Memoirs of the American Mathematical Society 2000; 74 pp; softcover Volume: 144 ISBN10: 0821819518 ISBN13: 9780821819517 List Price: US$47 Individual Members: US$28.20 Institutional Members: US$37.60 Order Code: MEMO/144/683
 First I will introduce a generalization of the notion of (right)exact functor between abelian categories to the case of nonadditive 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
