Equivariant Weiss Calculus

Abstract

In this paper, we introduce an equivariant analog of Weiss calculus of functors for all finite group $\mathrm{G}$. In our theory, Taylor approximations and derivatives are index by finite dimensional $\mathrm{G}$-representations, and homogeneous layers are classified by orthogonal $\mathrm{G}$-spectra. Further, our framework permits a notion of restriction as well as a notion of fixed-point at the level of Weiss functors. We establish various results comparing Taylor approximations and derivatives of fixed-point (resp. restrictions) functors to that of the fixed-point (resp. restrictions) of Taylor approximations and derivatives.