Abstract

We prove that the category $\text{G-Cat}$ 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 $\text{Cat}$. As a consequence, we prove that $\text{G-Cat}$ 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.

Final version, incorporating suggestions by referee (several changes to exposition). 42 pages

References in corpus (3)

• Quillen adjunctions induce adjunctions of quasicategories
• Global algebraic K-theory
• On the global homotopy theory of symmetric monoidal categories