Mackey functors, induction from restriction functors and coinduction from transfer functors

Boltje's plus constructions extend two well-known constructions on Mackey functors, the fixed-point functor and the fixed-quotient functor. In this paper, we show that the plus constructions are induction and coinduction functors of general module theory. As an application, we construct simple Mackey functors from simple restriction functors and simple transfer functors. We also give new proofs for the classification theorem for simple Mackey functors and semisimplicity theorem of Mackey functors.