First I will introduce a generalization of the notion of (right)-exact functor between abelian categories to the case of non-additive functors. The main result of this section is an extension theorem: any functor defined on a suitable subcategory can be extended uniquely to a right exact functor defined on the whole category.

Next I use those results to define various functors of generalized tensor induction, associated to finite bisets, between categories attached to finite groups. This includes a definition of tensor induction for Mackey functors, for cohomological Mackey functors, for \(p\)-permutation modules and algebras. This also gives a single formalism of bisets for restriction, inflation, and ordinary tensor induction for modules.

Readership

Graduate students and research mathematicians interested in representation theory of finite groups.

Table of Contents

• Introduction
• Non additive exact functors
• Permutation Mackey functors
• Tensor induction for Mackey functors
• Relations with the functors \({\mathcal L}_U\)
• Direct product of Mackey functors
• Tensor induction for Green functors
• Cohomological tensor induction
• Tensor induction for \(p\)-permutation modules
• Tensor induction for modules
• Bibliography