  In this article we define the $-_+$-construction and the $-^+$-construction,
that was crucial in the theory of canonical induction formulas (see
\cite{Boltje1998b}), in the setting of biset functors, thus providing the
necessary framework to define and construct canonical induction formulas for
representation rings that are most naturally viewed as biset functors.
Additionally, this provides a unified approach to the study of a class of
functors including the Burnside ring, the monomial Burnside ring and global
representation ring.
