Non-additive exact functors and tensor induction for Mackey functors
Author(s)
Bibliographic Information
Non-additive exact functors and tensor induction for Mackey functors
（Memoirs of the American Mathematical Society, no. 683）
American Mathematical Society, 2000
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Note
Bibliography: p. 74
"March 2000, volume 144, number 683 (first of 5 numbers)"
Description and Table of Contents
Description
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 selection 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.
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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