On some adjunctions in equivariant stable homotopy theory

TL;DR

This paper explores complex adjunction relationships in equivariant stable homotopy theory, revealing new chains of adjoint functors and their implications for the structure of equivariant spectra.

Contribution

It introduces novel adjunctions, including multiple right adjoints to key functors, expanding the understanding of categorical structures in equivariant stable homotopy theory.

Findings

Identifies a right adjoint to fixed points

Establishes a chain of adjoints to geometric fixed points

Reveals a chain of 6 or 7 adjoints involving restriction functors

Abstract

We investigate certain adjunctions in derived categories of equivariant spectra, including a right adjoint to fixed points, a right adjoint to pullback by an isometry of universes, and a chain of two right adjoints to geometric fixed points. This leads to a variety of interesting other adjunctions, including a chain of 6 (sometimes 7) adjoints involving the restriction functor to a subgroup of a finite group on equivariant spectra indexed over the trivial universe.