Closure properties for valued function minions

Determine a principled set of closure properties for families of N-ary weightings on PolFeas(A,B) (for valued promise templates (A,B)) so that the resulting notion of a valued function minion coincides exactly with the collection of plurimorphisms Plu(A,B).

Background

In the valued framework, polymorphisms are generalized to weightings over operations, and plurimorphisms are finite families of such weightings. The authors avoid introducing a concrete notion of a valued function minion (the valued analogue of a function minion) because it is unclear what closure operations are required to capture precisely the plurimorphisms of a valued template.

A resolution would provide an abstract algebraic object for valued PCSPs that parallels the role of minions in crisp PCSPs, enabling cleaner statements and proofs about reductions and complexity boundaries.