Non-Additive Exact Functors and Tensor Induction for Mackey Functors
Seiten
2000
American Mathematical Society (Verlag)
978-0-8218-1951-7 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-1951-7 (ISBN)
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Introduces 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.
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.
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.
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.
| Erscheint lt. Verlag | 1.5.2000 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-8218-1951-8 / 0821819518 |
| ISBN-13 | 978-0-8218-1951-7 / 9780821819517 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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