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 (4)

• On the non-existence of elements of Kervaire invariant one
• Models of G-spectra as presheaves of spectra
• Cyclonic spectra, cyclotomic spectra, and a conjecture of Kaledin
• On the fibrewise effective Burnside $\infty$-category

Cited by in corpus (6)

• Eilenberg-MacLane spectra as equivariant Thom spectra
• Genuine equivariant factorization homology
• $C_2$-equivariant Homology Operations: Results and Formulas
• Equivariant nonabelian Poincaré duality and equivariant factorization homology of Thom spectra
• Stable moduli spaces of hermitian forms
• Recollements and stratification