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Non-Additive Exact Functors and Tensor Induction for Mackey Functors
Serge Bouc, Université Paris, France
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Memoirs of the American Mathematical Society
2000; 74 pp; softcover
Volume: 144
ISBN-10: 0-8218-1951-8
ISBN-13: 978-0-8218-1951-7
List Price: US$47
Individual Members: US$28.20
Institutional Members: US$37.60
Order Code: MEMO/144/683
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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
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