  It is a classical result from universal algebra that the notions of
polymorphisms and invariants provide a Galois connection between suitably
closed classes (clones) of finitary operations $f\colon B^n\to B$, and classes
(coclones) of relations $r\subseteq B^k$. We will present a generalization of
this duality to classes of (multi-valued, partial) functions $f\colon B^n\to
B^m$, employing invariants valued in partially ordered monoids instead of
relations. In particular, our set-up encompasses the case of permutations
$f\colon B^n\to B^n$, motivated by problems in reversible computing.
