Non-additive exact functors and tensor induction for Mackey functors
About this Title
Publication: Memoirs of the American Mathematical Society
Publication Year 2000: Volume 144, Number 683
ISBNs: 978-0-8218-1951-7 (print); 978-1-4704-0274-7 (online)
MathSciNet review: 1662073
MSC (1991): Primary 19A22; Secondary 18A22, 20J05, 20J06, 55M35, 55N91
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.
Graduate students and research mathematicians interested in representation theory of finite groups.
Table of Contents
- 1. Introduction
- 2. Non additive exact functors
- 3. Permutation Mackey functors
- 4. Tensor induction for Mackey functors
- 5. Relations with the functors
- 6. Direct product of Mackey functors
- 7. Tensor induction for Green functors
- 8. Cohomological tensor induction
- 9. Tensor induction for -permutation modules
- 10. Tensor induction for modules