Derived Mackey functors

Abstract

For a finite group $G$, the so-called $G$-Mackey functors form an abelian category $M(G)$ that has many applications in the study of $G$-equivariant stable homotopy. One would expect that the derived category $D(M(G))$ would be similarly important as the "homological" counterpart of the $G$-equivariant stable homotopy category. It turns out that this is not so -- $D(M(G))$ is pathological in many respects. We propose and study a replacement for $D(M(G))$, a certain triangulated category $DM(G)$ of "derived Mackey functors" that contains $M(G)$ but is different from $D(M(G))$. We show that standard features of the $G$-equivariant stable homotopy category such as the fixed points functors of two types have exact analogs for the category $DM(G)$.

arXiv commentLaTeX2e, 106 pages. Minor revision: corrected some statements about A_\infty-coalgebras in the first section. The main body of the paper is not affected.

References in corpus (1)

• Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence

Cited by in corpus (1)

• Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence