A categorification of the Cartan-Eilenberg formula

TL;DR

This paper presents a categorification of the Cartan-Eilenberg stable elements formula, expressing derived and stable module categories of a group as bilimits over p-subgroups, advancing the understanding of their categorical structures.

Contribution

It introduces a new categorification of the classical stable elements formula, linking derived and stable categories through bilimits over p-subgroups.

Findings

Derived category expressed as a bilimit over p-subgroups

Stable module category expressed as a bilimit over p-subgroups

Provides a new categorical perspective on classical group cohomology results

Abstract

We prove a categorification of the stable elements formula of Cartan and Eilenberg. Our formula expresses the derived category and the stable module category of a group as a bilimit of the corresponding categories for the $p$-subgroups.