S.Bouc
Equipe des groupes finis
CNRS UMR 9994
UFR de Mathematiques
Universite Paris 7-Denis Diderot
2, Place Jussieu
75251 Paris cedex 05
France
 
Non-additive exact functors and tensor induction for Mackey functors
 
Abstract:
I give a possible generalization of the definition of a (right) exact functor
to the case of a non-additive functor F: A-->B between abelian categories. Every
functor from a suitable subcategory of A to B has a unique extension to a
right exact functor from A to B.
This leads to the definition of tensor induction for Mackey functors, associated to any finite biset. This is well behaved with respect to the usual 
constructions on Mackey and Green functors (direct sums, tensor products).
 This gives also a generalized tensor induction for p-permutation modules
and algebras. As a special case, one gets tensor induction for ordinary
modules, associated to a finite right-free biset.
 
Prepublication de l'Institut Mathematique de Jussieu n 132/ Juin 1997