# The dominant dimension of cohomological Mackey functors

## TL;DR

This paper demonstrates that the dominant dimension of cohomological Mackey functors for a p-block of a finite group with a nontrivial defect group is always 2, using properties of symmetric algebras and separable equivalences.

## Contribution

It establishes the invariant nature of dominant dimensions of certain endomorphism algebras under separable equivalences and applies this to cohomological Mackey functors.

## Key findings

- Dominant dimension of coMack(B) is 2 for nontrivial defect groups.
- Separable equivalences preserve dominant dimensions of specific endomorphism algebras.
- The result applies to p-blocks of finite groups with nontrivial defect groups.

## Abstract

We show that a separable equivalence between symmetric algebras preserves the dominant dimensions of certain endomorphism algebras of modules. We apply this to show that the dominant dimension of the category coMack(B) of cohomological Mackey functors of a p-block B of a finite group with a nontrivial defect group is 2.