  This note is motivated by the problem to understand, given a commutative ring
F, which G-sets X, Y give rise to isomorphic F[G]-representations F[X]\cong
F[Y]. A typical step in such investigations is an argument that uses induction
theorems to give very general sufficient conditions for all such relations to
come from proper subquotients of G. In the present paper we axiomatise the
situation, and prove such a result in the generality of Mackey functors and
Green functors with inflation. Our result includes, as special cases, a result
of Deligne on monomial relations, a result of the first author and Tim
Dokchitser on Brauer relations in characteristic 0, and a new result on Brauer
relations in characteristic p>0. We will need the new result in a forthcoming
paper on Brauer relations in positive characteristic.
