Parametrized higher category theory and higher algebra: Exposé IV -- Stability with respect to an orbital $\infty$-category

Abstract

In this paper we develop a theory of stability for $G$-categories (presheaf of categories on the orbit category of $G$), where $G$ is a finite group. We give a description of Mackey functors as $G$-commutative monoids exploit it to characterize $G$-spectra as the $G$-stabilization of $G$-spaces. As an application of this we provide an alternative proof of a theorem by Guillou and May. The theory here is developed in the more general setting of orbital categories.

References in corpus (1)

• On the fibrewise effective Burnside $\infty$-category

Cited by in corpus (2)

• Genuine equivariant factorization homology
• $C_2$-equivariant Homology Operations: Results and Formulas